THE EXEMPLAR PROGRAMME
Designed to be built around each child’s specific strengths and weaknesses.
Exemplar is available in maths, English and reading for children between the ages of 4 and 17 years old, based on their current strengths and weaknesses.Exemplar mathematics and English programmes have been fully aligned to the English National Curriculum.
Exemplar covers work required by students in Key Stage 1, Key Stage 2, Key Stage 3 and Key Stage 4. Whatever level your children are working at, you can rest assured that Exemplar will complement and work hand-in-hand with their current schoolwork.
Additionally, there is a range of GCSE revision courses for each of the major Examination Boards (AQA, Edexcel OCR and WJEC), depending on what your student is studying.
For those schools that offer the International Baccalaureate or Cambridge International Examinations curricula, these are also available within Exemplar as part of its standard curriculum library.
To see more detail about lessons covered within our subjects, just click on the year group titles below:Find out what each stage of Exemplar covers
- KS1 – Maths – Reception Mathematics
- KS1 – Maths – Year 1 Mathematics
- KS1 – Maths – Year 2 Mathematics
- KS2 – Maths – Year 3 Mathematics
- KS2 – Maths – Year 4 Mathematics
- KS2 – Maths – Year 5 Mathematics
- KS2 – Maths – Year 6 Mathematics
- KS3 – Maths – Year 7 Mathematics
- KS3 – Maths – Year 8 Mathematics
- KS3 – Maths – Year 9 Mathematics
- KS4 – Maths – Foundation Mathematics
- KS4 – Maths – Higher Mathematics
- KS5 – Maths – Core Mathematics
- KS5 – Maths – Statistics Mathematics
- EdExcel-GCSE Revision Foundation Mathematics
- EdExcel-GCSE Revision Higher Mathematics
- AQA-GCSE Revision Foundation Mathematics
- AQA-GCSE Revision Higher Mathematics
- OCR-GCSE Revision Foundation Mathematics
- OCR-GCSE Revision Higher Mathematics
- WJEC-GCSE Revision Foundation Mathematics
- WJEC-GCSE Revision Higher Mathematics
Exemplar Mathematics
KS1 – Maths – Reception Mathematics
| # | TOPIC | TITLE | |
| 1 | Using and applying number | The numbers 1 to 5 | |
| Objective: On completion of the lesson the student will be able to read, write and identify the words and numerals for the numbers 1 to 5 | |||
| 2 | Using and applying number | The numbers 6 to 9 | |
| Objective: On completion of the lesson the student will be able to match cardinal words and numbers with groups of 6-9 objects. | |||
| 3 | The number system | Ordinal numbers 1 to 9 | |
| Objective: On completion of the lesson the student will be able to match ordinal words and numbers with groups of 1-9 objects. | |||
| 4 | Using and applying number | Zero and counting numbers 1 to 9 | |
| Objective: On completion of the lesson the student will be able to recognise, write and match the numeral and word for the number zero. | |||
| 5 | Using and applying number | The number 10 | |
| Objective: On completion of the lesson the student will be able to write the numeral and word for the number 10, count up to 10 objects and to match a group of objects to the correct number. | |||
| 6 | Using and applying number | Numbers 11 to 20 | |
| Objective: On completion of the lesson the student will be able to write the numeral and word for the numbers 11 to 20, count up to 20 and match a group of objects to the correct number. | |||
| 7 | Reasoning | Simple addition up to the number 10 | |
| Objective: On completion of the lesson the student will be able to write simple number sentences that show numbers adding up to another number. | |||
| 8 | Time, months | Months and seasons of the year | |
| Objective: On completion of the lesson the student will be able to: name and order the months of the year, know the number of days in each month, name the seasons in order, and know the number of months in each season. | |||
| 9 | Time, days of week | Days of the week | |
| Objective: On completion of the lesson the student will be able to: name the days of the week in order, recognise them in a written form, be able to answer questions about the days of the week, and have an understanding of a diary. | |||
KS1 – Maths – Year 1 Mathematics
| # | TOPIC | TITLE | |
| 1 | Using and applying number | Zero and counting numbers 1 to 9 | |
| Objective: On completion of the lesson the student will be able to recognise, write and match the numeral and word for the number zero. | |||
| 2 | Using and applying number | The number 10 | |
| Objective: On completion of the lesson the student will be able to write the numeral and word for the number 10, count up to 10 objects and to match a group of objects to the correct number. | |||
| 3 | Using and applying number | Numbers 11 to 20 | |
| Objective: On completion of the lesson the student will be able to write the numeral and word for the numbers 11 to 20, count up to 20 and match a group of objects to the correct number. | |||
| 4 | Using and applying number | Using place value to order numbers up to 20 | |
| Objective: On completion of the lesson the student will be able to use place value to order numbers up to the value of 20. | |||
| 5 | Calculations | The numbers 20 to 99 | |
| Objective: On completion of the lesson the student will be able to identify, name and add groups of ten, counting to ninety-nine. | |||
| 6 | Calculation 10-100 | Counting by 1, 2, 5, and 10 to 100 | |
| Objective: On completion of the lesson the student will be able to skip count to one hundred and show that one hundred equals ten times ten. | |||
| 7 | Reasoning | Simple addition up to the number 10 | |
| Objective: On completion of the lesson the student will be able to write simple number sentences that show numbers adding up to another number. | |||
| 8 | Reasoning | Simple addition up to the number 20 | |
| Objective: On completion of the lesson the student will be able to write simple number sentences and also write addition in a vertical format using numbers up to 20. | |||
| 9 | Calculations | Subtraction up to the number 10 | |
| Objective: On completion of the lesson the student will be able to calculate the answer to take away or subtraction number sentences up to the number 10. | |||
| 10 | Calculations | Subtraction by Comparison | |
| Objective: On completion of the lesson the student will be able to calculate take away or subtraction number sentences by comparison methods. | |||
| 11 | Calculations | Subtraction up to the number 20 and beyond | |
| Objective: On completion of the lesson the student will be capable of subtraction using tens and units and calculating the answer to take away or subtraction number sentences. | |||
| 12 | Calculation-grouping | Multiplication using equal groups | |
| Objective: On completion of the lesson the student will be able to write about equal groups and rows and will understand how to count them. | |||
| 13 | Calculation-grouping | Multiplication using repeated addition | |
| Objective: On completion of the lesson the student will be able to write about equal groups and rows using another method and also learn different ways to count them. | |||
| 14 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe part of a whole | |
| Objective: On completion of the lesson the student will be able to: name fractions, and use fractions to describe equal parts of a whole. | |||
| 15 | Length | Compare length by using informal units of measurement | |
| Objective: On completion of the lesson the student will be able to measure objects around the student’s home and compare their length to each other. The student will also be able to compare the different ways the student measured the same object. | |||
| 16 | Weight/mass | Introducing the concept of mass | |
| Objective: On completion of the lesson the student will understand the concepts of mass. | |||
| 17 | Time, months | Months and seasons of the year | |
| Objective: On completion of the lesson the student will be able to: name and order the months of the year, know the number of days in each month, name the seasons in order, and know the number of months in each season. | |||
| 18 | Time, days of week | Days of the week | |
| Objective: On completion of the lesson the student will be able to: name the days of the week in order, recognise them in a written form, be able to answer questions about the days of the week, and have an understanding of a diary. | |||
| 19 | Time, duration | Duration | |
| Objective: On completion of the lesson the student will be able to estimate and measure the duration of an event using informal units, and compare and order the duration of an event using informal units. | |||
| 20 | Time, digital | O’clock and half past using digital time | |
| Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on a digital clock. | |||
| 21 | Time, analogue | O’clock and half past on the analogue clock | |
| Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on an analogue clock. | |||
| 22 | Lines and angles | Describing position. | |
| Objective: On completion of the lesson the student will be able to use and understand conventional location language to describe position. | |||
KS1 – Maths – Year 2 Mathematics
| # | TOPIC | TITLE | |
| 1 | Using and applying number | The number 10 | |
| Objective: On completion of the lesson the student will be able to write the numeral and word for the number 10, count up to 10 objects and to match a group of objects to the correct number. | |||
| 2 | Using and applying number | Numbers 11 to 20 | |
| Objective: On completion of the lesson the student will be able to write the numeral and word for the numbers 11 to 20, count up to 20 and match a group of objects to the correct number. | |||
| 3 | Using and applying number | Using place value to order numbers up to 20 | |
| Objective: On completion of the lesson the student will be able to use place value to order numbers up to the value of 20. | |||
| 4 | Calculations | The numbers 20 to 99 | |
| Objective: On completion of the lesson the student will be able to identify, name and add groups of ten, counting to ninety-nine. | |||
| 5 | Calculation 10-100 | Counting by 1, 2, 5, and 10 to 100 | |
| Objective: On completion of the lesson the student will be able to skip count to one hundred and show that one hundred equals ten times ten. | |||
| 6 | Reasoning | Simple addition up to the number 10 | |
| Objective: On completion of the lesson the student will be able to write simple number sentences that show numbers adding up to another number. | |||
| 7 | Reasoning | Simple addition up to the number 20 | |
| Objective: On completion of the lesson the student will be able to write simple number sentences and also write addition in a vertical format using numbers up to 20. | |||
| 8 | Addition | Addition to 99 | |
| Objective: On completion of the lesson the student will be able to use place value to add two 2-digit numbers together up to a total of 99. | |||
| 9 | Calculations | Subtraction up to the number 10 | |
| Objective: On completion of the lesson the student will be able to calculate the answer to take away or subtraction number sentences up to the number 10. | |||
| 10 | Calculations | Subtraction by Comparison | |
| Objective: On completion of the lesson the student will be able to calculate take away or subtraction number sentences by comparison methods. | |||
| 11 | Calculations | Subtraction up to the number 20 and beyond | |
| Objective: On completion of the lesson the student will be capable of subtraction using tens and units and calculating the answer to take away or subtraction number sentences. | |||
| 12 | Subtraction | Subtraction up to the number 99 | |
| Objective: On completion of the lesson the student will know how to find the answer to take away number sentences with bigger numbers and will also know how to write these number sentences. | |||
| 13 | Calculation-grouping | Multiplication using equal groups | |
| Objective: On completion of the lesson the student will be able to write about equal groups and rows and will understand how to count them. | |||
| 14 | Calculation-grouping | Multiplication using repeated addition | |
| Objective: On completion of the lesson the student will be able to write about equal groups and rows using another method and also learn different ways to count them. | |||
| 15 | Calculation-multiplication | The multiplication sign | |
| Objective: on completion of the lesson the student will be able to multiply single numbers to solve multiplication problems. | |||
| 16 | Calculation-multiples | Multiples of 10 up to 100 | |
| Objective: On completion of the lesson the student will be able to read, write, rename and add multiples of ten. | |||
| 17 | Multiplication | Multiplication – important facts. | |
| Objective: On completion of the lesson the student will know the connection between multiplication and division and recognise the strategies to help solve multiplication number sentences. | |||
| 18 | Calculation sharing/division | Strategies for division | |
| Objective: On completion of the lesson the student will be able to share objects equally and will also learn how to write about them. | |||
| 19 | Problems | Solve and record division using known facts and sharing | |
| Objective: On completion of the lesson the student will be able to use sharing concepts to solve and record division problems. | |||
| 20 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe part of a whole | |
| Objective: On completion of the lesson the student will be able to: name fractions, and use fractions to describe equal parts of a whole. | |||
| 21 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection | |
| Objective: On completion of the lesson the student will be able to use the fractions to describe equal parts of a collection of objects. | |||
| 22 | Length | Compare length by using informal units of measurement | |
| Objective: On completion of the lesson the student will be able to measure objects around the student’s home and compare their length to each other. The student will also be able to compare the different ways the student measured the same object. | |||
| 23 | Length | Using the metre as a formal unit to measure perimeter | |
| Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres. | |||
| 24 | Length | Using the formal unit of the centimetre to measure length and perimeter | |
| Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres. | |||
| 25 | Weight/mass | Introducing the concept of mass | |
| Objective: On completion of the lesson the student will understand the concepts of mass. | |||
| 26 | Weight/mass | The kilogram | |
| Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales. | |||
| 27 | Weight/mass | The gram and net mass | |
| Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams. | |||
| 28 | Capacity | Estimate, measure and compare the capacity of containers | |
| Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it. | |||
| 29 | Time, duration | Duration | |
| Objective: On completion of the lesson the student will be able to estimate and measure the duration of an event using informal units, and compare and order the duration of an event using informal units. | |||
| 30 | Time, digital | O’clock and half past using digital time | |
| Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on a digital clock. | |||
| 31 | Time, analogue | O’clock and half past on the analogue clock | |
| Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on an analogue clock. | |||
| 32 | Time, quarter to, past | Quarter past and quarter to | |
| Objective: On completion of the lesson the student will be able to associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes, and use the terms ‘quarter to’ and ‘quarter past’. | |||
| 33 | Lines and angles | Describing position. | |
| Objective: On completion of the lesson the student will be able to use and understand conventional location language to describe position. | |||
| 34 | 3-D shapes | Recognise and name prisms according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties. | |||
| 35 | 3-D shapes | Recognise and name pyramids according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties. | |||
| 36 | Data | Pictograms | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs. | |||
| 37 | Data | Bar Charts | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||
KS2 – Maths – Year 3 Mathematics
| # | TOPIC | TITLE | |
| 1 | Calculation-larger numbers | The numbers 100 to 999 | |
| Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999. | |||
| 2 | Addition | Addition to 99 | |
| Objective: On completion of the lesson the student will be able to use place value to add two 2-digit numbers together up to a total of 99. | |||
| 3 | Addition | Addition up to the number 999 | |
| Objective: On completion of the lesson the student will be able to use place value to solve and record addition problems with three digit numbers. | |||
| 4 | Subtraction | Subtraction up to the number 99 | |
| Objective: On completion of the lesson the student will know how to find the answer to take away number sentences with bigger numbers and will also know how to write these number sentences. | |||
| 5 | Subtraction | Subtraction with borrowing | |
| Objective: On completion of the lesson the student will be able to record subtraction number sentences and will understand the need to trade between place value columns using the renaming method | |||
| 6 | Subtraction | Subtraction of two-digit numbers Involving comparison. | |
| Objective: On completion of the lesson the student will know how to solve and record the answer to word problems and will understand how estimation helps to find out if an answer is correct. | |||
| 7 | Calculation-multiples | Multiples of 10 up to 100 | |
| Objective: On completion of the lesson the student will be able to read, write, rename and add multiples of ten. | |||
| 8 | Multiplication | Multiplication – important facts. | |
| Objective: On completion of the lesson the student will know the connection between multiplication and division and recognise the strategies to help solve multiplication number sentences. | |||
| 9 | Multiplication | Multiplication using extended algorithms. | |
| Objective: On completion of the lesson the student will have understood multiplication using extended algorithms. | |||
| 10 | Multiplication | Multiplying 2-digit numbers by multiple of 10 | |
| Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any multiple of 10 using the process of long multiplication. | |||
| 11 | Calculation sharing/division | Strategies for division | |
| Objective: On completion of the lesson the student will be able to share objects equally and will also learn how to write about them. | |||
| 12 | Problems | Solve and record division using known facts and sharing | |
| Objective: On completion of the lesson the student will be able to use sharing concepts to solve and record division problems. | |||
| 13 | Sign word problems | Solving Word Problems by recognising Sign Words | |
| Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division. | |||
| 14 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe part of a whole | |
| Objective: On completion of the lesson the student will be able to: name fractions, and use fractions to describe equal parts of a whole. | |||
| 15 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection | |
| Objective: On completion of the lesson the student will be able to use the fractions to describe equal parts of a collection of objects. | |||
| 16 | Fractions | Comparing and ordering fractions | |
| Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts. | |||
| 17 | Fractions | Adding and subtracting fractions with the same denominator | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator. | |||
| 18 | Length | Compare length by using informal units of measurement | |
| Objective: On completion of the lesson the student will be able to measure objects around the student’s home and compare their length to each other. The student will also be able to compare the different ways the student measured the same object. | |||
| 19 | Length | Using the metre as a formal unit to measure perimeter | |
| Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres. | |||
| 20 | Length | Using the formal unit of the centimetre to measure length and perimeter | |
| Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres. | |||
| 21 | Length | Compare and convert formal units of measurement | |
| Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert. | |||
| 22 | Weight/mass | Introducing the concept of mass | |
| Objective: On completion of the lesson the student will understand the concepts of mass. | |||
| 23 | Weight/mass | The kilogram | |
| Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales. | |||
| 24 | Weight/mass | The gram and net mass | |
| Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams. | |||
| 25 | Capacity | The relationship between the common units of capacity, the litre and the millilitre | |
| Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre. | |||
| 26 | Capacity | Estimate, measure and compare the capacity of containers | |
| Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it. | |||
| 27 | Time, minutes | Analogue – Telling time – minutes in the hour | |
| Objective: On completion of the lesson the student will be able to recognize the coordinated movements of the hands on an analogue clock. | |||
| 28 | Time, units | Units of time | |
| Objective: On completion of the lesson the student will be able to convert units of time and read and interpret simple timetables, timelines and calendars. | |||
| 29 | Time, a.m. p.m. | AM and PM time | |
| Objective: On completion of the lesson the student will be able to talk about am and pm time and use the correct notation for am and pm time. | |||
| 30 | Time, quarter to, past | Quarter past and quarter to | |
| Objective: On completion of the lesson the student will be able to associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes, and use the terms ‘quarter to’ and ‘quarter past’. | |||
| 31 | Time, minutes past the hour | Minutes past | |
| Objective: On completion of the lesson the student will be able to understand and read the minutes past the hour on an analogue clock. | |||
| 32 | Time, minutes to the hour | Minutes to | |
| Objective: On completion of the lesson the student will be able to understand and read the minutes to the hour on an analogue clock. | |||
| 33 | Time, digital, analogue | Comparing analogue and digital time | |
| Objective: On completion of the lesson the student will be able to: read analogue and digital clocks to the minute, be familiar with the recording of digital time, and tell the same time using both analogue and digital clocks. | |||
| 34 | Time, digital | O’clock and half past using digital time | |
| Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on a digital clock. | |||
| 35 | Time, analogue | O’clock and half past on the analogue clock | |
| Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on an analogue clock. | |||
| 36 | Time, 24-hour | 24 hour time | |
| Objective: On completion of the lesson the student will be able to: tell the time accurately using twenty-four hour time, change the time from am and pm time to twenty-four hour time, and change the time from twenty-four hour time to am and pm time. | |||
| 37 | Time zones | Time zones | |
| Objective: On completion of the lesson the student will be able to: recognise that there are different time zones, compare time zones, understand daylight saving and adjust times accordingly, and determine the local time in different regions. | |||
| 38 | Lines and angles | Describing position. | |
| Objective: On completion of the lesson the student will be able to use and understand conventional location language to describe position. | |||
| 39 | Data | Pictograms | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs. | |||
| 40 | Data | Bar Charts | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||
KS2 – Maths – Year 4 Mathematics
| # | TOPIC | TITLE | |
| 1 | Calculation-larger numbers | The numbers 100 to 999 | |
| Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999. | |||
| 2 | Place value | The numbers 1000 to 9999 | |
| Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999. | |||
| 3 | Counting and numeration | The numbers 10 000 to 99 999 | |
| Objective: On completion of the lesson the student will be able to count to 99 999 and use place value to read the value of the numerals within the larger numbers. | |||
| 4 | Counting and numeration | Seven digit numbers | |
| Objective: On completion of the lesson the student will be able to use place value knowledge to read and write seven digit whole numbers. | |||
| 5 | Addition | Addition up to the number 999 | |
| Objective: On completion of the lesson the student will be able to use place value to solve and record addition problems with three digit numbers. | |||
| 6 | Counting and numeration | Addition to 9999 and beyond | |
| Objective: On completion of the lesson the student will be able to use the student’s knowledge of place value to solve addition problems with 3, 4 and 5 digit numbers and word problems. | |||
| 7 | Subtraction | Subtraction with borrowing | |
| Objective: On completion of the lesson the student will be able to record subtraction number sentences and will understand the need to trade between place value columns using the renaming method | |||
| 8 | Subtraction | Subtraction up to the number 999 using the renaming method | |
| Objective: On completion of the lesson the student will know another way to trade between columns in subtraction using the renaming method. The student will also learn how to solve number sentences with missing numbers. | |||
| 9 | Subtraction | Subtraction involving four digit numbers and beyond using the renaming method. | |
| Objective: On completion of the lesson the student will be able to use written methods to solve subtraction problems involving 4 and 5 digit whole numbers. | |||
| 10 | Multiplication | Multiplication using extended algorithms. | |
| Objective: On completion of the lesson the student will have understood multiplication using extended algorithms. | |||
| 11 | Multiplication | Multiplication by 2 and 3 digits | |
| Objective: On completion of the lesson the student will be able to solve and record 2 and 3 digit multiplication problems in extended and short form. | |||
| 12 | Multiplication | Multiplying 2-digit numbers by multiple of 10 | |
| Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any multiple of 10 using the process of long multiplication. | |||
| 13 | Multiplication | Multiplying 3 and 4-digit numbers by multiples of 100 | |
| Objective: On completion of the lesson the student will be able to multiply any 3 or 4 digit numbers by any multiple of 100 using long multiplication. | |||
| 14 | Division | Division with and without a remainder. | |
| Objective: On completion of the lesson the student will understand division with and without a Remainder. | |||
| 15 | Division | Dividing two and three digit numbers by a single digit number. | |
| Objective: On completion of the lesson the student will understand dividing two and three digit numbers by a single digit number. | |||
| 16 | Sign word problems | Solving Word Problems by recognising Sign Words | |
| Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division. | |||
| 17 | Equations | Problem solving strategies | |
| Objective: On completion of the lesson the student will be able to recall the steps in a strategy for solving word problems. | |||
| 18 | Fractions | Comparing and ordering fractions | |
| Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts. | |||
| 19 | Fractions | Adding and subtracting fractions with the same denominator | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator. | |||
| 20 | Fractions | Fractions 1/5, 1/10, 1/100 | |
| Objective: On completion of the lesson the student will be able to: compare fractions with the denominators 5, 10, 100, and represent fractions with the denominator 5, 10, 100. | |||
| 21 | Fractions | Finding equivalent fractions | |
| Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines. | |||
| 22 | Decimals | Introduction to decimals | |
| Objective: On completion of the lesson the student will be able to represent decimals to two decimal places. | |||
| 23 | Decimals | Comparing and ordering decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to compare and order decimals to two decimal places and understand decimal notation to two places. | |||
| 24 | Decimals | Decimals with whole numbers 10th and 100th | |
| Objective: On completion of the lesson the student will be able to use and understand place value to show whole numbers, tenths and hundredths as decimals. | |||
| 25 | Decimals | Using decimals – shopping problems | |
| Objective: On completion of the lesson the student will be able to: read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money. | |||
| 26 | Length | Using the metre as a formal unit to measure perimeter | |
| Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres. | |||
| 27 | Length | Using the formal unit of the centimetre to measure length and perimeter | |
| Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres. | |||
| 28 | Length | Compare and convert formal units of measurement | |
| Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert. | |||
| 29 | Area | Introduction to the square centimetre. | |
| Objective: On completion of the lesson the student will be able to calculate the area in square centimetres of surfaces or objects and record their results correctly. | |||
| 30 | Weight/mass | Introducing the concept of mass | |
| Objective: On completion of the lesson the student will understand the concepts of mass. | |||
| 31 | Weight/mass | The kilogram | |
| Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales. | |||
| 32 | Weight/mass | The gram and net mass | |
| Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams. | |||
| 33 | Weight/mass | The tonne – converting units and problems | |
| Objective: On completion of the lesson the student should be able to: choose the correct unit to measure the mass of small, medium or large objects, and convert measurements from one unit to another. | |||
| 34 | Capacity | The relationship between the common units of capacity, the litre and the millilitre | |
| Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre. | |||
| 35 | Capacity | Estimate, measure and compare the capacity of containers | |
| Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it. | |||
| 36 | Capacity | Converting between volume and capacity using kilolitres and litres | |
| Objective: On completion of the lesson the student will know the formal units of measurement for volume and capacity for bigger objects. The student will also be able to use the knowledge of volume to work out capacity. | |||
| 37 | Time, minutes | Analogue – Telling time – minutes in the hour | |
| Objective: On completion of the lesson the student will be able to recognize the coordinated movements of the hands on an analogue clock. | |||
| 38 | Time, a.m. p.m. | AM and PM time | |
| Objective: On completion of the lesson the student will be able to talk about am and pm time and use the correct notation for am and pm time. | |||
| 39 | Time, minutes past the hour | Minutes past | |
| Objective: On completion of the lesson the student will be able to understand and read the minutes past the hour on an analogue clock. | |||
| 40 | Time, minutes to the hour | Minutes to | |
| Objective: On completion of the lesson the student will be able to understand and read the minutes to the hour on an analogue clock. | |||
| 41 | Time, digital, analogue | Comparing analogue and digital time | |
| Objective: On completion of the lesson the student will be able to: read analogue and digital clocks to the minute, be familiar with the recording of digital time, and tell the same time using both analogue and digital clocks. | |||
| 42 | Time, 24-hour | 24 hour time | |
| Objective: On completion of the lesson the student will be able to: tell the time accurately using twenty-four hour time, change the time from am and pm time to twenty-four hour time, and change the time from twenty-four hour time to am and pm time. | |||
| 43 | Time zones | Time zones | |
| Objective: On completion of the lesson the student will be able to: recognise that there are different time zones, compare time zones, understand daylight saving and adjust times accordingly, and determine the local time in different regions. | |||
| 44 | Angles | Measure and classify angles | |
| Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle. | |||
| 45 | 2-D shapes | Recognise and name triangles | |
| Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties. | |||
| 46 | 2-D shapes | Spatial properties of quadrilaterals | |
| Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals. | |||
| 47 | Geometry-quadrilaterals | Quadrilaterals | |
| Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees. | |||
| 48 | Geometry-quadrilaterals | Classifying Quadrilaterals | |
| Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. | |||
| 49 | Geometry-quadrilaterals | Using the Properties of a Parallelogram | |
| Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram. | |||
| 50 | Geometry-quadrilaterals | Proving a Shape is a Parallelogram | |
| Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram. | |||
| 51 | Geometry-quadrilaterals | Properties of the Rectangle, Square and Rhombus | |
| Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values. | |||
| 52 | Geometry-quadrilaterals | Properties of the Trapezium and Kite | |
| Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values. | |||
| 53 | Geometry-quadrilaterals | The quadrilateral family and coordinate methods in geometry | |
| Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties. | |||
| 54 | 3-D shapes | Recognise and name prisms according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties. | |||
| 55 | 3-D shapes | Recognise and name pyramids according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties. | |||
| 56 | Lines and angles | Informal coordinate system | |
| Objective: On completion of the lesson the student will be able to use an informal coordinate system to specify location, and locate coordinate points on grid paper. | |||
| 57 | Data | Pictograms | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs. | |||
| 58 | Data | Bar Charts | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||
| 59 | Data | Line graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||
KS2 – Maths – Year 5 Mathematics
| # | TOPIC | TITLE | |
| 1 | Counting and numeration | The numbers 10 000 to 99 999 | |
| Objective: On completion of the lesson the student will be able to count to 99 999 and use place value to read the value of the numerals within the larger numbers. | |||
| 2 | Counting and numeration | Seven digit numbers | |
| Objective: On completion of the lesson the student will be able to use place value knowledge to read and write seven digit whole numbers. | |||
| 3 | Counting and numeration | Addition to 9999 and beyond | |
| Objective: On completion of the lesson the student will be able to use the student’s knowledge of place value to solve addition problems with 3, 4 and 5 digit numbers and word problems. | |||
| 4 | Subtraction | Subtraction involving four digit numbers and beyond using the renaming method. | |
| Objective: On completion of the lesson the student will be able to use written methods to solve subtraction problems involving 4 and 5 digit whole numbers. | |||
| 5 | Multiplication | Multiples and factors of whole numbers | |
| Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers. | |||
| 6 | Multiplication | Multiplying 2-digit numbers by 2-digit numbers | |
| Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number. | |||
| 7 | Multiplication | Multiplying 4-digit numbers by 3-digit numbers | |
| Objective: On completion of the lesson the student will be able to multiply any 4 digit numbers by any 3 digit numbers using long multiplication. | |||
| 8 | Multiplication | Multiplying 4-digit numbers by 4-digit number | |
| Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication. | |||
| 9 | Division | Divide whole numbers by a 2 digit divisor | |
| Objective: On completion of the lesson the student will be able to solve and record division problems with whole numbers using a two-digit divisor and show any remainders as a fraction. | |||
| 10 | Division/repeat subtraction | Repeated subtraction with divisors less than 20 with no remainders | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 20. | |||
| 11 | Division/repeat subtraction | Repeated subtraction by multiples of 10 with divisors less than 20 with no remainders | |
| Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 with divisors less than 20 and no remainders. | |||
| 12 | Division/repeat subtraction | Repeated subtraction by multiples of 2, 3 and 4 with divisors greater than 20 with no remainders | |
| Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 2,3,4 where divisors are greater than 20 and there are no remainders. | |||
| 13 | Division/repeat subtraction | Repeated subtraction by multiples of 1,2 and 3 with divisors less than 20 with remainders | |
| Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 1,2,3 where the divisors are less than 20 and there are remainders. | |||
| 14 | Division/repeat subtraction | Repeated subtraction by multiples of 10 with divisors less than 20 with remainders | |
| Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 where the divisors are greater than 12 and less than 20, and the dividend is any 3 digit number, and there are remainders. | |||
| 15 | Division/repeat subtraction | Repeated subtraction with divisors greater than 20 with remainders as fractions | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors greater than 20 and remainders expressed as fractions | |||
| 16 | Division/repeat subtraction | Repeated subtraction with divisors less than 35 with some remainders | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 35, with some remainders. | |||
| 17 | Division/repeat subtraction | Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 55 and where dividends are 3 and 4 digit numbers, and there are some remainders. | |||
| 18 | Division/repeat subtraction | Repeated subtraction with divisors greater than 50 with dividends of thousands and some remainders | |
| Objective: On completion of the lesson the student will able to use Long Division by repeated subtraction with divisors greater than 50 including division of thousands, and some remainders. | |||
| 19 | Multiplication | Multiplying 2-digit numbers by multiple of 10 | |
| Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any multiple of 10 using the process of long multiplication. | |||
| 20 | Multiplication | Multiplying 3 and 4-digit numbers by multiples of 100 | |
| Objective: On completion of the lesson the student will be able to multiply any 3 or 4 digit numbers by any multiple of 100 using long multiplication. | |||
| 21 | Decimals | Multiplying decimals by 10, 100 and 1000 | |
| Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand. | |||
| 22 | Decimals | Dividing decimals by 10, 100 and 1000 | |
| Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand. | |||
| 23 | Sign word problems | Solving Word Problems by recognising Sign Words | |
| Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division. | |||
| 24 | Equations | Problem solving strategies | |
| Objective: On completion of the lesson the student will be able to recall the steps in a strategy for solving word problems. | |||
| 25 | Number problems | Problems with numbers. | |
| Objective: On completion of the lesson the student will be able to solve problems with numbers using a problem solving strategy. | |||
| 26 | Money | Problems involving money | |
| Objective: On completion of the lesson the student will be able to solve problems with money. | |||
| 27 | Fractions | Comparing and ordering fractions | |
| Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts. | |||
| 28 | Fractions | mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one. | |||
| 29 | Fractions | Improper fractions | |
| Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally. | |||
| 30 | Fractions | Fractions 1/5, 1/10, 1/100 | |
| Objective: On completion of the lesson the student will be able to: compare fractions with the denominators 5, 10, 100, and represent fractions with the denominator 5, 10, 100. | |||
| 31 | Fractions | Finding equivalent fractions | |
| Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines. | |||
| 32 | Fractions | Multiplying and dividing to obtain equivalent fractions | |
| Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form. | |||
| 33 | Fractions | Reducing fractions to lowest equivalent form | |
| Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor. | |||
| 34 | Fractions | Comparing and ordering fractions greater than (>) 1 | |
| Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one. | |||
| 35 | Fractions | Subtracting fractions from whole numbers | |
| Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from | |||
| 36 | Fractions | Adding and subtracting fractions with the same denominator | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator. | |||
| 37 | Fractions | Adding and subtracting fractions with different denominators | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other. | |||
| 38 | Decimals | Introduction to decimals | |
| Objective: On completion of the lesson the student will be able to represent decimals to two decimal places. | |||
| 39 | Decimals | Comparing and ordering decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to compare and order decimals to two decimal places and understand decimal notation to two places. | |||
| 40 | Decimals | Decimals with whole numbers 10th and 100th | |
| Objective: On completion of the lesson the student will be able to use and understand place value to show whole numbers, tenths and hundredths as decimals. | |||
| 41 | Decimals | Adding decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to add decimals with the same number of decimal places (to two decimal places) | |||
| 42 | Decimals | Subtracting decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to subtract decimals with the same number of decimal places (to two decimal places) | |||
| 43 | Decimals | Using decimals – shopping problems | |
| Objective: On completion of the lesson the student will be able to: read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money. | |||
| 44 | Decimals | Using decimals to record length | |
| Objective: On completion of the lesson the student will be able to interpret the everyday use of fractions and decimals and use their knowledge of decimals to record measurements. | |||
| 45 | Decimals | Rounding decimals | |
| Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number. | |||
| 46 | Decimals | Decimals to three decimal places | |
| Objective: On completion of the lesson the student will be able to express thousandths as a decimal and interpret decimal notation for thousandths. | |||
| 47 | Percentages | Introduction to percentages, including relating common fractions to percentages | |
| Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage. | |||
| 48 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion. | |||
| 49 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||
| 50 | Length | Using the metre as a formal unit to measure perimeter | |
| Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres. | |||
| 51 | Length | Using the formal unit of the centimetre to measure length and perimeter | |
| Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres. | |||
| 52 | Length | Compare and convert formal units of measurement | |
| Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert. | |||
| 53 | Area | Introduction to the square centimetre. | |
| Objective: On completion of the lesson the student will be able to calculate the area in square centimetres of surfaces or objects and record their results correctly. | |||
| 54 | Area | Introducing the rules for finding the area of a rectangle and a parallelogram. | |
| Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides. | |||
| 55 | Volume | Introduction to volume. using the cubic centimetre as a standard unit | |
| Objective: On completion of the lesson the student will be able to: recognise the need for a formal unit to measure volume, use the abbreviation for cubic centimetre, construct three dimensional objects using cubic centimetre blocks, and use counting to determine vo | |||
| 56 | Capacity | Using the cubic cm and displacement to measure volume and capacity | |
| Objective: On completion of the lesson the student will know a way to find volume and capacity. | |||
| 57 | Capacity | Using the cubic cm as a standard unit of measurement for volume and capacity | |
| Objective: On completion of the lesson the student will understand what a cubic centimetre is and how it can be used to find out the volume and capacity of a three dimensional shape. | |||
| 58 | Capacity | The relationship between the common units of capacity, the litre and the millilitre | |
| Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre. | |||
| 59 | Capacity | Converting between volume and capacity using kilolitres and litres | |
| Objective: On completion of the lesson the student will know the formal units of measurement for volume and capacity for bigger objects. The student will also be able to use the knowledge of volume to work out capacity. | |||
| 60 | Capacity | Estimate, measure and compare the capacity of containers | |
| Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it. | |||
| 61 | Capacity | Converting between volume and capacity using millilitres and litres | |
| Objective: On completion of the lesson the student will be able to convert between units of capacity. | |||
| 62 | Weight/mass | The kilogram | |
| Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales. | |||
| 63 | Weight/mass | The gram and net mass | |
| Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams. | |||
| 64 | Weight/mass | The tonne – converting units and problems | |
| Objective: On completion of the lesson the student should be able to: choose the correct unit to measure the mass of small, medium or large objects, and convert measurements from one unit to another. | |||
| 65 | Length | Problems with length. | |
| Objective: On completion of the lesson the student will be able to solve problems with length. | |||
| 66 | Mass | Problems with mass. | |
| Objective: On completion of the lesson the student will be able to solve problems with mass. | |||
| 67 | Area | Problems with area. | |
| Objective: On completion of the lesson the student will be able to solve problems with area. | |||
| 68 | Volume/capacity | Problems with volume/capacity. | |
| Objective: Problem Solving: problems involving volume/capacity | |||
| 69 | Time, 24-hour | 24 hour time | |
| Objective: On completion of the lesson the student will be able to: tell the time accurately using twenty-four hour time, change the time from am and pm time to twenty-four hour time, and change the time from twenty-four hour time to am and pm time. | |||
| 70 | Time zones | Time zones | |
| Objective: On completion of the lesson the student will be able to: recognise that there are different time zones, compare time zones, understand daylight saving and adjust times accordingly, and determine the local time in different regions. | |||
| 71 | Geometry-angles | Measuring angles | |
| Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is. | |||
| 72 | Geometry-angles | Adjacent angles | |
| Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems. | |||
| 73 | Geometry-angles | Complementary and supplementary angles | |
| Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems. | |||
| 74 | Geometry-angles | Vertically opposite angles | |
| Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems. | |||
| 75 | Geometry-angles | Angles at a Point. | |
| Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems. | |||
| 76 | Geometry-triangles | Angle sum of a triangle | |
| Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. | |||
| 77 | Angles | Measure and classify angles | |
| Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle. | |||
| 78 | 2-D shapes | Recognise and name triangles | |
| Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties. | |||
| 79 | 2-D shapes | Spatial properties of quadrilaterals | |
| Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals. | |||
| 80 | Geometry-quadrilaterals | Quadrilaterals | |
| Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees. | |||
| 81 | Geometry-quadrilaterals | Classifying Quadrilaterals | |
| Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. | |||
| 82 | Geometry-quadrilaterals | Using the Properties of a Parallelogram | |
| Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram. | |||
| 83 | Geometry-quadrilaterals | Proving a Shape is a Parallelogram | |
| Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram. | |||
| 84 | Geometry-quadrilaterals | Properties of the Rectangle, Square and Rhombus | |
| Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values. | |||
| 85 | Geometry-quadrilaterals | Properties of the Trapezium and Kite | |
| Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values. | |||
| 86 | Geometry-quadrilaterals | The quadrilateral family and coordinate methods in geometry | |
| Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties. | |||
| 87 | 3-D shapes | Recognise and name prisms according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties. | |||
| 88 | 3-D shapes | Recognise and name pyramids according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties. | |||
| 89 | Data | Pictograms | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs. | |||
| 90 | Data | Bar Charts | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||
| 91 | Data | Line graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||
KS2 – Maths – Year 6 Mathematics
| # | TOPIC | TITLE | |
| 1 | Counting and numeration | The numbers 10 000 to 99 999 | |
| Objective: On completion of the lesson the student will be able to count to 99 999 and use place value to read the value of the numerals within the larger numbers. | |||
| 2 | Counting and numeration | Seven digit numbers | |
| Objective: On completion of the lesson the student will be able to use place value knowledge to read and write seven digit whole numbers. | |||
| 3 | Algebraic expressions | Directed numbers: addition and subtraction. | |
| Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals. | |||
| 4 | Algebraic expressions | Directed numbers: multiplication and division. | |
| Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer. | |||
| 5 | Multiplication | Multiplying 2-digit numbers by 2-digit numbers | |
| Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number. | |||
| 6 | Multiplication | Multiplying 4-digit numbers by 3-digit numbers | |
| Objective: On completion of the lesson the student will be able to multiply any 4 digit numbers by any 3 digit numbers using long multiplication. | |||
| 7 | Multiplication | Multiplying 4-digit numbers by 4-digit number | |
| Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication. | |||
| 8 | Division/repeat subtraction | Repeated subtraction by multiples of 10 with divisors less than 20 with no remainders | |
| Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 with divisors less than 20 and no remainders. | |||
| 9 | Division/repeat subtraction | Repeated subtraction by multiples of 2, 3 and 4 with divisors greater than 20 with no remainders | |
| Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 2,3,4 where divisors are greater than 20 and there are no remainders. | |||
| 10 | Division/repeat subtraction | Repeated subtraction by multiples of 1,2 and 3 with divisors less than 20 with remainders | |
| Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 1,2,3 where the divisors are less than 20 and there are remainders. | |||
| 11 | Division/repeat subtraction | Repeated subtraction by multiples of 10 with divisors less than 20 with remainders | |
| Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 where the divisors are greater than 12 and less than 20, and the dividend is any 3 digit number, and there are remainders. | |||
| 12 | Division/repeat subtraction | Repeated subtraction with divisors greater than 20 with remainders as fractions | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors greater than 20 and remainders expressed as fractions | |||
| 13 | Division/repeat subtraction | Repeated subtraction with divisors less than 35 with some remainders | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 35, with some remainders. | |||
| 14 | Division/repeat subtraction | Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 55 and where dividends are 3 and 4 digit numbers, and there are some remainders. | |||
| 15 | Division/repeat subtraction | Repeated subtraction with divisors greater than 50 with dividends of thousands and some remainders | |
| Objective: On completion of the lesson the student will able to use Long Division by repeated subtraction with divisors greater than 50 including division of thousands, and some remainders. | |||
| 16 | Multiplication | Multiples and factors of whole numbers | |
| Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers. | |||
| 17 | Rules properties | Using Order of Operation procedures (BIDMAS) with Fractions | |
| Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions. | |||
| 18 | Equations | Problem solving strategies | |
| Objective: On completion of the lesson the student will be able to recall the steps in a strategy for solving word problems. | |||
| 19 | Number problems | Problems with numbers. | |
| Objective: On completion of the lesson the student will be able to solve problems with numbers using a problem solving strategy. | |||
| 20 | Money | Problems involving money | |
| Objective: On completion of the lesson the student will be able to solve problems with money. | |||
| 21 | Fractions | Comparing and ordering fractions | |
| Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts. | |||
| 22 | Fractions | mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one. | |||
| 23 | Fractions | Improper fractions | |
| Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally. | |||
| 24 | Fractions | Finding equivalent fractions | |
| Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines. | |||
| 25 | Fractions | Multiplying and dividing to obtain equivalent fractions | |
| Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form. | |||
| 26 | Fractions | Reducing fractions to lowest equivalent form | |
| Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor. | |||
| 27 | Fractions | Comparing and ordering fractions greater than (>) 1 | |
| Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one. | |||
| 28 | Fractions | Subtracting fractions from whole numbers | |
| Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from | |||
| 29 | Fractions | Adding and subtracting fractions with the same denominator | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator. | |||
| 30 | Fractions | Adding and subtracting fractions with different denominators | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other. | |||
| 31 | Fractions | Multiplying fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers. | |||
| 32 | Fractions | Fractions of whole numbers | |
| Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection. | |||
| 33 | Fractions | Multiplying fractions | |
| Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form. | |||
| 34 | Fractions | Dividing fractions | |
| Objective: On completion of the lesson the student will be able to divide fractions. | |||
| 35 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion. | |||
| 36 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||
| 37 | Decimals | Multiplying decimals by 10, 100 and 1000 | |
| Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand. | |||
| 38 | Decimals | Dividing decimals by 10, 100 and 1000 | |
| Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand. | |||
| 39 | Decimals | Rounding decimals | |
| Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number. | |||
| 40 | Decimals | Decimals to three decimal places | |
| Objective: On completion of the lesson the student will be able to express thousandths as a decimal and interpret decimal notation for thousandths. | |||
| 41 | Decimals | Adding decimals with a different number of decimal places | |
| Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places. | |||
| 42 | Decimals | Subtracting decimals with a different number of places | |
| Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places. | |||
| 43 | Decimals | Multiplying decimals by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers. | |||
| 44 | Decimals | Dividing decimal fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. | |||
| 45 | Percentages | Calculating Percentages and Fractions of Quantities | |
| Objective: To find percentages and fractions of quantities and solve problems with percentages | |||
| 46 | Algebraic expressions | Substitution into algebraic expressions. | |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. | |||
| 47 | Algebraic equations | Solving equations containing addition and subtraction | |
| Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side. | |||
| 48 | Algebraic equations | Solving equations containing multiplication and division | |
| Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. | |||
| 49 | Length | Compare and convert formal units of measurement | |
| Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert. | |||
| 50 | Length | Problems with length. | |
| Objective: On completion of the lesson the student will be able to solve problems with length. | |||
| 51 | Mass | Problems with mass. | |
| Objective: On completion of the lesson the student will be able to solve problems with mass. | |||
| 52 | Area | Problems with area. | |
| Objective: On completion of the lesson the student will be able to solve problems with area. | |||
| 53 | Volume/capacity | Problems with volume/capacity. | |
| Objective: Problem Solving: problems involving volume/capacity | |||
| 54 | Capacity | Using the cubic cm and displacement to measure volume and capacity | |
| Objective: On completion of the lesson the student will know a way to find volume and capacity. | |||
| 55 | Capacity | The relationship between the common units of capacity, the litre and the millilitre | |
| Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre. | |||
| 56 | Area | Introduction to the square centimetre. | |
| Objective: On completion of the lesson the student will be able to calculate the area in square centimetres of surfaces or objects and record their results correctly. | |||
| 57 | Area | Introducing the rules for finding the area of a rectangle and a parallelogram. | |
| Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides. | |||
| 58 | Area | Finding the area of a triangle and other composite shapes. | |
| Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas. | |||
| 59 | Area | Larger areas: square metre, hectare, square kilometre. | |
| Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit. | |||
| 60 | Area | Comparing and ordering areas. | |
| Objective: On completion of the lesson the student will be able to estimate and compare the area of shapes using a standard unit and order shapes according to their area. | |||
| 61 | Geometry-quadrilaterals | Quadrilaterals | |
| Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees. | |||
| 62 | Geometry-quadrilaterals | Classifying Quadrilaterals | |
| Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. | |||
| 63 | Geometry-quadrilaterals | Using the Properties of a Parallelogram | |
| Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram. | |||
| 64 | Geometry-quadrilaterals | Proving a Shape is a Parallelogram | |
| Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram. | |||
| 65 | Geometry-quadrilaterals | Properties of the Rectangle, Square and Rhombus | |
| Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values. | |||
| 66 | Geometry-quadrilaterals | Properties of the Trapezium and Kite | |
| Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values. | |||
| 67 | Geometry-quadrilaterals | The quadrilateral family and coordinate methods in geometry | |
| Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties. | |||
| 68 | 2-D shapes | Using the prefix to determine polygons | |
| Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides. | |||
| 69 | 3-D shapes | Recognise and name prisms according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties. | |||
| 70 | 3-D shapes | Recognise and name pyramids according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties. | |||
| 71 | 3-D shapes | Recognise nets for prisms, pyramids, cubes and cones | |
| Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones. | |||
| 72 | Geometry-angles | Adjacent angles | |
| Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems. | |||
| 73 | Geometry-angles | Complementary and supplementary angles | |
| Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems. | |||
| 74 | Geometry-angles | Vertically opposite angles | |
| Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems. | |||
| 75 | Geometry-angles | Angles at a Point. | |
| Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems. | |||
| 76 | Geometry-triangles | Angle sum of a triangle | |
| Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. | |||
| 77 | Geometry-triangles | Exterior angle theorem | |
| Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions. | |||
| 78 | Geometry-polygons | Angles of regular polygons | |
| Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees. | |||
| 79 | Trig complementary angles | Complementary angle results. | |
| Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations. | |||
| 80 | Data | Line graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||
| 81 | Data | Pie and bar graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs. | |||
| 82 | Statistic-probability | The mean | |
| Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||
KS3 – Maths – Year 7 Mathematics
| # | TOPIC | TITLE | |
| 1 | Counting and numeration | Addition to 9999 and beyond | |
| Objective: On completion of the lesson the student will be able to use the student’s knowledge of place value to solve addition problems with 3, 4 and 5 digit numbers and word problems. | |||
| 2 | Subtraction | Subtraction involving four digit numbers and beyond using the renaming method. | |
| Objective: On completion of the lesson the student will be able to use written methods to solve subtraction problems involving 4 and 5 digit whole numbers. | |||
| 3 | Multiplication | Multiplying 2-digit numbers by 2-digit numbers | |
| Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number. | |||
| 4 | Multiplication | Multiplying 4-digit numbers by 3-digit numbers | |
| Objective: On completion of the lesson the student will be able to multiply any 4 digit numbers by any 3 digit numbers using long multiplication. | |||
| 5 | Multiplication | Multiplying 4-digit numbers by 4-digit number | |
| Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication. | |||
| 6 | Division/repeat subtraction | Repeated subtraction with divisors greater than 20 with remainders as fractions | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors greater than 20 and remainders expressed as fractions | |||
| 7 | Division/repeat subtraction | Repeated subtraction with divisors less than 35 with some remainders | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 35, with some remainders. | |||
| 8 | Division/repeat subtraction | Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 55 and where dividends are 3 and 4 digit numbers, and there are some remainders. | |||
| 9 | Division/repeat subtraction | Repeated subtraction with divisors greater than 50 with dividends of thousands and some remainders | |
| Objective: On completion of the lesson the student will able to use Long Division by repeated subtraction with divisors greater than 50 including division of thousands, and some remainders. | |||
| 10 | Algebraic expressions | Directed numbers: addition and subtraction. | |
| Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals. | |||
| 11 | Algebraic expressions | Directed numbers: multiplication and division. | |
| Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer. | |||
| 12 | Decimals | Comparing and ordering decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to compare and order decimals to two decimal places and understand decimal notation to two places. | |||
| 13 | Decimals | Adding decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to add decimals with the same number of decimal places (to two decimal places) | |||
| 14 | Decimals | Subtracting decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to subtract decimals with the same number of decimal places (to two decimal places) | |||
| 15 | Decimals | Using decimals – shopping problems | |
| Objective: On completion of the lesson the student will be able to: read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money. | |||
| 16 | Decimals | Rounding decimals | |
| Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number. | |||
| 17 | Decimals | Decimals to three decimal places | |
| Objective: On completion of the lesson the student will be able to express thousandths as a decimal and interpret decimal notation for thousandths. | |||
| 18 | Decimals | Adding decimals with a different number of decimal places | |
| Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places. | |||
| 19 | Decimals | Subtracting decimals with a different number of places | |
| Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places. | |||
| 20 | Decimals | Multiplying decimals by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers. | |||
| 21 | Decimals | Multiplication of decimals by decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to multiply decimals to two digits. | |||
| 22 | Decimals | Dividing decimal fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. | |||
| 23 | Decimals | Dividing numbers by a decimal fraction | |
| Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction. | |||
| 24 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe part of a whole | |
| Objective: On completion of the lesson the student will be able to: name fractions, and use fractions to describe equal parts of a whole. | |||
| 25 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection | |
| Objective: On completion of the lesson the student will be able to use the fractions to describe equal parts of a collection of objects. | |||
| 26 | Fractions | Comparing and ordering fractions | |
| Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts. | |||
| 27 | Fractions | mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one. | |||
| 28 | Fractions | Improper fractions | |
| Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally. | |||
| 29 | Fractions | Fractions 1/5, 1/10, 1/100 | |
| Objective: On completion of the lesson the student will be able to: compare fractions with the denominators 5, 10, 100, and represent fractions with the denominator 5, 10, 100. | |||
| 30 | Fractions | Finding equivalent fractions | |
| Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines. | |||
| 31 | Fractions | Multiplying and dividing to obtain equivalent fractions | |
| Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form. | |||
| 32 | Fractions | Reducing fractions to lowest equivalent form | |
| Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor. | |||
| 33 | Fractions | Comparing and ordering fractions greater than (>) 1 | |
| Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one. | |||
| 34 | Fractions | Subtracting fractions from whole numbers | |
| Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from | |||
| 35 | Fractions | Adding and subtracting fractions with the same denominator | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator. | |||
| 36 | Fractions | Adding and subtracting fractions with different denominators | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other. | |||
| 37 | Fractions | Multiplying fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers. | |||
| 38 | Fractions | Fractions of whole numbers | |
| Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection. | |||
| 39 | Percentages | Calculating Percentages and Fractions of Quantities | |
| Objective: To find percentages and fractions of quantities and solve problems with percentages | |||
| 40 | Percentages | Introduction to percentages, including relating common fractions to percentages | |
| Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage. | |||
| 41 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion. | |||
| 42 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||
| 43 | Multiplication | Multiples and factors of whole numbers | |
| Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers. | |||
| 44 | Algebra-highest common factor | Highest common factor. | |
| Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression. | |||
| 45 | Factors by grouping | Factors by grouping. | |
| Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression. | |||
| 46 | Length | Compare and convert formal units of measurement | |
| Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert. | |||
| 47 | Length | Read and calculate distances on a map using the formal unit kilometre | |
| Objective: On completion of the lesson the student will be able to read distances in kilometres and calculate total distances between different locations on a map. | |||
| 48 | Lines and angles | Describing position. | |
| Objective: On completion of the lesson the student will be able to use and understand conventional location language to describe position. | |||
| 49 | Area | Introduction to the square centimetre. | |
| Objective: On completion of the lesson the student will be able to calculate the area in square centimetres of surfaces or objects and record their results correctly. | |||
| 50 | Area | Introducing the rules for finding the area of a rectangle and a parallelogram. | |
| Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides. | |||
| 51 | Area | Finding the area of a triangle and other composite shapes. | |
| Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas. | |||
| 52 | Area | Larger areas: square metre, hectare, square kilometre. | |
| Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit. | |||
| 53 | Area | Comparing and ordering areas. | |
| Objective: On completion of the lesson the student will be able to estimate and compare the area of shapes using a standard unit and order shapes according to their area. | |||
| 54 | Area | Area of a trapezium. | |
| Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula. | |||
| 55 | Volume | Introduction to volume. using the cubic centimetre as a standard unit | |
| Objective: On completion of the lesson the student will be able to: recognise the need for a formal unit to measure volume, use the abbreviation for cubic centimetre, construct three dimensional objects using cubic centimetre blocks, and use counting to determine vo | |||
| 56 | Volume | Using the cubic centimetre to measure volume. | |
| Objective: On completion of the lesson the student will be able to: recognise the relationship between the length, breadth, height and volume of a rectangular prism, calculate the volume of rectangular prisms, and find the volume of rectangular prisms by counting. | |||
| 57 | Volume | Introducing the formula for volume. | |
| Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula. | |||
| 58 | Volume | Using the cubic metre to measure volume. | |
| Objective: On completion of the lesson the student will be able to: recognise the need for a unit larger than the cubic centimetre, use the cubic metre as a formal unit for measuring large volumes, and explain why volume is measured in cubic metres in certain situat | |||
| 59 | Volume | Solving Problems about Volume – Part 1. | |
| Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms. | |||
| 60 | Volume | Solving Problems about Volume – Part 2. | |
| Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit. | |||
| 61 | Angles | Measure and classify angles | |
| Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle. | |||
| 62 | Geometry-angles | Measuring angles | |
| Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is. | |||
| 63 | Geometry-angles | Adjacent angles | |
| Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems. | |||
| 64 | Geometry-angles | Complementary and supplementary angles | |
| Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems. | |||
| 65 | Geometry-angles | Vertically opposite angles | |
| Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems. | |||
| 66 | Geometry-angles | Angles at a Point. | |
| Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems. | |||
| 67 | Geometry-angles | Parallel Lines. | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. | |||
| 68 | Geometry-problems | Additional questions involving parallel lines | |
| Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them. | |||
| 69 | Geometry-triangles | Angle sum of a triangle | |
| Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. | |||
| 70 | 2-D shapes | Recognise and name triangles | |
| Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties. | |||
| 71 | Geometry-quadrilaterals | Quadrilaterals | |
| Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees. | |||
| 72 | Geometry-quadrilaterals | Classifying Quadrilaterals | |
| Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. | |||
| 73 | Geometry-quadrilaterals | Using the Properties of a Parallelogram | |
| Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram. | |||
| 74 | Geometry-quadrilaterals | Proving a Shape is a Parallelogram | |
| Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram. | |||
| 75 | Geometry-quadrilaterals | Properties of the Rectangle, Square and Rhombus | |
| Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values. | |||
| 76 | Geometry-quadrilaterals | Properties of the Trapezium and Kite | |
| Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values. | |||
| 77 | Geometry-quadrilaterals | The quadrilateral family and coordinate methods in geometry | |
| Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties. | |||
| 78 | Trigonometry-compass | Bearings – the compass. | |
| Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. | |||
| 79 | Geometry-constructions | Geometric constructions | |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. | |||
| 80 | Tessellating 2-D shapes | Use grids to enlarge/reduce 2D shapes | |
| Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate. | |||
| 81 | Transformations | Special transformations – reflections, rotations and enlargements. | |
| Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable. | |||
| 82 | Translations | Transformations – reflections | |
| Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection. | |||
| 83 | Geometric transformations | Geometry transformations without matrices: reflection (Stage 2) | |
| Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane. | |||
| 84 | Geometric transformations | Geometry transformations without matrices: translation (Stage 2) | |
| Objective: On completion of this lesson the student will perform translations in a number plane. | |||
| 85 | Geometric transformations | Geometry transformations without matrices: rotation (Stage 2) | |
| Objective: On completion of this lesson the student will perform and construct rotations. | |||
| 86 | Geometric transformations | Geometry transformations without matrices: dilation or enlargement (Stage 2) | |
| Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor. | |||
| 87 | Geometry-congruence | Congruent triangles, Test 1 and 2 | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent. | |||
| 88 | Geometry-congruence | Congruent triangles, Test 3 and 4 | |
| Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent. | |||
| 89 | 2-D shapes | Using the prefix to determine polygons | |
| Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides. | |||
| 90 | 3-D shapes | Recognise and name prisms according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties. | |||
| 91 | 3-D shapes | Recognise and name pyramids according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties. | |||
| 92 | 3-D shapes | Recognise nets for prisms, pyramids, cubes and cones | |
| Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones. | |||
| 93 | 3-D shapes | Viewing 3-D shapes. | |
| Objective: On completion of the lesson the student will be able to use conventional representations of three-dimensional shapes to show depth etc when drawing or viewing shapes from various angles. | |||
| 94 | 3-D shapes | Constructing models. | |
| Objective: On completion of the lesson the student will be able to: Construct rectangular prisms using cubic centimetre blocks and counting to determine volume. Explain the advantages of using a cube to measure volume. Construct different rectangular prisms. | |||
| 95 | Sequences and Series | General sequences. | |
| Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula. | |||
| 96 | Algebraic expressions | Algebraic expressions. | |
| Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand. | |||
| 97 | Algebraic expressions | Simplifying algebraic expressions: adding like terms. | |
| Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms. | |||
| 98 | Algebraic expressions | Simplifying algebraic Expressions: subtracting like terms. | |
| Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction. | |||
| 99 | Algebraic expressions | Simplifying Algebraic expressions: combining addition and subtraction. | |
| Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes. | |||
| 100 | Algebraic expressions | Simplifying algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form. | |||
| 101 | Algebraic expressions | Simplifying algebraic expressions: division | |
| Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. | |||
| 102 | Algebraic expressions | Expanding algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step. | |||
| 103 | Algebraic expressions | Expanding algebraic expressions: negative multiplier | |
| Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier. | |||
| 104 | Algebraic expressions | Expanding and simplifying algebraic expressions | |
| Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. | |||
| 105 | Algebraic expressions | Substitution into algebraic expressions. | |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. | |||
| 106 | Algebraic equations | Solving equations containing addition and subtraction | |
| Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side. | |||
| 107 | Algebraic equations | Solving equations containing multiplication and division | |
| Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. | |||
| 108 | Algebraic equations | Solving two step equations | |
| Objective: On completion of the lesson the student will be able to solve two step equations. | |||
| 109 | Statistics | The range. | |
| Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. | |||
| 110 | Statistic-probability | The mode | |
| Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. | |||
| 111 | Statistic-probability | The mean | |
| Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||
| 112 | Statistic-probability | The median | |
| Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||
| 113 | Data | Bar Charts | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||
| 114 | Data | Line graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||
| 115 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||
| 116 | Statistics | Frequency distribution table | |
| Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. | |||
| 117 | Statistics | Relative frequency | |
| Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. | |||
| 118 | Statistic-probability | Probability of Simple Events | |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||
| 119 | Statistic-probability | Rolling a pair of dice | |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. | |||
KS3 – Maths – Year 8 Mathematics
| # | TOPIC | TITLE | |
| 1 | Counting and numeration | Addition to 9999 and beyond | |
| Objective: On completion of the lesson the student will be able to use the student’s knowledge of place value to solve addition problems with 3, 4 and 5 digit numbers and word problems. | |||
| 2 | Subtraction | Subtraction involving four digit numbers and beyond using the renaming method. | |
| Objective: On completion of the lesson the student will be able to use written methods to solve subtraction problems involving 4 and 5 digit whole numbers. | |||
| 3 | Multiplication | Multiplying 2-digit numbers by 2-digit numbers | |
| Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number. | |||
| 4 | Multiplication | Multiplying 4-digit numbers by 3-digit numbers | |
| Objective: On completion of the lesson the student will be able to multiply any 4 digit numbers by any 3 digit numbers using long multiplication. | |||
| 5 | Multiplication | Multiplying 4-digit numbers by 4-digit number | |
| Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication. | |||
| 6 | Division/repeat subtraction | Repeated subtraction with divisors greater than 20 with remainders as fractions | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors greater than 20 and remainders expressed as fractions | |||
| 7 | Division/repeat subtraction | Repeated subtraction with divisors less than 35 with some remainders | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 35, with some remainders. | |||
| 8 | Division/repeat subtraction | Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 55 and where dividends are 3 and 4 digit numbers, and there are some remainders. | |||
| 9 | Division/repeat subtraction | Repeated subtraction with divisors greater than 50 with dividends of thousands and some remainders | |
| Objective: On completion of the lesson the student will able to use Long Division by repeated subtraction with divisors greater than 50 including division of thousands, and some remainders. | |||
| 10 | Multiplication | Multiples and factors of whole numbers | |
| Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers. | |||
| 11 | Algebra-highest common factor | Highest common factor. | |
| Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression. | |||
| 12 | Factors by grouping | Factors by grouping. | |
| Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression. | |||
| 13 | Fractions | Comparing and ordering fractions | |
| Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts. | |||
| 14 | Fractions | mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one. | |||
| 15 | Fractions | Improper fractions | |
| Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally. | |||
| 16 | Fractions | Reducing fractions to lowest equivalent form | |
| Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor. | |||
| 17 | Fractions | Comparing and ordering fractions greater than (>) 1 | |
| Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one. | |||
| 18 | Fractions | Subtracting fractions from whole numbers | |
| Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from | |||
| 19 | Fractions | Adding and subtracting fractions with the same denominator | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator. | |||
| 20 | Fractions | Adding and subtracting fractions with different denominators | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other. | |||
| 21 | Fractions | Multiplying fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers. | |||
| 22 | Fractions | Fractions of whole numbers | |
| Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection. | |||
| 23 | Fractions | Multiplying fractions | |
| Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form. | |||
| 24 | Fractions | Multiplying mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form. | |||
| 25 | Fractions | Finding reciprocals of fractions and mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals). | |||
| 26 | Fractions | Dividing fractions | |
| Objective: On completion of the lesson the student will be able to divide fractions. | |||
| 27 | Fractions | Dividing mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals). | |||
| 28 | Percentages | Calculating Percentages and Fractions of Quantities | |
| Objective: To find percentages and fractions of quantities and solve problems with percentages | |||
| 29 | Percentages | Introduction to percentages, including relating common fractions to percentages | |
| Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage. | |||
| 30 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion. | |||
| 31 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||
| 32 | Percentages | One quantity as a percentage of another | |
| Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another. | |||
| 33 | Decimals | Adding decimals with a different number of decimal places | |
| Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places. | |||
| 34 | Decimals | Subtracting decimals with a different number of places | |
| Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places. | |||
| 35 | Decimals | Multiplying decimals by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers. | |||
| 36 | Decimals | Multiplication of decimals by decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to multiply decimals to two digits. | |||
| 37 | Decimals | Dividing decimal fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. | |||
| 38 | Decimals | Dividing numbers by a decimal fraction | |
| Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction. | |||
| 39 | Area | Introducing the rules for finding the area of a rectangle and a parallelogram. | |
| Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides. | |||
| 40 | Area | Finding the area of a triangle and other composite shapes. | |
| Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas. | |||
| 41 | Area | Larger areas: square metre, hectare, square kilometre. | |
| Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit. | |||
| 42 | Area | Comparing and ordering areas. | |
| Objective: On completion of the lesson the student will be able to estimate and compare the area of shapes using a standard unit and order shapes according to their area. | |||
| 43 | Area | Area of a trapezium. | |
| Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula. | |||
| 44 | Area | Area of a rhombus. | |
| Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems. | |||
| 45 | Area | Area of a circle. | |
| Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle. | |||
| 46 | Volume | Introducing the formula for volume. | |
| Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula. | |||
| 47 | Volume | Using the cubic metre to measure volume. | |
| Objective: On completion of the lesson the student will be able to: recognise the need for a unit larger than the cubic centimetre, use the cubic metre as a formal unit for measuring large volumes, and explain why volume is measured in cubic metres in certain situat | |||
| 48 | Volume | Solving Problems about Volume – Part 1. | |
| Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms. | |||
| 49 | Volume | Solving Problems about Volume – Part 2. | |
| Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit. | |||
| 50 | Volume | Finding the volume of prisms | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume. | |||
| 51 | Surface area | Surface area of a cube/rectangular prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula. | |||
| 52 | Surface area | Surface area of a triangular/trapezoidal prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula. | |||
| 53 | Angles | Measure and classify angles | |
| Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle. | |||
| 54 | Geometry-angles | Measuring angles | |
| Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is. | |||
| 55 | Geometry-angles | Adjacent angles | |
| Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems. | |||
| 56 | Geometry-angles | Complementary and supplementary angles | |
| Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems. | |||
| 57 | Geometry-angles | Vertically opposite angles | |
| Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems. | |||
| 58 | Geometry-angles | Angles at a Point. | |
| Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems. | |||
| 59 | Geometry-angles | Parallel Lines. | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. | |||
| 60 | Geometry-problems | Additional questions involving parallel lines | |
| Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them. | |||
| 61 | Geometry-triangles | Angle sum of a triangle | |
| Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. | |||
| 62 | Geometry-triangles | Exterior angle theorem | |
| Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions. | |||
| 63 | Geometry – angles | To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra | |
| Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles. | |||
| 64 | Geometry problems | More difficult exercises involving parallel lines | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log | |||
| 65 | Geometry-polygons | Angles of regular polygons | |
| Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees. | |||
| 66 | Trig complementary angles | Complementary angle results. | |
| Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations. | |||
| 67 | Trigonometry-compass | Bearings – the compass. | |
| Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. | |||
| 68 | 2-D shapes | Recognise and name triangles | |
| Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties. | |||
| 69 | Geometry-constructions | Geometric constructions | |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. | |||
| 70 | Geometry | To identify collinear points, coplanar lines and points in 2 and 3 dimensions | |
| Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays. | |||
| 71 | Geometry-constructions | Angle bisector construction and its properties (Stage 2) | |
| Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge. | |||
| 72 | Geometry-constructions | Circumcentre and incentre (Stage 2) | |
| Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values. | |||
| 73 | Geometry-constructions | Orthocentre and centroids (Stage 2) | |
| Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values. | |||
| 74 | Geometry-locus | Constructions and loci – single condition | |
| Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. | |||
| 75 | Geometry-locus | Constructions and loci – multiple conditions | |
| Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. | |||
| 76 | Tessellating 2-D shapes | Use grids to enlarge/reduce 2D shapes | |
| Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate. | |||
| 77 | Transformations | Special transformations – reflections, rotations and enlargements. | |
| Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable. | |||
| 78 | Translations | Transformations – reflections | |
| Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection. | |||
| 79 | Geometric transformations | Geometry transformations without matrices: reflection (Stage 2) | |
| Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane. | |||
| 80 | Geometric transformations | Geometry transformations without matrices: translation (Stage 2) | |
| Objective: On completion of this lesson the student will perform translations in a number plane. | |||
| 81 | Geometric transformations | Geometry transformations without matrices: rotation (Stage 2) | |
| Objective: On completion of this lesson the student will perform and construct rotations. | |||
| 82 | Geometric transformations | Geometry transformations without matrices: dilation or enlargement (Stage 2) | |
| Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor. | |||
| 83 | Geometric transformations | The definition and concept of combined transformations resulting in an equivalent single transformation. | |
| Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations. | |||
| 84 | Rules properties | Using Order of Operation procedures (BIDMAS) with Fractions | |
| Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions. | |||
| 85 | Number theory – equations | Transformations that produce equivalent equations | |
| Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations. | |||
| 86 | Rules for indices/exponents | Adding indices when multiplying terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base. | |||
| 87 | Rules for indices/exponents | Subtracting indices when dividing terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base. | |||
| 88 | Rules for indices/exponents | Multiplying indices when raising a power to a power | |
| Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power. | |||
| 89 | Algebraic expressions | Algebraic expressions. | |
| Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand. | |||
| 90 | Algebraic expressions | Substitution into algebraic expressions. | |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. | |||
| 91 | Algebra- formulae | Equations resulting from substitution into formulae. | |
| Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. | |||
| 92 | Algebraic expressions | Simplifying algebraic expressions: adding like terms. | |
| Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms. | |||
| 93 | Algebraic expressions | Simplifying algebraic Expressions: subtracting like terms. | |
| Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction. | |||
| 94 | Algebraic expressions | Simplifying Algebraic expressions: combining addition and subtraction. | |
| Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes. | |||
| 95 | Algebraic expressions | Simplifying algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form. | |||
| 96 | Algebraic expressions | Simplifying algebraic expressions: division | |
| Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. | |||
| 97 | Algebraic expressions | Expanding algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step. | |||
| 98 | Algebraic expressions | Expanding algebraic expressions: negative multiplier | |
| Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier. | |||
| 99 | Algebraic expressions | Expanding and simplifying algebraic expressions | |
| Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. | |||
| 100 | Algebraic equations | Solving equations containing addition and subtraction | |
| Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side. | |||
| 101 | Algebraic equations | Solving equations containing multiplication and division | |
| Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. | |||
| 102 | Algebraic equations | Solving two step equations | |
| Objective: On completion of the lesson the student will be able to solve two step equations. | |||
| 103 | Algebraic equations | Solving equations containing binomial expressions | |
| Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||
| 104 | Algebraic equations | Equations involving grouping symbols. | |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||
| 105 | Algebraic equations | Equations involving fractions. | |
| Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||
| 106 | Algebra- formulae | Changing the subject of the formula. | |
| Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously. | |||
| 107 | Sequences and Series | General sequences. | |
| Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula. | |||
| 108 | Sequences and Series | Finding Tn given Sn. | |
| Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term. | |||
| 109 | Statistics | The range. | |
| Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. | |||
| 110 | Statistic-probability | The mode | |
| Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. | |||
| 111 | Statistic-probability | The mean | |
| Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||
| 112 | Statistic-probability | The median | |
| Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||
| 113 | Statistic-probability | Calculating the median from a frequency distribution | |
| Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. | |||
| 114 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |
| Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. | |||
| 115 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |
| Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. | |||
| 116 | Data | Bar Charts | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||
| 117 | Data | Line graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||
| 118 | Data | Pie and bar graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs. | |||
| 119 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||
| 120 | Statistics | Frequency distribution table | |
| Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. | |||
| 121 | Statistics | Relative frequency | |
| Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. | |||
| 122 | Statistic-probability | Probability of Simple Events | |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||
| 123 | Statistic-probability | Rolling a pair of dice | |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. | |||
| 124 | Statistic-probability | Experimental probability | |
| Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||
KS3 – Maths – Year 9 Mathematics
| # | TOPIC | TITLE | |
| 1 | Number problems | Problems with numbers. | |
| Objective: On completion of the lesson the student will be able to solve problems with numbers using a problem solving strategy. | |||
| 2 | Money | Problems involving money | |
| Objective: On completion of the lesson the student will be able to solve problems with money. | |||
| 3 | Fractions | Comparing and ordering fractions | |
| Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts. | |||
| 4 | Fractions | Comparing and ordering fractions greater than (>) 1 | |
| Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one. | |||
| 5 | Fractions | Adding and subtracting fractions with different denominators | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other. | |||
| 6 | Fractions | Multiplying fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers. | |||
| 7 | Fractions | Fractions of whole numbers | |
| Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection. | |||
| 8 | Fractions | Multiplying fractions | |
| Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form. | |||
| 9 | Fractions | Multiplying mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form. | |||
| 10 | Fractions | Finding reciprocals of fractions and mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals). | |||
| 11 | Fractions | Dividing fractions | |
| Objective: On completion of the lesson the student will be able to divide fractions. | |||
| 12 | Fractions | Dividing mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals). | |||
| 13 | Algebraic fractions | Simplifying algebraic fractions using the index laws. | |
| Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies. | |||
| 14 | Decimals | Rounding decimals | |
| Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number. | |||
| 15 | Decimals | Decimals to three decimal places | |
| Objective: On completion of the lesson the student will be able to express thousandths as a decimal and interpret decimal notation for thousandths. | |||
| 16 | Significant figures | Significant figures | |
| Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures. | |||
| 17 | Decimals | Adding decimals with a different number of decimal places | |
| Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places. | |||
| 18 | Decimals | Subtracting decimals with a different number of places | |
| Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places. | |||
| 19 | Decimals | Multiplying decimals by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers. | |||
| 20 | Decimals | Multiplication of decimals by decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to multiply decimals to two digits. | |||
| 21 | Decimals | Dividing decimal fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. | |||
| 22 | Decimals | Dividing numbers by a decimal fraction | |
| Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction. | |||
| 23 | Percentages | Calculating Percentages and Fractions of Quantities | |
| Objective: To find percentages and fractions of quantities and solve problems with percentages | |||
| 24 | Percentages | Introduction to percentages, including relating common fractions to percentages | |
| Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage. | |||
| 25 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion. | |||
| 26 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||
| 27 | Percentages | One quantity as a percentage of another | |
| Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another. | |||
| 28 | Sequences and Series-Compound interest | Compound interest | |
| Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods. | |||
| 29 | Scientific notation | Scientific notation with larger numbers | |
| Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation. | |||
| 30 | Scientific notation | Scientific notation with small numbers | |
| Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation. | |||
| 31 | Scientific notation | Changing scientific notation to numerals | |
| Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation. | |||
| 32 | Multiplication | Multiples and factors of whole numbers | |
| Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers. | |||
| 33 | Algebra-highest common factor | Highest common factor. | |
| Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression. | |||
| 34 | Factors by grouping | Factors by grouping. | |
| Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression. | |||
| 35 | Time, distance, speed | Average speed | |
| Objective: On completion of the lesson the student will be able to understand what is meant by the speed of an object, read the instantaneous speed of a vehicle on a speedometer and find the average speed of an object. | |||
| 36 | Rules for indices/exponents | Adding indices when multiplying terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base. | |||
| 37 | Rules for indices/exponents | Subtracting indices when dividing terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base. | |||
| 38 | Rules for indices/exponents | Multiplying indices when raising a power to a power | |
| Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power. | |||
| 39 | Rules for indices/exponents | Multiplying indices when raising to more than one term | |
| Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power. | |||
| 40 | Rules for indices/exponents | Terms raised to the power of zero | |
| Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero. | |||
| 41 | Rules for indices/exponents | Negative Indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices. | |||
| 42 | Fractional indices/exponents | Fractional indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. | |||
| 43 | Area | Introducing the rules for finding the area of a rectangle and a parallelogram. | |
| Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides. | |||
| 44 | Area | Finding the area of a triangle and other composite shapes. | |
| Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas. | |||
| 45 | Area | Larger areas: square metre, hectare, square kilometre. | |
| Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit. | |||
| 46 | Area | Comparing and ordering areas. | |
| Objective: On completion of the lesson the student will be able to estimate and compare the area of shapes using a standard unit and order shapes according to their area. | |||
| 47 | Area | Area of a trapezium. | |
| Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula. | |||
| 48 | Area | Area of a rhombus. | |
| Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems. | |||
| 49 | Area | Area of a circle. | |
| Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle. | |||
| 50 | Area | Area of regular polygons and composite figures. | |
| Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula. | |||
| 51 | Volume | Introduction to volume. using the cubic centimetre as a standard unit | |
| Objective: On completion of the lesson the student will be able to: recognise the need for a formal unit to measure volume, use the abbreviation for cubic centimetre, construct three dimensional objects using cubic centimetre blocks, and use counting to determine vo | |||
| 52 | Volume | Using the cubic centimetre to measure volume. | |
| Objective: On completion of the lesson the student will be able to: recognise the relationship between the length, breadth, height and volume of a rectangular prism, calculate the volume of rectangular prisms, and find the volume of rectangular prisms by counting. | |||
| 53 | Volume | Introducing the formula for volume. | |
| Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula. | |||
| 54 | Volume | Using the cubic metre to measure volume. | |
| Objective: On completion of the lesson the student will be able to: recognise the need for a unit larger than the cubic centimetre, use the cubic metre as a formal unit for measuring large volumes, and explain why volume is measured in cubic metres in certain situat | |||
| 55 | Volume | Solving Problems about Volume – Part 1. | |
| Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms. | |||
| 56 | Volume | Solving Problems about Volume – Part 2. | |
| Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit. | |||
| 57 | Volume | Finding the volume of prisms | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume. | |||
| 58 | Length | Problems with length. | |
| Objective: On completion of the lesson the student will be able to solve problems with length. | |||
| 59 | Mass | Problems with mass. | |
| Objective: On completion of the lesson the student will be able to solve problems with mass. | |||
| 60 | Area | Problems with area. | |
| Objective: On completion of the lesson the student will be able to solve problems with area. | |||
| 61 | Volume/capacity | Problems with volume/capacity. | |
| Objective: Problem Solving: problems involving volume/capacity | |||
| 62 | Surface area | Surface area of a cube/rectangular prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula. | |||
| 63 | Surface area | Surface area of a triangular/trapezoidal prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula. | |||
| 64 | Geometry-angles | Adjacent angles | |
| Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems. | |||
| 65 | Geometry-angles | Complementary and supplementary angles | |
| Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems. | |||
| 66 | Geometry-angles | Vertically opposite angles | |
| Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems. | |||
| 67 | Geometry-angles | Angles at a Point. | |
| Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems. | |||
| 68 | Geometry-angles | Parallel Lines. | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. | |||
| 69 | Geometry-problems | Additional questions involving parallel lines | |
| Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them. | |||
| 70 | Geometry-triangles | Angle sum of a triangle | |
| Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. | |||
| 71 | Geometry-triangles | Exterior angle theorem | |
| Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions. | |||
| 72 | Geometry – angles | To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra | |
| Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles. | |||
| 73 | Geometry problems | More difficult exercises involving parallel lines | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log | |||
| 74 | Geometry-polygons | Angles of regular polygons | |
| Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees. | |||
| 75 | Trig complementary angles | Complementary angle results. | |
| Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations. | |||
| 76 | Trigonometry-compass | Bearings – the compass. | |
| Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. | |||
| 77 | 2-D shapes | Recognise and name triangles | |
| Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties. | |||
| 78 | Geometry-quadrilaterals | Midsegments of Triangles | |
| Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle. | |||
| 79 | Geometry-congruence | Congruent triangles, Test 1 and 2 | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent. | |||
| 80 | Geometry-congruence | Congruent triangles, Test 3 and 4 | |
| Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent. | |||
| 81 | 2-D shapes | Spatial properties of quadrilaterals | |
| Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals. | |||
| 82 | Pythagoras | Find the hypotenuse | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. | |||
| 83 | Pythagoras | Pythagorean triples | |
| Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. | |||
| 84 | Pythagoras | Find the hypotenuse Part 2 | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds. | |||
| 85 | Pythagoras | Calculating a leg of a right-angled triangle | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle. | |||
| 86 | Geometry-constructions | Geometric constructions | |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. | |||
| 87 | Geometry | To identify collinear points, coplanar lines and points in 2 and 3 dimensions | |
| Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays. | |||
| 88 | Geometry-constructions | Angle bisector construction and its properties (Stage 2) | |
| Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge. | |||
| 89 | Geometry-constructions | Circumcentre and incentre (Stage 2) | |
| Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values. | |||
| 90 | Geometry-constructions | Orthocentre and centroids (Stage 2) | |
| Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values. | |||
| 91 | Geometry-locus | Constructions and loci – single condition | |
| Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. | |||
| 92 | Geometry-locus | Constructions and loci – multiple conditions | |
| Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. | |||
| 93 | Tessellating 2-D shapes | Use grids to enlarge/reduce 2D shapes | |
| Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate. | |||
| 94 | Transformations | Special transformations – reflections, rotations and enlargements. | |
| Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable. | |||
| 95 | Translations | Transformations – reflections | |
| Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection. | |||
| 96 | Geometric transformations | Geometry transformations without matrices: reflection (Stage 2) | |
| Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane. | |||
| 97 | Geometric transformations | Geometry transformations without matrices: translation (Stage 2) | |
| Objective: On completion of this lesson the student will perform translations in a number plane. | |||
| 98 | Geometric transformations | Geometry transformations without matrices: rotation (Stage 2) | |
| Objective: On completion of this lesson the student will perform and construct rotations. | |||
| 99 | Geometric transformations | Geometry transformations without matrices: dilation or enlargement (Stage 2) | |
| Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor. | |||
| 100 | Geometric transformations | The definition and concept of combined transformations resulting in an equivalent single transformation. | |
| Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations. | |||
| 101 | Trigonometry-ratios | Trigonometric ratios. | |
| Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op | |||
| 102 | Trigonometry-ratios | Using the calculator. | |
| Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles. | |||
| 103 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |
| Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances. | |||
| 104 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |
| Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle. | |||
| 105 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |
| Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle. | |||
| 106 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |
| Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown. | |||
| 107 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |
| Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio. | |||
| 108 | Trigonometry- ratios | Using the trigonometric ratios to find an angle in a right-angled triangle. | |
| Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides. | |||
| 109 | Sequences and Series | General sequences. | |
| Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula. | |||
| 110 | Sequences and Series | Finding Tn given Sn. | |
| Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term. | |||
| 111 | Algebraic expressions | Algebraic expressions. | |
| Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand. | |||
| 112 | Algebraic expressions | Substitution into algebraic expressions. | |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. | |||
| 113 | Algebra- formulae | Equations resulting from substitution into formulae. | |
| Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. | |||
| 114 | Algebra- formulae | Changing the subject of the formula. | |
| Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously. | |||
| 115 | Algebraic expressions | Simplifying algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form. | |||
| 116 | Algebraic expressions | Simplifying algebraic expressions: division | |
| Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. | |||
| 117 | Algebraic expressions | Expanding algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step. | |||
| 118 | Algebraic expressions | Expanding algebraic expressions: negative multiplier | |
| Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier. | |||
| 119 | Algebraic expressions | Expanding and simplifying algebraic expressions | |
| Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. | |||
| 120 | Algebraic equations | Solving equations containing addition and subtraction | |
| Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side. | |||
| 121 | Algebraic equations | Solving equations containing multiplication and division | |
| Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. | |||
| 122 | Algebraic equations | Solving two step equations | |
| Objective: On completion of the lesson the student will be able to solve two step equations. | |||
| 123 | Algebraic equations | Solving equations containing binomial expressions | |
| Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||
| 124 | Algebraic equations | Equations involving grouping symbols. | |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||
| 125 | Algebraic equations | Equations involving fractions. | |
| Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||
| 126 | Simultaneous equns | Simultaneous equations | |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method. | |||
| 127 | Simultaneous equns | Elimination method | |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. | |||
| 128 | Simultaneous equns | Elimination method part 2 | |
| Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method. | |||
| 129 | Simultaneous equns | Applications of simultaneous equations | |
| Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations. | |||
| 130 | Functions and graphs | Quadratic polynomials of the form y = ax. + bx + c. | |
| Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis. | |||
| 131 | Factorising | Expansions leading to the difference of two squares | |
| Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares. | |||
| 132 | Common fact and diff | Common factor and the difference of two squares | |
| Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. | |||
| 133 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. | |
| Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||
| 134 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. | |
| Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||
| 135 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. | |
| Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||
| 136 | Algebra-inequalities | Solving Inequalities. | |
| Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities. | |||
| 137 | Co-ordinate Geometry-Inequalities | Inequalities on the number plane. | |
| Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities. | |||
| 138 | Statistics | The range. | |
| Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. | |||
| 139 | Statistic-probability | The mode | |
| Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. | |||
| 140 | Statistic-probability | The mean | |
| Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||
| 141 | Statistic-probability | The median | |
| Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||
| 142 | Statistic-probability | Calculating the median from a frequency distribution | |
| Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. | |||
| 143 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |
| Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. | |||
| 144 | Statistics – Interquartile range | Measures of spread: the interquartile range | |
| Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range | |||
| 145 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |
| Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. | |||
| 146 | Data | Bar Charts | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||
| 147 | Statistic-probability | Cumulative frequency | |
| Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. | |||
| 148 | Statistics | Frequency histograms and polygons | |
| Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. | |||
| 149 | Data | Line graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||
| 150 | Data | Pie and bar graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs. | |||
| 151 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||
| 152 | Statistics | Frequency distribution table | |
| Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. | |||
| 153 | Statistics | Relative frequency | |
| Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. | |||
| 154 | Statistic-probability | Probability of Simple Events | |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||
| 155 | Statistic-probability | Rolling a pair of dice | |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. | |||
| 156 | Statistic-probability | Experimental probability | |
| Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||
| 157 | Statistic-probability | Tree diagrams – not depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes. | |||
| 158 | Statistic-probability | Tree diagrams – depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes. | |||
KS4 – Maths – Foundation Mathematics
| # | TOPIC | TITLE | |
| 1 | Multiplication | Multiplication by 2 and 3 digits | |
| Objective: On completion of the lesson the student will be able to solve and record 2 and 3 digit multiplication problems in extended and short form. | |||
| 2 | Multiplication | Multiplying 2-digit numbers by multiple of 10 | |
| Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any multiple of 10 using the process of long multiplication. | |||
| 3 | Multiplication | Multiplying 3 and 4-digit numbers by multiples of 100 | |
| Objective: On completion of the lesson the student will be able to multiply any 3 or 4 digit numbers by any multiple of 100 using long multiplication. | |||
| 4 | Multiplication | Multiplying 2-digit numbers by 2-digit numbers | |
| Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number. | |||
| 5 | Multiplication | Multiplying 4-digit numbers by 3-digit numbers | |
| Objective: On completion of the lesson the student will be able to multiply any 4 digit numbers by any 3 digit numbers using long multiplication. | |||
| 6 | Multiplication | Multiplying 4-digit numbers by 4-digit number | |
| Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication. | |||
| 7 | Decimals | Multiplying decimals by 10, 100 and 1000 | |
| Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand. | |||
| 8 | Division/repeat subtraction | Repeated subtraction with divisors greater than 20 with remainders as fractions | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors greater than 20 and remainders expressed as fractions | |||
| 9 | Division/repeat subtraction | Repeated subtraction with divisors less than 35 with some remainders | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 35, with some remainders. | |||
| 10 | Division/repeat subtraction | Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 55 and where dividends are 3 and 4 digit numbers, and there are some remainders. | |||
| 11 | Division/repeat subtraction | Repeated subtraction with divisors greater than 50 with dividends of thousands and some remainders | |
| Objective: On completion of the lesson the student will able to use Long Division by repeated subtraction with divisors greater than 50 including division of thousands, and some remainders. | |||
| 12 | Division/repeat subtraction | Using divide, multiply and subtraction in the bring down method | |
| Objective: On completion of the lesson the student will be able to use Long Division using the Divide, Multiply, Subtract and Bring Down method. | |||
| 13 | Decimals | Dividing decimals by 10, 100 and 1000 | |
| Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand. | |||
| 14 | Rules properties | Using Order of Operation procedures (BIDMAS) with Fractions | |
| Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions. | |||
| 15 | Number theory – equations | Transformations that produce equivalent equations | |
| Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations. | |||
| 16 | Algebraic expressions | Directed numbers: addition and subtraction. | |
| Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals. | |||
| 17 | Algebraic expressions | Directed numbers: multiplication and division. | |
| Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer. | |||
| 18 | Decimals | Adding decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to add decimals with the same number of decimal places (to two decimal places) | |||
| 19 | Decimals | Subtracting decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to subtract decimals with the same number of decimal places (to two decimal places) | |||
| 20 | Decimals | Using decimals – shopping problems | |
| Objective: On completion of the lesson the student will be able to: read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money. | |||
| 21 | Decimals | Rounding decimals | |
| Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number. | |||
| 22 | Decimals | Decimals to three decimal places | |
| Objective: On completion of the lesson the student will be able to express thousandths as a decimal and interpret decimal notation for thousandths. | |||
| 23 | Decimals | Adding decimals with a different number of decimal places | |
| Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places. | |||
| 24 | Decimals | Subtracting decimals with a different number of places | |
| Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places. | |||
| 25 | Decimals | Multiplying decimals by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers. | |||
| 26 | Decimals | Multiplication of decimals by decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to multiply decimals to two digits. | |||
| 27 | Decimals | Dividing decimal fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. | |||
| 28 | Decimals | Dividing numbers by a decimal fraction | |
| Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction. | |||
| 29 | Fractions | Comparing and ordering fractions | |
| Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts. | |||
| 30 | Fractions | mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one. | |||
| 31 | Fractions | Improper fractions | |
| Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally. | |||
| 32 | Fractions | Finding equivalent fractions | |
| Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines. | |||
| 33 | Fractions | Multiplying and dividing to obtain equivalent fractions | |
| Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form. | |||
| 34 | Fractions | Reducing fractions to lowest equivalent form | |
| Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor. | |||
| 35 | Fractions | Comparing and ordering fractions greater than (>) 1 | |
| Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one. | |||
| 36 | Fractions | Subtracting fractions from whole numbers | |
| Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from | |||
| 37 | Fractions | Adding and subtracting fractions with the same denominator | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator. | |||
| 38 | Fractions | Adding and subtracting fractions with different denominators | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other. | |||
| 39 | Fractions | Multiplying fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers. | |||
| 40 | Fractions | Fractions of whole numbers | |
| Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection. | |||
| 41 | Fractions | Multiplying fractions | |
| Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form. | |||
| 42 | Fractions | Multiplying mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form. | |||
| 43 | Fractions | Finding reciprocals of fractions and mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals). | |||
| 44 | Fractions | Dividing fractions | |
| Objective: On completion of the lesson the student will be able to divide fractions. | |||
| 45 | Fractions | Dividing mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals). | |||
| 46 | Number problems | Problems with numbers. | |
| Objective: On completion of the lesson the student will be able to solve problems with numbers using a problem solving strategy. | |||
| 47 | Money | Problems involving money | |
| Objective: On completion of the lesson the student will be able to solve problems with money. | |||
| 48 | Multiplication | Multiples and factors of whole numbers | |
| Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers. | |||
| 49 | Algebra-highest common factor | Highest common factor. | |
| Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression. | |||
| 50 | Factors by grouping | Factors by grouping. | |
| Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression. | |||
| 51 | Rules for indices/exponents | Adding indices when multiplying terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base. | |||
| 52 | Rules for indices/exponents | Subtracting indices when dividing terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base. | |||
| 53 | Rules for indices/exponents | Multiplying indices when raising a power to a power | |
| Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power. | |||
| 54 | Rules for indices/exponents | Multiplying indices when raising to more than one term | |
| Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power. | |||
| 55 | Rules for indices/exponents | Terms raised to the power of zero | |
| Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero. | |||
| 56 | Percentages | Calculating Percentages and Fractions of Quantities | |
| Objective: To find percentages and fractions of quantities and solve problems with percentages | |||
| 57 | Percentages | Introduction to percentages, including relating common fractions to percentages | |
| Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage. | |||
| 58 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion. | |||
| 59 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||
| 60 | Percentages | One quantity as a percentage of another | |
| Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another. | |||
| 61 | Time, 24-hour | 24 hour time | |
| Objective: On completion of the lesson the student will be able to: tell the time accurately using twenty-four hour time, change the time from am and pm time to twenty-four hour time, and change the time from twenty-four hour time to am and pm time. | |||
| 62 | Time zones | Time zones | |
| Objective: On completion of the lesson the student will be able to: recognise that there are different time zones, compare time zones, understand daylight saving and adjust times accordingly, and determine the local time in different regions. | |||
| 63 | Length | Read and calculate distances on a map using the formal unit kilometre | |
| Objective: On completion of the lesson the student will be able to read distances in kilometres and calculate total distances between different locations on a map. | |||
| 64 | Lines and angles | Describing position. | |
| Objective: On completion of the lesson the student will be able to use and understand conventional location language to describe position. | |||
| 65 | Lines and angles | Mapping and grid references | |
| Objective: On completion of the lesson the student will be able to identify specific places on a map and use regions on a grid to locate objects or places. | |||
| 66 | Lines and angles | Main and intermediate compass points | |
| Objective: On completion of the lesson the student will be able to use main and intermediate compass points to specify location. | |||
| 67 | Length | Using the metre as a formal unit to measure perimeter | |
| Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres. | |||
| 68 | Length | Using the formal unit of the centimetre to measure length and perimeter | |
| Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres. | |||
| 69 | Length | Compare and convert formal units of measurement | |
| Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert. | |||
| 70 | Weight/mass | The kilogram | |
| Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales. | |||
| 71 | Weight/mass | The gram and net mass | |
| Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams. | |||
| 72 | Weight/mass | The tonne – converting units and problems | |
| Objective: On completion of the lesson the student should be able to: choose the correct unit to measure the mass of small, medium or large objects, and convert measurements from one unit to another. | |||
| 73 | Capacity | Converting between volume and capacity using millilitres and litres | |
| Objective: On completion of the lesson the student will be able to convert between units of capacity. | |||
| 74 | Capacity | Using the cubic cm and displacement to measure volume and capacity | |
| Objective: On completion of the lesson the student will know a way to find volume and capacity. | |||
| 75 | Capacity | The relationship between the common units of capacity, the litre and the millilitre | |
| Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre. | |||
| 76 | Capacity | Converting between volume and capacity using kilolitres and litres | |
| Objective: On completion of the lesson the student will know the formal units of measurement for volume and capacity for bigger objects. The student will also be able to use the knowledge of volume to work out capacity. | |||
| 77 | Capacity | Estimate, measure and compare the capacity of containers | |
| Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it. | |||
| 78 | Area | Introducing the rules for finding the area of a rectangle and a parallelogram. | |
| Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides. | |||
| 79 | Area | Finding the area of a triangle and other composite shapes. | |
| Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas. | |||
| 80 | Area | Larger areas: square metre, hectare, square kilometre. | |
| Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit. | |||
| 81 | Area | Comparing and ordering areas. | |
| Objective: On completion of the lesson the student will be able to estimate and compare the area of shapes using a standard unit and order shapes according to their area. | |||
| 82 | Area | Area of a trapezium. | |
| Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula. | |||
| 83 | Area | Area of a rhombus. | |
| Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems. | |||
| 84 | Area | Area of a circle. | |
| Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle. | |||
| 85 | Volume | Introduction to volume. using the cubic centimetre as a standard unit | |
| Objective: On completion of the lesson the student will be able to: recognise the need for a formal unit to measure volume, use the abbreviation for cubic centimetre, construct three dimensional objects using cubic centimetre blocks, and use counting to determine vo | |||
| 86 | Volume | Using the cubic centimetre to measure volume. | |
| Objective: On completion of the lesson the student will be able to: recognise the relationship between the length, breadth, height and volume of a rectangular prism, calculate the volume of rectangular prisms, and find the volume of rectangular prisms by counting. | |||
| 87 | Volume | Introducing the formula for volume. | |
| Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula. | |||
| 88 | Volume | Using the cubic metre to measure volume. | |
| Objective: On completion of the lesson the student will be able to: recognise the need for a unit larger than the cubic centimetre, use the cubic metre as a formal unit for measuring large volumes, and explain why volume is measured in cubic metres in certain situat | |||
| 89 | Volume | Solving Problems about Volume – Part 1. | |
| Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms. | |||
| 90 | Volume | Solving Problems about Volume – Part 2. | |
| Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit. | |||
| 91 | Volume | Finding the volume of prisms | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume. | |||
| 92 | Surface area | Surface area of a cube/rectangular prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula. | |||
| 93 | Surface area | Surface area of a triangular/trapezoidal prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula. | |||
| 94 | Length | Problems with length. | |
| Objective: On completion of the lesson the student will be able to solve problems with length. | |||
| 95 | Mass | Problems with mass. | |
| Objective: On completion of the lesson the student will be able to solve problems with mass. | |||
| 96 | Area | Problems with area. | |
| Objective: On completion of the lesson the student will be able to solve problems with area. | |||
| 97 | Volume/capacity | Problems with volume/capacity. | |
| Objective: Problem Solving: problems involving volume/capacity | |||
| 98 | 2-D shapes | Using the prefix to determine polygons | |
| Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides. | |||
| 99 | 3-D shapes | Recognise and name prisms according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties. | |||
| 100 | 3-D shapes | Recognise and name pyramids according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties. | |||
| 101 | 3-D shapes | Recognise nets for prisms, pyramids, cubes and cones | |
| Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones. | |||
| 102 | 3-D shapes | Viewing 3-D shapes. | |
| Objective: On completion of the lesson the student will be able to use conventional representations of three-dimensional shapes to show depth etc when drawing or viewing shapes from various angles. | |||
| 103 | 3-D shapes | Constructing models. | |
| Objective: On completion of the lesson the student will be able to: Construct rectangular prisms using cubic centimetre blocks and counting to determine volume. Explain the advantages of using a cube to measure volume. Construct different rectangular prisms. | |||
| 104 | Angles | Measure and classify angles | |
| Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle. | |||
| 105 | Geometry-angles | Measuring angles | |
| Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is. | |||
| 106 | Geometry-angles | Adjacent angles | |
| Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems. | |||
| 107 | Geometry-angles | Complementary and supplementary angles | |
| Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems. | |||
| 108 | Geometry-angles | Vertically opposite angles | |
| Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems. | |||
| 109 | Geometry-angles | Angles at a Point. | |
| Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems. | |||
| 110 | Geometry-angles | Parallel Lines. | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. | |||
| 111 | Geometry-problems | Additional questions involving parallel lines | |
| Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them. | |||
| 112 | Geometry-triangles | Angle sum of a triangle | |
| Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. | |||
| 113 | Geometry-triangles | Exterior angle theorem | |
| Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions. | |||
| 114 | Geometry – angles | To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra | |
| Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles. | |||
| 115 | Geometry problems | More difficult exercises involving parallel lines | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log | |||
| 116 | Geometry-polygons | Angles of regular polygons | |
| Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees. | |||
| 117 | Trig complementary angles | Complementary angle results. | |
| Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations. | |||
| 118 | Trigonometry-compass | Bearings – the compass. | |
| Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. | |||
| 119 | Geometry-constructions | Geometric constructions | |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. | |||
| 120 | Geometry | To identify collinear points, coplanar lines and points in 2 and 3 dimensions | |
| Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays. | |||
| 121 | Geometry-constructions | Angle bisector construction and its properties (Stage 2) | |
| Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge. | |||
| 122 | Geometry-constructions | Circumcentre and incentre (Stage 2) | |
| Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values. | |||
| 123 | Geometry-constructions | Orthocentre and centroids (Stage 2) | |
| Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values. | |||
| 124 | Geometry-locus | Constructions and loci – single condition | |
| Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. | |||
| 125 | Geometry-locus | Constructions and loci – multiple conditions | |
| Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. | |||
| 126 | 2-D shapes | Recognise and name triangles | |
| Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties. | |||
| 127 | Similar triangles | Similar triangles | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. | |||
| 128 | Similar triangles | Using similar triangles to calculate lengths | |
| Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles. | |||
| 129 | Geometry-quadrilaterals | Midsegments of Triangles | |
| Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle. | |||
| 130 | Geometry-congruence | Congruent triangles, Test 1 and 2 | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent. | |||
| 131 | Geometry-congruence | Congruent triangles, Test 3 and 4 | |
| Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent. | |||
| 132 | 2-D shapes | Spatial properties of quadrilaterals | |
| Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals. | |||
| 133 | Tessellating 2-D shapes | Use grids to enlarge/reduce 2D shapes | |
| Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate. | |||
| 134 | Transformations | Special transformations – reflections, rotations and enlargements. | |
| Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable. | |||
| 135 | Translations | Transformations – reflections | |
| Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection. | |||
| 136 | Geometric transformations | Geometry transformations without matrices: reflection (Stage 2) | |
| Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane. | |||
| 137 | Geometric transformations | Geometry transformations without matrices: translation (Stage 2) | |
| Objective: On completion of this lesson the student will perform translations in a number plane. | |||
| 138 | Geometric transformations | Geometry transformations without matrices: rotation (Stage 2) | |
| Objective: On completion of this lesson the student will perform and construct rotations. | |||
| 139 | Geometric transformations | Geometry transformations without matrices: dilation or enlargement (Stage 2) | |
| Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor. | |||
| 140 | Geometric transformations | The definition and concept of combined transformations resulting in an equivalent single transformation. | |
| Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations. | |||
| 141 | Pythagoras | Find the hypotenuse | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. | |||
| 142 | Pythagoras | Pythagorean triples | |
| Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. | |||
| 143 | Pythagoras | Find the hypotenuse Part 2 | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds. | |||
| 144 | Pythagoras | Calculating a leg of a right-angled triangle | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle. | |||
| 145 | Sequences and Series | General sequences. | |
| Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula. | |||
| 146 | Sequences and Series | Finding Tn given Sn. | |
| Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term. | |||
| 147 | Algebraic expressions | Algebraic expressions. | |
| Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand. | |||
| 148 | Algebraic expressions | Simplifying algebraic expressions: adding like terms. | |
| Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms. | |||
| 149 | Algebraic expressions | Simplifying algebraic Expressions: subtracting like terms. | |
| Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction. | |||
| 150 | Algebraic expressions | Simplifying Algebraic expressions: combining addition and subtraction. | |
| Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes. | |||
| 151 | Algebraic expressions | Simplifying algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form. | |||
| 152 | Algebraic expressions | Simplifying algebraic expressions: division | |
| Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. | |||
| 153 | Algebraic expressions | Expanding algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step. | |||
| 154 | Algebraic expressions | Expanding algebraic expressions: negative multiplier | |
| Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier. | |||
| 155 | Algebraic expressions | Expanding and simplifying algebraic expressions | |
| Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. | |||
| 156 | Algebraic fractions | Simplifying algebraic fractions using the index laws. | |
| Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies. | |||
| 157 | Algebraic equations | Solving equations containing addition and subtraction | |
| Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side. | |||
| 158 | Algebraic equations | Solving equations containing multiplication and division | |
| Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. | |||
| 159 | Algebraic equations | Solving two step equations | |
| Objective: On completion of the lesson the student will be able to solve two step equations. | |||
| 160 | Algebraic equations | Solving equations containing binomial expressions | |
| Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||
| 161 | Algebraic equations | Equations involving grouping symbols. | |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||
| 162 | Factorising | Expansions leading to the difference of two squares | |
| Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares. | |||
| 163 | Common fact and diff | Common factor and the difference of two squares | |
| Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. | |||
| 164 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. | |
| Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||
| 165 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. | |
| Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||
| 166 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. | |
| Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||
| 167 | Algebraic expressions | Substitution into algebraic expressions. | |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. | |||
| 168 | Algebra- formulae | Equations resulting from substitution into formulae. | |
| Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. | |||
| 169 | Algebra- formulae | Changing the subject of the formula. | |
| Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously. | |||
| 170 | Algebra-inequalities | Solving Inequalities. | |
| Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities. | |||
| 171 | Co-ordinate Geometry-Inequalities | Inequalities on the number plane. | |
| Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities. | |||
| 172 | Statistics | The range. | |
| Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. | |||
| 173 | Statistic-probability | The mode | |
| Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. | |||
| 174 | Statistic-probability | The mean | |
| Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||
| 175 | Statistic-probability | The median | |
| Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||
| 176 | Statistic-probability | Calculating the median from a frequency distribution | |
| Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. | |||
| 177 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |
| Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. | |||
| 178 | Data | Bar Charts | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||
| 179 | Data | Line graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||
| 180 | Data | Pictograms | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs. | |||
| 181 | Data | Pie and bar graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs. | |||
| 182 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||
| 183 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |
| Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. | |||
| 184 | Statistics | Frequency distribution table | |
| Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. | |||
| 185 | Statistics | Relative frequency | |
| Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. | |||
| 186 | Statistic-probability | Probability of Simple Events | |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||
| 187 | Statistic-probability | Rolling a pair of dice | |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. | |||
| 188 | Statistic-probability | Experimental probability | |
| Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||
| 189 | Statistic-probability | Tree diagrams – not depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes. | |||
| 190 | Statistic-probability | Tree diagrams – depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes. | |||
KS4 – Maths – Higher Mathematics
| # | TOPIC | TITLE | |
| 1 | Multiplication | Multiplying 4-digit numbers by 3-digit numbers | |
| Objective: On completion of the lesson the student will be able to multiply any 4 digit numbers by any 3 digit numbers using long multiplication. | |||
| 2 | Multiplication | Multiplying 4-digit numbers by 4-digit number | |
| Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication. | |||
| 3 | Decimals | Multiplying decimals by 10, 100 and 1000 | |
| Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand. | |||
| 4 | Division/repeat subtraction | Repeated subtraction with divisors greater than 20 with remainders as fractions | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors greater than 20 and remainders expressed as fractions | |||
| 5 | Division/repeat subtraction | Repeated subtraction with divisors less than 35 with some remainders | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 35, with some remainders. | |||
| 6 | Division/repeat subtraction | Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders | |
| Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 55 and where dividends are 3 and 4 digit numbers, and there are some remainders. | |||
| 7 | Division/repeat subtraction | Repeated subtraction with divisors greater than 50 with dividends of thousands and some remainders | |
| Objective: On completion of the lesson the student will able to use Long Division by repeated subtraction with divisors greater than 50 including division of thousands, and some remainders. | |||
| 8 | Division/repeat subtraction | Using divide, multiply and subtraction in the bring down method | |
| Objective: On completion of the lesson the student will be able to use Long Division using the Divide, Multiply, Subtract and Bring Down method. | |||
| 9 | Decimals | Dividing decimals by 10, 100 and 1000 | |
| Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand. | |||
| 10 | Algebraic expressions | Directed numbers: addition and subtraction. | |
| Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals. | |||
| 11 | Algebraic expressions | Directed numbers: multiplication and division. | |
| Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer. | |||
| 12 | Rules properties | Using Order of Operation procedures (BIDMAS) with Fractions | |
| Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions. | |||
| 13 | Multiplication | Multiples and factors of whole numbers | |
| Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers. | |||
| 14 | Algebra-highest common factor | Highest common factor. | |
| Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression. | |||
| 15 | Factors by grouping | Factors by grouping. | |
| Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression. | |||
| 16 | Decimals | Rounding decimals | |
| Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number. | |||
| 17 | Decimals | Decimals to three decimal places | |
| Objective: On completion of the lesson the student will be able to express thousandths as a decimal and interpret decimal notation for thousandths. | |||
| 18 | Decimals | Adding decimals with a different number of decimal places | |
| Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places. | |||
| 19 | Decimals | Subtracting decimals with a different number of places | |
| Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places. | |||
| 20 | Decimals | Multiplying decimals by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers. | |||
| 21 | Decimals | Multiplication of decimals by decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to multiply decimals to two digits. | |||
| 22 | Decimals | Dividing decimal fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. | |||
| 23 | Decimals | Dividing numbers by a decimal fraction | |
| Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction. | |||
| 24 | Fractions | Adding and subtracting fractions with different denominators | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other. | |||
| 25 | Fractions | Multiplying fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers. | |||
| 26 | Fractions | Fractions of whole numbers | |
| Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection. | |||
| 27 | Fractions | Multiplying fractions | |
| Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form. | |||
| 28 | Fractions | Multiplying mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form. | |||
| 29 | Fractions | Finding reciprocals of fractions and mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals). | |||
| 30 | Fractions | Dividing fractions | |
| Objective: On completion of the lesson the student will be able to divide fractions. | |||
| 31 | Fractions | Dividing mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals). | |||
| 32 | Rules for indices/exponents | Adding indices when multiplying terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base. | |||
| 33 | Rules for indices/exponents | Subtracting indices when dividing terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base. | |||
| 34 | Rules for indices/exponents | Multiplying indices when raising a power to a power | |
| Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power. | |||
| 35 | Rules for indices/exponents | Multiplying indices when raising to more than one term | |
| Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power. | |||
| 36 | Rules for indices/exponents | Terms raised to the power of zero | |
| Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero. | |||
| 37 | Rules for indices/exponents | Negative Indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices. | |||
| 38 | Fractional indices/exponents | Fractional indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. | |||
| 39 | Fractional indices/exponents | Complex fractions as indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices. | |||
| 40 | Percentages | Calculating Percentages and Fractions of Quantities | |
| Objective: To find percentages and fractions of quantities and solve problems with percentages | |||
| 41 | Percentages | Introduction to percentages, including relating common fractions to percentages | |
| Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage. | |||
| 42 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion. | |||
| 43 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||
| 44 | Percentages | One quantity as a percentage of another | |
| Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another. | |||
| 45 | Sequences and Series-Compound interest | Compound interest | |
| Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods. | |||
| 46 | Significant figures | Significant figures | |
| Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures. | |||
| 47 | Time, distance, speed | Average speed | |
| Objective: On completion of the lesson the student will be able to understand what is meant by the speed of an object, read the instantaneous speed of a vehicle on a speedometer and find the average speed of an object. | |||
| 48 | Scientific notation | Scientific notation with larger numbers | |
| Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation. | |||
| 49 | Scientific notation | Scientific notation with small numbers | |
| Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation. | |||
| 50 | Scientific notation | Changing scientific notation to numerals | |
| Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation. | |||
| 51 | Surds | Introducing surds | |
| Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers. | |||
| 52 | Surds | Some rules for the operations with surds | |
| Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds. | |||
| 53 | Surds | Simplifying surds | |
| Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication. | |||
| 54 | Surds | Creating entire surds | |
| Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds | |||
| 55 | Surds | Adding and subtracting like surds | |
| Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds. | |||
| 56 | Surds | Expanding surds | |
| Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds. | |||
| 57 | Surds | Conjugate binomials with surds | |
| Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds. | |||
| 58 | Surds | Rationalising the denominator | |
| Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds. | |||
| 59 | Surds | Rationalising binomial denominators | |
| Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions. | |||
| 60 | Length | Compare and convert formal units of measurement | |
| Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert. | |||
| 61 | Capacity | Estimate, measure and compare the capacity of containers | |
| Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it. | |||
| 62 | Area | Introducing the rules for finding the area of a rectangle and a parallelogram. | |
| Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides. | |||
| 63 | Area | Finding the area of a triangle and other composite shapes. | |
| Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas. | |||
| 64 | Area | Area of a trapezium. | |
| Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula. | |||
| 65 | Area | Area of a rhombus. | |
| Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems. | |||
| 66 | Area | Area of a circle. | |
| Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle. | |||
| 67 | Area | Area of regular polygons and composite figures. | |
| Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula. | |||
| 68 | Surface area | Surface area of a cube/rectangular prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula. | |||
| 69 | Surface area | Surface area of a triangular/trapezoidal prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula. | |||
| 70 | Surface area | Surface area of a cylinder and sphere. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula. | |||
| 71 | Surface area | Surface area of pyramids | |
| Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. | |||
| 72 | Surface area | Surface area of cones | |
| Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul | |||
| 73 | Surface area | Surface area of composite solids | |
| Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. | |||
| 74 | Volume | Introducing the formula for volume. | |
| Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula. | |||
| 75 | Volume | Using the cubic metre to measure volume. | |
| Objective: On completion of the lesson the student will be able to: recognise the need for a unit larger than the cubic centimetre, use the cubic metre as a formal unit for measuring large volumes, and explain why volume is measured in cubic metres in certain situat | |||
| 76 | Volume | Solving Problems about Volume – Part 1. | |
| Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms. | |||
| 77 | Volume | Solving Problems about Volume – Part 2. | |
| Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit. | |||
| 78 | Volume | Finding the volume of prisms | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume. | |||
| 79 | Volume | Volume of a cylinder and sphere. | |
| Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume. | |||
| 80 | Volume | Volume of pyramids and cones. | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones. | |||
| 81 | Volume | Composite solids. | |
| Objective: On completion of the lesson the student will be able to: dissect composite solids into simpler shapes so that the volume can be calculated, calculate the volume of a variety of composite solids, and use formulae appropriately. | |||
| 82 | Length | Problems with length. | |
| Objective: On completion of the lesson the student will be able to solve problems with length. | |||
| 83 | Mass | Problems with mass. | |
| Objective: On completion of the lesson the student will be able to solve problems with mass. | |||
| 84 | Area | Problems with area. | |
| Objective: On completion of the lesson the student will be able to solve problems with area. | |||
| 85 | Volume/capacity | Problems with volume/capacity. | |
| Objective: Problem Solving: problems involving volume/capacity | |||
| 86 | 2-D shapes | Using the prefix to determine polygons | |
| Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides. | |||
| 87 | 3-D shapes | Recognise and name prisms according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties. | |||
| 88 | 3-D shapes | Recognise and name pyramids according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties. | |||
| 89 | 3-D shapes | Recognise nets for prisms, pyramids, cubes and cones | |
| Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones. | |||
| 90 | 3-D shapes | Viewing 3-D shapes. | |
| Objective: On completion of the lesson the student will be able to use conventional representations of three-dimensional shapes to show depth etc when drawing or viewing shapes from various angles. | |||
| 91 | 3-D shapes | Constructing models. | |
| Objective: On completion of the lesson the student will be able to: Construct rectangular prisms using cubic centimetre blocks and counting to determine volume. Explain the advantages of using a cube to measure volume. Construct different rectangular prisms. | |||
| 92 | Geometry-angles | Adjacent angles | |
| Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems. | |||
| 93 | Geometry-angles | Complementary and supplementary angles | |
| Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems. | |||
| 94 | Geometry-angles | Vertically opposite angles | |
| Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems. | |||
| 95 | Geometry-angles | Angles at a Point. | |
| Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems. | |||
| 96 | Geometry-angles | Parallel Lines. | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. | |||
| 97 | Geometry-problems | Additional questions involving parallel lines | |
| Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them. | |||
| 98 | Geometry-triangles | Angle sum of a triangle | |
| Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. | |||
| 99 | Geometry-triangles | Exterior angle theorem | |
| Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions. | |||
| 100 | Geometry – angles | To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra | |
| Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles. | |||
| 101 | Geometry problems | More difficult exercises involving parallel lines | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log | |||
| 102 | Geometry-polygons | Angles of regular polygons | |
| Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees. | |||
| 103 | Trig complementary angles | Complementary angle results. | |
| Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations. | |||
| 104 | Trigonometry-compass | Bearings – the compass. | |
| Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. | |||
| 105 | Circle Geometry | Theorem – Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem – Equal angles at the centre of a circle on equal arcs. | |
| Objective: On completion of the lesson the student will be able to prove that ‘Equal arcs on circles of equal radii, subtend equal angles at the centre’, and that ‘Equal angles at the centre of a circle stand on equal arcs.’ They should then be able to use these pro | |||
| 106 | Circle Geometry | Theorem – The perpendicular from the centre of a circle to a chord bisects the chord. Theorem – The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord. | |
| Objective: On completion of the lesson the student will be able to prove that ‘The perpendicular from the centre of a circle to a chord bisects the chord.’ and its converse theorem ‘The line from the centre of a circle to the mid-point of the chord is perpendicular’ | |||
| 107 | Circle Geometry | Theorem – Equal chords in equal circles are equidistant from the centres. Theorem – Chords in a circle which are equidistant from the centre are equal. | |
| Objective: On completion of the lesson the student will be able to prove that equal chords in equal circles are equidistant from the centre. | |||
| 108 | Circle Geometry | Theorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc. | |
| Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc. | |||
| 109 | Circle Geometry | Theorem – Angles in the same segment of a circle are equal. | |
| Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal. | |||
| 110 | Circle Geometry | Theorem – The angle of a semi-circle is a right angle. | |
| Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’ | |||
| 111 | Circle Geometry | Theorem – The opposite angles of a cyclic quadrilateral are supplementary. | |
| Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary. | |||
| 112 | Circle Geometry | Theorem – The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle. | |
| Objective: On completion of the lesson the student will be able to prove that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite. | |||
| 113 | Circle Geometry | Theorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact. | |
| Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact. | |||
| 114 | Circle Geometry | Theorem – Tangents to a circle from an external point are equal. | |
| Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal. | |||
| 115 | Circle Geometry | Theorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. | |
| Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. | |||
| 116 | Circle Geometry-chords | Theorem – The products of the intercepts of two intersecting chords are equal. | |
| Objective: On completion of the lesson the student will be able to prove that ‘The product of the intercepts of two intersecting chords are equal.’, and use this result to complete questions that require this knowledge. | |||
| 117 | Circle Geometry-tangents | Theorem – The square of the length of the tangent from an external point is equal to the product of the intercepts of the secant passing through this point. [Including Alternate Proof] | |
| Objective: On completion of the lesson the student will be able to prove and apply ‘The square of the length of the tangent from an external point is equal to the product of the intercepts of the secant passing through this point ‘, and use this result to complete q | |||
| 118 | Circle Geometry-cyclic quads | Theorem – If the opposite angles in a quadrilateral are supplementary then the quadrilateral is cyclic. | |
| Objective: On completion of the lesson the student will be able to prove that a quadrilateral is cyclic using the supplementary angles theorem. | |||
| 119 | Circle Geometry-subtending | Theorem – If an interval subtends equal angles at two points on the same side of it, then the end points of the interval and the two points are concyclic. | |
| Objective: On completion of the lesson the student will be able to prove that ‘ If an interval subtends equal angles at two points on the same side of it, then the end points of the interval and the two points are concyclic’, and use this result to complete the ques | |||
| 120 | Circle Geometry | Theorem – When circles touch, the line of the centres passes through the point of contact. | |
| Objective: On completion of the lesson the student will be able to prove that ‘ When two circles touch, the line of the centres passes through the point of contact’, and use this result to complete questions that require it. | |||
| 121 | Circle Geometry-non-collinear | Theorem – Any three non-collinear points lie on a unique circle whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining these points. | |
| Objective: On completion of the lesson the student will be able to prove that ‘ Any three non-collinear points lie on a unique circle whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining these points’, and use this knowled | |||
| 122 | Geometry-constructions | Geometric constructions | |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. | |||
| 123 | Geometry | To identify collinear points, coplanar lines and points in 2 and 3 dimensions | |
| Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays. | |||
| 124 | Geometry-constructions | Angle bisector construction and its properties (Stage 2) | |
| Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge. | |||
| 125 | Geometry-constructions | Circumcentre and incentre (Stage 2) | |
| Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values. | |||
| 126 | Geometry-constructions | Orthocentre and centroids (Stage 2) | |
| Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values. | |||
| 127 | Geometry-locus | Constructions and loci – single condition | |
| Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. | |||
| 128 | Geometry-locus | Constructions and loci – multiple conditions | |
| Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. | |||
| 129 | 2-D shapes | Spatial properties of quadrilaterals | |
| Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals. | |||
| 130 | Similar triangles | Similar triangles | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. | |||
| 131 | Similar triangles | Using similar triangles to calculate lengths | |
| Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles. | |||
| 132 | Special triangles | Special triangles | |
| Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles. | |||
| 133 | Tessellating 2-D shapes | Use grids to enlarge/reduce 2D shapes | |
| Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate. | |||
| 134 | Transformations | Special transformations – reflections, rotations and enlargements. | |
| Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable. | |||
| 135 | Translations | Transformations – reflections | |
| Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection. | |||
| 136 | Geometric transformations | Geometry transformations without matrices: reflection (Stage 2) | |
| Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane. | |||
| 137 | Geometric transformations | Geometry transformations without matrices: translation (Stage 2) | |
| Objective: On completion of this lesson the student will perform translations in a number plane. | |||
| 138 | Geometric transformations | Geometry transformations without matrices: rotation (Stage 2) | |
| Objective: On completion of this lesson the student will perform and construct rotations. | |||
| 139 | Geometric transformations | Geometry transformations without matrices: dilation or enlargement (Stage 2) | |
| Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor. | |||
| 140 | Geometric transformations | The definition and concept of combined transformations resulting in an equivalent single transformation. | |
| Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations. | |||
| 141 | 2-D shapes | Recognise and name triangles | |
| Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties. | |||
| 142 | Geometry-quadrilaterals | Midsegments of Triangles | |
| Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle. | |||
| 143 | Geometry-congruence | Congruent triangles, Test 1 and 2 | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent. | |||
| 144 | Geometry-congruence | Congruent triangles, Test 3 and 4 | |
| Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent. | |||
| 145 | Geometry-congruence | Proofs and congruent triangles. | |
| Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent. | |||
| 146 | Overlapping triangles | Examples involving overlapping triangles | |
| Objective: On completion of the lesson the student will be able to calculate unknown sides in overlapping or adjacent similar triangles. | |||
| 147 | Pythagoras | Find the hypotenuse | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. | |||
| 148 | Pythagoras | Pythagorean triples | |
| Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. | |||
| 149 | Pythagoras | Find the hypotenuse Part 2 | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds. | |||
| 150 | Pythagoras | Calculating a leg of a right-angled triangle | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle. | |||
| 151 | Graph sine | Graphing the trigonometric ratios – I Sine curve. | |
| Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period. | |||
| 152 | Graph cosine | Graphing the trigonometric ratios – II Cosine curve. | |
| Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period. | |||
| 153 | Graphs tan curve | Graphing the trigonometric ratios – III Tangent curve. | |
| Objective: On completion of the lesson the student will know how to recognise and draw the tan curve. | |||
| 154 | Graph reciprocals | Graphing the trigonometric ratios – IV Reciprocal ratios. | |
| Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot. | |||
| 155 | Trigonometry-ratios | Trigonometric ratios. | |
| Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op | |||
| 156 | Trigonometry-ratios | Using the calculator. | |
| Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles. | |||
| 157 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |
| Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances. | |||
| 158 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |
| Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle. | |||
| 159 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |
| Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle. | |||
| 160 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |
| Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown. | |||
| 161 | Trigonometry-elevation | Angles of elevation and depression. | |
| Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them. | |||
| 162 | Trigonometry-practical | Trigonometric ratios in practical situations. | |
| Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation. | |||
| 163 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |
| Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio. | |||
| 164 | Trigonometry- ratios | Using the trigonometric ratios to find an angle in a right-angled triangle. | |
| Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides. | |||
| 165 | Trigonometry-exact ratios | Trigonometric ratios of 30., 45. and 60. – exact ratios. | |
| Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60. | |||
| 166 | Trigonometry-cosine rule | The cosine rule to find an unknown side. [Case 1 SAS]. | |
| Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle. | |||
| 167 | Trigonometry-cosine rule | The cosine rule to find an unknown angle. [Case 2 SSS]. | |
| Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides. | |||
| 168 | Trigonometry-sine rule | The sine rule to find an unknown side. Case 1. | |
| Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides. | |||
| 169 | Trigonometry-sine rule | The sine rule to find an unknown angle. Case 2. | |
| Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle. | |||
| 170 | Trigonometry-areas | The area formula | |
| Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle. | |||
| 171 | Trig-reciprocal ratios | Reciprocal ratios. | |
| Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios. | |||
| 172 | Trig larger angles | Angles of any magnitude | |
| Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle. | |||
| 173 | Trig larger angles | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | |
| Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees. | |||
| 174 | Coordinate Geometry-the plane | Distance formula. | |
| Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results. | |||
| 175 | Coordinate Geometry-midpoint, slope | Mid-point formula | |
| Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically. | |||
| 176 | Coordinate Geometry-gradient | Gradient | |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run. | |||
| 177 | Coordinate Geometry-gradient | Gradient formula. | |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines. | |||
| 178 | Coordinate Geometry-straight line | The straight line. | |
| Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists. | |||
| 179 | Coordinate Geometry-slope, etc. | Lines through the origin. | |
| Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems. | |||
| 180 | Coordinate Geometry-equation of line | General form of a line and the x and y Intercepts. | |
| Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa. | |||
| 181 | Sequences and Series | General sequences. | |
| Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula. | |||
| 182 | Sequences and Series | Finding Tn given Sn. | |
| Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term. | |||
| 183 | Algebraic expressions | Algebraic expressions. | |
| Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand. | |||
| 184 | Algebraic expressions | Simplifying Algebraic expressions: combining addition and subtraction. | |
| Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes. | |||
| 185 | Algebraic expressions | Simplifying algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form. | |||
| 186 | Algebraic expressions | Simplifying algebraic expressions: division | |
| Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. | |||
| 187 | Algebraic expressions | Expanding algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step. | |||
| 188 | Algebraic expressions | Expanding algebraic expressions: negative multiplier | |
| Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier. | |||
| 189 | Algebraic expressions | Expanding and simplifying algebraic expressions | |
| Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. | |||
| 190 | Algebraic fractions | Simplifying algebraic fractions using the index laws. | |
| Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies. | |||
| 191 | Algebra-negative indices | Algebraic fractions resulting in negative indices. | |
| Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index. | |||
| 192 | Algebraic fractions-binomial | Cancelling binomial factors in algebraic fractions. | |
| Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions. | |||
| 193 | Algebraic expressions-products | Products in simplification of algebraic expressions | |
| Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing. | |||
| 194 | Algebraic expressions-larger expansions | Algebraic Expressions – Larger expansions. | |
| Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. | |||
| 195 | Algebraic fractions | Simplifying algebraic fractions. | |
| Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point. | |||
| 196 | Functions and graphs | Quadratic polynomials of the form y = ax. + bx + c. | |
| Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis. | |||
| 197 | Functions and graphs | Graphing perfect squares: y=(a-x) squared | |
| Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve. | |||
| 198 | Coordinate geometry | Solve by graphing | |
| Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection. | |||
| 199 | Graphing-cubic curves | Graphing cubic curves | |
| Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information. | |||
| 200 | Algebraic equations | Solving equations containing addition and subtraction | |
| Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side. | |||
| 201 | Algebraic equations | Solving equations containing multiplication and division | |
| Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. | |||
| 202 | Algebraic equations | Solving two step equations | |
| Objective: On completion of the lesson the student will be able to solve two step equations. | |||
| 203 | Algebraic equations | Solving equations containing binomial expressions | |
| Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||
| 204 | Algebraic equations | Equations involving grouping symbols. | |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||
| 205 | Algebraic equations | Equations involving fractions. | |
| Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||
| 206 | Simultaneous equns | Simultaneous equations | |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method. | |||
| 207 | Simultaneous equns | Elimination method | |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. | |||
| 208 | Simultaneous equns | Elimination method part 2 | |
| Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method. | |||
| 209 | Simultaneous equns | Applications of simultaneous equations | |
| Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations. | |||
| 210 | Factorising | Expansions leading to the difference of two squares | |
| Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares. | |||
| 211 | Common fact and diff | Common factor and the difference of two squares | |
| Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. | |||
| 212 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. | |
| Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||
| 213 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. | |
| Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||
| 214 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. | |
| Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||
| 215 | Factorising quads | Factorisation of non-monic quadratic trinomials | |
| Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial. | |||
| 216 | Factorising quads | Factorisation of non-monic quadratic trinomials – moon method | |
| Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method. | |||
| 217 | Algebraic expressions | Substitution into algebraic expressions. | |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. | |||
| 218 | Algebra- formulae | Equations resulting from substitution into formulae. | |
| Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. | |||
| 219 | Algebra- formulae | Changing the subject of the formula. | |
| Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously. | |||
| 220 | Algebra-factorising | Simplifying easy algebraic fractions. | |
| Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. | |||
| 221 | Factorisation | Factorisation of algebraic fractions including binomials. | |
| Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods. | |||
| 222 | Algebra-inequalities | Solving Inequalities. | |
| Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities. | |||
| 223 | Co-ordinate Geometry-Inequalities | Inequalities on the number plane. | |
| Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities. | |||
| 224 | Difference of 2 squares | Difference of two squares | |
| Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors. | |||
| 225 | Quadratic trinomials | Quadratic trinomials [monic] – Case 1. | |
| Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive. | |||
| 226 | Quadratic equations | Introduction to quadratic equations. | |
| Objective: On completion of the lesson the student will understand simple quadratic equations. | |||
| 227 | Quadratic equations | Quadratic equations with factorisation. | |
| Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising. | |||
| 228 | Quadratic equations | Solving quadratic equations. | |
| Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations. | |||
| 229 | Quadratic equations | The quadratic formula | |
| Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||
| 230 | Quadratic equations | Problem solving with quadratic equations | |
| Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it. | |||
| 231 | Quadratic equations | Solving simultaneous quadratic equations graphically | |
| Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically.. | |||
| 232 | Vectors | Vectors | |
| Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram. | |||
| 233 | Statistics | The range. | |
| Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. | |||
| 234 | Statistic-probability | The mode | |
| Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. | |||
| 235 | Statistic-probability | The mean | |
| Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||
| 236 | Statistic-probability | The median | |
| Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||
| 237 | Statistic-probability | Calculating the median from a frequency distribution | |
| Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. | |||
| 238 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |
| Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. | |||
| 239 | Statistics – Range and dispersion | Range as a measure of dispersion | |
| Objective: On completion of the lesson the student will be able to determine the range and using it in decision making. | |||
| 240 | Statistics – Spread | Measures of spread | |
| Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator. | |||
| 241 | Statistics – Interquartile range | Measures of spread: the interquartile range | |
| Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range | |||
| 242 | Data | Pie and bar graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs. | |||
| 243 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||
| 244 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |
| Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. | |||
| 245 | Statistic-probability | Cumulative frequency | |
| Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. | |||
| 246 | Statistics | Frequency histograms and polygons | |
| Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. | |||
| 247 | Data | Line graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||
| 248 | Statistics | Frequency distribution table | |
| Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. | |||
| 249 | Statistics | Relative frequency | |
| Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. | |||
| 250 | Statistic-probability | Probability of Simple Events | |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||
| 251 | Statistic-probability | Rolling a pair of dice | |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. | |||
| 252 | Statistic-probability | Experimental probability | |
| Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||
| 253 | Statistic-probability | Tree diagrams – not depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes. | |||
| 254 | Statistic-probability | Tree diagrams – depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes. | |||
KS5 – Maths – Core Mathematics
| # | TOPIC | TITLE | |
| 1 | Rules for indices/exponents | Adding indices when multiplying terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base. | |||
| 2 | Rules for indices/exponents | Subtracting indices when dividing terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base. | |||
| 3 | Rules for indices/exponents | Multiplying indices when raising a power to a power | |
| Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power. | |||
| 4 | Rules for indices/exponents | Multiplying indices when raising to more than one term | |
| Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power. | |||
| 5 | Rules for indices/exponents | Terms raised to the power of zero | |
| Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero. | |||
| 6 | Rules for indices/exponents | Negative Indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices. | |||
| 7 | Fractional indices/exponents | Fractional indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. | |||
| 8 | Fractional indices/exponents | Complex fractions as indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices. | |||
| 9 | Surds | Introducing surds | |
| Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers. | |||
| 10 | Surds | Some rules for the operations with surds | |
| Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds. | |||
| 11 | Surds | Simplifying surds | |
| Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication. | |||
| 12 | Surds | Creating entire surds | |
| Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds | |||
| 13 | Surds | Adding and subtracting like surds | |
| Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds. | |||
| 14 | Surds | Expanding surds | |
| Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds. | |||
| 15 | Surds | Conjugate binomials with surds | |
| Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds. | |||
| 16 | Surds | Rationalising the denominator | |
| Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds. | |||
| 17 | Surds | Rationalising binomial denominators | |
| Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions. | |||
| 18 | Graphing roots | Graphing irrational roots | |
| Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational. | |||
| 19 | Simultaneous equns | Simultaneous equations | |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method. | |||
| 20 | Simultaneous equns | Elimination method | |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. | |||
| 21 | Simultaneous equns | Elimination method part 2 | |
| Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method. | |||
| 22 | Simultaneous equns | Applications of simultaneous equations | |
| Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations. | |||
| 23 | Algebra-inequalities | Solving Inequalities. | |
| Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities. | |||
| 24 | Algebraic fractions | Simplifying algebraic fractions. | |
| Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point. | |||
| 25 | Algebraic fractions | Simplifying algebraic fractions using the index laws. | |
| Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies. | |||
| 26 | Algebra-negative indices | Algebraic fractions resulting in negative indices. | |
| Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index. | |||
| 27 | Algebraic fractions-binomial | Cancelling binomial factors in algebraic fractions. | |
| Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions. | |||
| 28 | Common fact and diff | Common factor and the difference of two squares | |
| Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. | |||
| 29 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. | |
| Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||
| 30 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. | |
| Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||
| 31 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. | |
| Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||
| 32 | Factorising quads | Factorisation of non-monic quadratic trinomials | |
| Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial. | |||
| 33 | Factorising quads | Factorisation of non-monic quadratic trinomials – moon method | |
| Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method. | |||
| 34 | Difference of 2 squares | Difference of two squares | |
| Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors. | |||
| 35 | Quadratic equations | Quadratic equations with factorisation. | |
| Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising. | |||
| 36 | Quadratic equations | Solving quadratic equations. | |
| Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations. | |||
| 37 | Quadratic equations | Completing the square | |
| Objective: On completion of the lesson the student will understand the process of completing the square. | |||
| 38 | Quadratic equations | Solving quadratic equations by completing the square | |
| Objective: On completion of the lesson the student will understand the reasoning behind completing the square. | |||
| 39 | Quadratic equations | The quadratic formula | |
| Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||
| 40 | Quadratic equations | Problem solving with quadratic equations | |
| Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it. | |||
| 41 | Quadratic equations | Solving simultaneous quadratic equations graphically | |
| Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically.. | |||
| 42 | Functions and graphs | Quadratic polynomials of the form y = ax. + bx + c. | |
| Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis. | |||
| 43 | Functions and graphs | Graphing perfect squares: y=(a-x) squared | |
| Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve. | |||
| 44 | Coordinate geometry | Solve by graphing | |
| Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection. | |||
| 45 | Graphing-polynomials | Graphing complex polynomials: quadratics with no real roots | |
| Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it. | |||
| 46 | Graphing-polynomials | General equation of a circle: determine and graph the equation | |
| Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student’s skills in logic and reasoning. | |||
| 47 | Graphing-cubic curves | Graphing cubic curves | |
| Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information. | |||
| 48 | Graphs, polynomials | Graphs of polynomials | |
| Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves. | |||
| 49 | Algebra-polynomials | Introduction to polynomials | |
| Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not. | |||
| 50 | Algebra-polynomials | The sum, difference and product of two polynomials. | |
| Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers. | |||
| 51 | Algebra-polynomials | Polynomials and long division. | |
| Objective: On completion of the lesson the student will understand the long division process with polynomials. | |||
| 52 | Polynomial equations | Polynomial equations | |
| Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms. | |||
| 53 | Factor theorem | The factor theorem | |
| Objective: On completion of the lesson the student will be able to use the factor theorem and determine if a term in the form of x minus a is a factor of a given polynomial. | |||
| 54 | Factor theorem | More on the factor theorem | |
| Objective: On completion of the lesson the student will fully understand the factor theorem and how it can be applied to solve some questions on finding unknown coefficients of polynomials. | |||
| 55 | Factor theorem | Complete factorisations using the factor theorem | |
| Objective: On completion of the lesson the student will be able to factorise polynomials of a higher degree than 2 and to find their zeros. | |||
| 56 | Factorising | Expansions leading to the difference of two squares | |
| Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares. | |||
| 57 | Remainder theorem | The remainder theorem. | |
| Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied. | |||
| 58 | Remainder theorem | More on remainder theorem | |
| Objective: On completion of the lesson the student will understand the remainder theorem and how it can be applied to solve some interesting questions on finding unknown coefficients of polynomials. | |||
| 59 | Absolute value equations | Absolute value equations | |
| Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio | |||
| 60 | Sum/diff 2 cubes | Sum and difference of two cubes. | |
| Objective: On completion of the lesson the student will be cognisant of the sum and difference of 2 cubes and be capable of factorising them. | |||
| 61 | Roots quad equations | Sum and product of roots of quadratic equations | |
| Objective: On completion of the lesson the student will understand the formulas for the sum and product of roots of quadratic polynomials and how to use them. The student will understand how to form a quadratic equation given its roots. | |||
| 62 | Roots quad equations | Sum and product of roots of cubic and quartic equations | |
| Objective: On completion of the lesson the student will be able to do problems on the sum and products of roots of cubic and quartic equations. | |||
| 63 | Approx roots | Methods of approximating roots | |
| Objective: On completion of the lesson the student will be capable of finding approximate roots of polynomial equations using half the interval method. The student will be able to make a number of applications of this rule within the one question. | |||
| 64 | Logic | Inductive and deductive reasoning | |
| Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive. | |||
| 65 | Logic | Definition and use of counter examples | |
| Objective: On completion of this lesson the student will be able to create counter examples to statements. | |||
| 66 | Logic | Indirect proofs | |
| Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved. | |||
| 67 | Logic | Mathematical induction | |
| Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series. | |||
| 68 | Logic | Conditional statements (converse, inverse and contrapositive) (Stage 2) | |
| Objective: On completion of the lesson the student will be able to form related conditional statements. | |||
| 69 | Tessellating 2-D shapes | Use grids to enlarge/reduce 2D shapes | |
| Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate. | |||
| 70 | Transformations | Special transformations – reflections, rotations and enlargements. | |
| Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable. | |||
| 71 | Translations | Transformations – reflections | |
| Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection. | |||
| 72 | Geometric transformations | The definition and concept of combined transformations resulting in an equivalent single transformation. | |
| Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations. | |||
| 73 | Coordinate Geometry-the plane | Distance formula. | |
| Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results. | |||
| 74 | Coordinate Geometry-midpoint, slope | Mid-point formula | |
| Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically. | |||
| 75 | Coordinate Geometry-gradient | Gradient | |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run. | |||
| 76 | Coordinate Geometry-gradient | Gradient formula. | |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines. | |||
| 77 | Coordinate Geometry-straight line | The straight line. | |
| Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists. | |||
| 78 | Coordinate Geometry-slope, etc. | Lines through the origin. | |
| Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems. | |||
| 79 | Coordinate Geometry-equation of line | General form of a line and the x and y Intercepts. | |
| Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa. | |||
| 80 | Coordinate Geometry-intercept | Slope intercept form of a line. | |
| Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation. | |||
| 81 | Coordinate Geometry-point slope | Point slope form of a line | |
| Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line. | |||
| 82 | Co-ordinate Geometry-Two point formula | Two point formula: equation of a line which joins a pair of points. | |
| Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line. | |||
| 83 | Co-ordinate Geometry-Intercept form | Intercept form of a straight line: find the equation when given x and y | |
| Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line. | |||
| 84 | Co-ordinate Geometry-Parallel lines equations | Parallel lines: identify equation of a line parallel to another | |
| Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines. | |||
| 85 | Co-ordinate Geometry-Perpendicular lines | Perpendicular lines. | |
| Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line. | |||
| 86 | Co-ordinate Geometry-Theorems | Perpendicular distance | |
| Objective: On completion of the lesson the student will be able to derive the formula to calculate the distance between a given point and a given line. The student will also be able to calculate the distance between parallel lines. | |||
| 87 | Co-ordinate Geometry-Theorems | Line through intersection of two given lines | |
| Objective: On completion of the lesson the student will be able to calculate the equation of a line which goes through the intersection of two given lines and also through another named point or satisfies some other specified condition. | |||
| 88 | Co-ordinate Geometry-Theorems | Angles between two lines | |
| Objective: On completion of the lesson the student will be able to calculate the angle between given lines and derive the equation of a line given its angle to another line. | |||
| 89 | Co-ordinate Geometry-Theorems | Internal and external division of an interval | |
| Objective: On completion of the lesson the student will be able to divide an interval according to a given ratio and to calculate what point divides an interval in a given ratio for both internal and external divisions. | |||
| 90 | Geometry – triangles | Triangle inequality theorem | |
| Objective: On completion of the lesson the student will understand and use the triangle inequality theorem. | |||
| 91 | Geometry-circles | The equation of a circle: to find radii of circles | |
| Objective: On completion of the lesson the student will be able to describe a circle mathematically given its equation or its graph. Additionally, the student will be able to work out the equation of a circle given its centre and radius. | |||
| 92 | Geometry-circles | The semicircle: to select the equation given the semi circle and vice versa | |
| Objective: On completion of the lesson the student will be able to sketch a semicircle given its equation and derive the equation of a given semicircle. | |||
| 93 | Surds | Binomial expansions | |
| Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds. | |||
| 94 | Graphing binomials | Binomial products. | |
| Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression. | |||
| 95 | Graphing binomials | Binomial products with negative multiplier | |
| Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products. | |||
| 96 | Graphing binomials | Binomial products [non-monic]. | |
| Objective: On completion of the lesson, the student will have examined more complex examples with binomial products. | |||
| 97 | Squaring binomial | Squaring a binomial. [monic] | |
| Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial. | |||
| 98 | Squaring binomial | Squaring a binomial [non-monic]. | |
| Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials. | |||
| 99 | Statistic-probability | Binomial Theorem – Pascal’s Triangle | |
| Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers. | |||
| 100 | Calculus=1st prin | Differentiation from first principles. | |
| Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve. | |||
| 101 | Calculus=1st prin | Differentiation of y = x to the power of n. | |
| Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n. | |||
| 102 | Calculus-differential, integ | Meaning of dy over dx – equations of tangents and normals. | |
| Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve. | |||
| 103 | Calculus-differential, integ | Function of a function rule, product rule, quotient rule. | |
| Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule. | |||
| 104 | Calculus-differential, integ | Increasing, decreasing and stationary functions. | |
| Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions. | |||
| 105 | Calculus | First Derivative – turning points and curve sketching | |
| Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve. | |||
| 106 | Calculus-2nd derivative | The second derivative – concavity. | |
| Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion. | |||
| 107 | Calculus – Curve sketching | Curve sketching | |
| Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve. | |||
| 108 | Calculus – Maxima minima | Practical applications of maxima and minima | |
| Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems. | |||
| 109 | Calculus | Limits | |
| Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule. | |||
| 110 | Calculus – Integration | Integration – anti-differentiation, primitive function | |
| Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions. | |||
| 111 | Calculus – Computation area | Computation of an area | |
| Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area. | |||
| 112 | Calculus – Computation volumes | Computation of volumes of revolution | |
| Objective: On completion of the Calculus lesson the student will know how to choose an appropriate volume formula, re-arrange an expression to suit the formula, and then calculate a result to a prescribed accuracy. | |||
| 113 | Calculus – Trapezoidal and Simpson’s rules | The Trapezium rule and Simpson’s rule | |
| Objective: On completion of the Calculus lesson the student will know how to calculate sub-intervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson’s Rule to approximate an area beneath a curve. | |||
| 114 | Arithmetic Progression | The arithmetic progression | |
| Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts. | |||
| 115 | Arithmetic Progression | Finding the position of a term in an A.P. | |
| Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression. | |||
| 116 | Arithmetic Progression | Given two terms of A.P., find the sequence. | |
| Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms | |||
| 117 | Arithmetic Progression | Arithmetic means | |
| Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means. | |||
| 118 | Arithmetic Progression | The sum to n terms of an A.P. | |
| Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems. | |||
| 119 | Geometric Progression | The geometric progression. | |
| Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts. | |||
| 120 | Geometric Progression | Finding the position of a term in a G.P. | |
| Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems. | |||
| 121 | Geometric Progression | Given two terms of G.P., find the sequence. | |
| Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression. | |||
| 122 | Sequences and Series-Geometric means | Geometric means. | |
| Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means. | |||
| 123 | Sequences and Series-Sum of gp | The sum to n terms of a G.P. | |
| Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P). | |||
| 124 | Sequences and Series-Sigma notation | Sigma notation | |
| Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates. | |||
| 125 | Sequences and Series-Sum-infinity | Limiting sum or sum to infinity. | |
| Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems. | |||
| 126 | Sequences and Series-Recurring decimal infinity | Recurring decimals and the infinite G.P. | |
| Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number. | |||
| 127 | Sequences and Series-Superannuation | Superannuation. | |
| Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P. | |||
| 128 | Sequences and Series-Time payments | Time payments. | |
| Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan. | |||
| 129 | Sequences and Series | Applications of arithmetic sequences | |
| Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series. | |||
| 130 | Graph sine | Graphing the trigonometric ratios – I Sine curve. | |
| Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period. | |||
| 131 | Graph cosine | Graphing the trigonometric ratios – II Cosine curve. | |
| Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period. | |||
| 132 | Graphs tan curve | Graphing the trigonometric ratios – III Tangent curve. | |
| Objective: On completion of the lesson the student will know how to recognise and draw the tan curve. | |||
| 133 | Graph reciprocals | Graphing the trigonometric ratios – IV Reciprocal ratios. | |
| Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot. | |||
| 134 | Trigonometry-ratios | Trigonometric ratios. | |
| Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op | |||
| 135 | Trigonometry-ratios | Using the calculator. | |
| Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles. | |||
| 136 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |
| Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances. | |||
| 137 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |
| Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle. | |||
| 138 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |
| Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle. | |||
| 139 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |
| Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown. | |||
| 140 | Trigonometry-elevation | Angles of elevation and depression. | |
| Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them. | |||
| 141 | Trigonometry-practical | Trigonometric ratios in practical situations. | |
| Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation. | |||
| 142 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |
| Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio. | |||
| 143 | Trigonometry- ratios | Using the trigonometric ratios to find an angle in a right-angled triangle. | |
| Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides. | |||
| 144 | Trigonometry-exact ratios | Trigonometric ratios of 30., 45. and 60. – exact ratios. | |
| Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60. | |||
| 145 | Trigonometry-cosine rule | The cosine rule to find an unknown side. [Case 1 SAS]. | |
| Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle. | |||
| 146 | Trigonometry-cosine rule | The cosine rule to find an unknown angle. [Case 2 SSS]. | |
| Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides. | |||
| 147 | Trigonometry-sine rule | The sine rule to find an unknown side. Case 1. | |
| Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides. | |||
| 148 | Trigonometry-sine rule | The sine rule to find an unknown angle. Case 2. | |
| Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle. | |||
| 149 | Trigonometry-areas | The area formula | |
| Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle. | |||
| 150 | Trig-reciprocal ratios | Reciprocal ratios. | |
| Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios. | |||
| 151 | Trig identities | Trigonometric identities | |
| Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities. | |||
| 152 | Trig larger angles | Angles of any magnitude | |
| Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle. | |||
| 153 | Trig larger angles | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | |
| Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees. | |||
| 154 | Trig larger angles | Using one ratio to find another. | |
| Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude. | |||
| 155 | Trig equations | Solving trigonometric equations – Type I. | |
| Objective: On completion of the lesson the student will solve simple trig equations with restricted domains. | |||
| 156 | Trig equations | Solving trigonometric equations – Type II. | |
| Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains. | |||
| 157 | Trig equations | Solving trigonometric equations – Type III. | |
| Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains. | |||
| 158 | Polar coordinates | Plotting polar coordinates and converting polar to rectangular | |
| Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system. | |||
| 159 | Polar coordinates | Converting rectangular coordinates to polar form | |
| Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates. | |||
| 160 | Polar coordinates | Write and graph points in polar form with negative vectors (Stage 2) | |
| Objective: On completion of the lesson the student will be using negative angles and negative vector lengths. | |||
| 161 | Trigonometry | Sin(A+B) etc sum and difference identities (Stage 2) | |
| Objective: On completion of the lesson the student will be using the reference triangles for 30, 45 and 60 degrees with the sum and difference of angles to find additional exact values of trigonometric ratios. | |||
| 162 | Trigonometry | Double angle formulas (Stage 2) | |
| Objective: On completion of the lesson the student will derive and use the double angle trig identities. | |||
| 163 | Trigonometry | Half angle identities (Stage 2) | |
| Objective: On completion of the lesson the student will derive and use the power reducing formulas and the half angle trig identities. | |||
| 164 | Trigonometry | t Formulas (Stage 2) | |
| Objective: On completion of the lesson the student will solve trig equations using the t substitution. | |||
| 165 | Exponential function | The exponential function. | |
| Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1. | |||
| 166 | Log functions | Logarithmic functions. | |
| Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit | |||
| 167 | Logarithms-Power of 2 | Powers of 2. | |
| Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2. | |||
| 168 | Logarithms-Equations and logs | Equations of type log x to the base 3 = 4. | |
| Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves. | |||
| 169 | Logarithms-Equations and logs | Equations of type log 32 to the base x = 5. | |
| Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came. | |||
| 170 | Logarithms-Log laws | Laws of logarithms. | |
| Objective: On completion of the lesson the student will be familiar with 5 logarithm laws. | |||
| 171 | Logarithms-Log laws expansion | Using the log laws to expand logarithmic expressions. | |
| Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions. | |||
| 172 | Logarithms-Log laws simplifying | Using the log laws to simplify expressions involving logarithms. | |
| Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws. | |||
| 173 | Logarithms-Log laws numbers | Using the log laws to find the logarithms of numbers. | |
| Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples. | |||
| 174 | Logarithms-Equations and logs | Equations involving logarithms. | |
| Objective: On completion of the lesson the student will be able to solve equations with log terms. | |||
| 175 | Logarithms-Logs to solve equations | Using logarithms to solve equations. | |
| Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator. | |||
| 176 | Logarithms-Change base formula | Change of base formula | |
| Objective: On completion of the lesson the student will have seen the change of base formula for logarithms and be capable of using it to change the logarithm of one base to another base. | |||
| 177 | Logarithms-Graph-log curve | The graph of the logarithmic curve | |
| Objective: On completion of the lesson the student will be able to draw a logarithmic curve to a given base and know the general properties of log curves. | |||
| 178 | Logarithms-Log curves | Working with log curves. | |
| Objective: On completion of the lesson the student will be able to solve problems with log curves | |||
| 179 | Functions | Definition, domain and range | |
| Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range. | |||
| 180 | Functions | Notation and evaluations | |
| Objective: On completion of the lesson the student will be understand different notations for functions. | |||
| 181 | Functions | More on domain and range | |
| Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation. | |||
| 182 | Functions | Domain and range from graphical representations | |
| Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations. | |||
| 183 | Functions | Evaluating and graphing piecewise functions | |
| Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions. | |||
| 184 | Functions | Functions combinations | |
| Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains. | |||
| 185 | Functions | Composition of functions | |
| Objective: On completion of the lesson the student will understand composition of functions or a function of a function. | |||
| 186 | Functions | Inverse functions | |
| Objective: On completion of the lesson the student will be able to find inverse functions, use the notation correctly and the horizontal line test will be used. | |||
| 187 | Functions | Rational functions Part 1 | |
| Objective: On completion of the lesson the student will be able to work with the division of functions and to interpret this on the coordinate number plane showing vertical and horizontal asymptotes. | |||
| 188 | Functions | Rational functions Part 2 | |
| Objective: On completion of the lesson the student will be able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes. | |||
| 189 | Functions | Parametric equations (Stage 2) | |
| Objective: On completion of the lesson the student will be able to eliminate the parameter from a set of equations and identify appropriate restrictions on the domain and range. | |||
| 190 | Functions | Polynomial addition etc in combining and simplifying functions (Stage 2) | |
| Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra. | |||
| 191 | Functions | Parametric functions (Stage 2) | |
| Objective: On completion of the lesson the student will understand some standard parametric forms using trigonometric identities, appreciate the beauty of the the graphs that can be generated and an application to projectile motion. | |||
| 192 | Vectors | Vectors | |
| Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram. | |||
| 193 | Uniform motion | Average speed | |
| Objective: On completion of the lesson the student will be able to convert units for speed, distance and time. | |||
| 194 | Uniform motion | Using subscripted variables | |
| Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, distance and time. | |||
| 195 | Uniform motion | Uniform motion with equal distances | |
| Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, equal distances and time. | |||
| 196 | Uniform motion | Uniform motion adding the distances | |
| Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, adding distances for total distance and time. | |||
| 197 | Uniform motion | Uniform motion with unequal distances | |
| Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, unequal distances and time. | |||
| 198 | Uniform motion | Uniform motion of all types | |
| Objective: On completion of the lesson the student will use all types of subscripted variables for calculations to determine speed, distance and time. | |||
| 199 | Motion under acceleration | Motion under gravity – objects in vertical motion | |
| Objective: On completion of the lesson the student will convert rates and use equations of motion that include uniform acceleration. | |||
| 200 | Motion under acceleration | Introducing initial velocity | |
| Objective: On completion of the lesson the student will use equations of motion that include uniform acceleration and an initial velocity. | |||
| 201 | Newton’s approx | Newton’s method of approximation | |
| Objective: On completion of the lesson the student will be able to use Newton’s method in finding approximate roots of polynomial equations and be capable of more than one application of this method. | |||
| 202 | Logarithms-Complex numbers | Imaginary numbers and standard form | |
| Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction. | |||
| 203 | Logarithms-Complex numbers | Complex numbers – multiplication and division | |
| Objective: On completion of the lesson the student will use the a+bi form of complex numbers for multiplication and division. | |||
| 204 | Logarithms-Complex numbers | Plotting complex number and graphical representation | |
| Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers. | |||
| 205 | Logarithms-Complex numbers | Absolute value | |
| Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers | |||
| 206 | Logarithms-Complex numbers | Trigonometric form of a complex number | |
| Objective: On completion of the lesson the student will write complex numbers in trigonometric or polar form. This may also be known as mod-ard form. | |||
| 207 | Logarithms-Complex numbers | Multiplication and division of complex numbers in trig form (Stage 2) | |
| Objective: On completion of the lesson the student will use the trig form of complex numbers for multiplication and division. | |||
| 208 | Logarithms-Complex numbers | DeMoivre’s theorem (Stage 2) | |
| Objective: On completion of the lesson the student will use DeMoivre’s theorem to find powers of complex numbers in trig form. | |||
| 209 | Logarithms-Complex numbers | The nth root of real and complex numbers (Stage 2) | |
| Objective: On completion of the lesson the student will use DeMoivre’s theorem to find roots of complex numbers in trig form. | |||
| 210 | Logarithms-Complex numbers | Fundamental theorem of algebra (Stage 2) | |
| Objective: On completion of the lesson the student will recognise and use the fundamental theorem of algebra to find factors for polynomials with real coefficients over the complex number field. | |||
| 211 | Matrices | Basic concepts – Matrices | |
| Objective: On completion of the lesson the student will have had an introduction to matrices | |||
| 212 | Matrices | Addition and subtraction of matrices | |
| Objective: On completion of this lesson the student will be able to recognise when addition and subtraction of matrices is possible, and perform these operations. | |||
| 213 | Matrices | Scalar matrix multiplication | |
| Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix. | |||
| 214 | Matrices | Multiplication of one matrix by another matrix | |
| Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication. | |||
| 215 | Matrices | Translation in the number plane | |
| Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix. | |||
| 216 | Matrices | Translation by matrix multiplication | |
| Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane. | |||
| 217 | Simultaneous equations | Number of solutions (Stage 2) | |
| Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same. | |||
| 218 | Vectors | 2 vector addition in 2 and 3D (stage 2) | |
| Objective: On completion of the lesson the student will understand and use component forms for vector resolution. | |||
| 219 | Linear systems | Optimal solutions (Stage 2) – Vectors | |
| Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions. | |||
| 220 | Linear systems | Linear systems with matrices (Stage 2) | |
| Objective: On completion of the lesson the student will process matrices formed from linear systems of equations. | |||
| 221 | Linear systems | Row-echelon form (Stage 2) | |
| Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form. | |||
| 222 | Linear systems | Gauss Jordan elimination method (Stage 2) | |
| Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method. | |||
| 223 | Geometry-parabola | The parabola: to describe properties of a parabola from its equation | |
| Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions. | |||
| 224 | Rect.hyperbola | The rectangular hyperbola. | |
| Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features. | |||
| 225 | Conic sections | Introduction to conic sections and their general equation | |
| Objective: On completion of the lesson the student will identify the conic section from the coefficients of the equation. | |||
| 226 | Conic sections | The parabola x. = 4ay | |
| Objective: On completion of the lesson the student will identify the focus and directrix for a parabola given in standard form. | |||
| 227 | Conic sections | Circles | |
| Objective: On completion of the lesson the student will identify the radius of a circle given in standard form. | |||
| 228 | Conic sections | Ellipses | |
| Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse. | |||
| 229 | Conic sections | Hyperbola | |
| Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola. | |||
KS5 – Maths – Statistics Mathematics
| # | TOPIC | TITLE | |
| 1 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||
| 2 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |
| Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. | |||
| 3 | Statistic-probability | Cumulative frequency | |
| Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. | |||
| 4 | Statistics | Frequency histograms and polygons | |
| Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. | |||
| 5 | Statistics | The range. | |
| Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. | |||
| 6 | Statistic-probability | The mode | |
| Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. | |||
| 7 | Statistic-probability | The mean | |
| Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||
| 8 | Statistic-probability | The median | |
| Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||
| 9 | Statistic-probability | Calculating the median from a frequency distribution | |
| Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. | |||
| 10 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |
| Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. | |||
| 11 | Statistics – Range and dispersion | Range as a measure of dispersion | |
| Objective: On completion of the lesson the student will be able to determine the range and using it in decision making. | |||
| 12 | Statistics – Spread | Measures of spread | |
| Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator. | |||
| 13 | Statistics – Standard deviation | Standard deviation applications | |
| Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean. | |||
| 14 | Statistics – Interquartile range | Measures of spread: the interquartile range | |
| Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range | |||
| 15 | Statistics – Standard deviation | Normal distribution | |
| Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges. | |||
| 16 | Statistics | Frequency distribution table | |
| Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. | |||
| 17 | Statistics | Relative frequency | |
| Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. | |||
| 18 | Statistic-probability | Probability of Simple Events | |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||
| 19 | Statistic-probability | Rolling a pair of dice | |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. | |||
| 20 | Statistic-probability | Experimental probability | |
| Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||
| 21 | Statistic-probability | Tree diagrams – not depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes. | |||
| 22 | Statistic-probability | Tree diagrams – depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes. | |||
| 23 | Statistic-probability | The complementary result .. | |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved. | |||
| 24 | Statistic-probability | P[A or B] When A and B are both mutually and NOT mutually exclusive | |
| Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both. | |||
| 25 | Statistic-probability | Binomial probabilities using the Binomial Theorem | |
| Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theorem | |||
| 26 | Statistic-probability | Counting techniques and ordered selections – permutations | |
| Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability. | |||
| 27 | Statistic-probability | Unordered selections – combinations | |
| Objective: On completion of the lesson the student will be able to use the formula, n c r both with and without a calculator and be able to use it to solve probability problems where unordered selections happen. | |||
EdExcel-GCSE Revision Foundation Mathematics
| # | TOPIC | TITLE | |
| 1 | Rules properties | Using Order of Operation procedures (BIDMAS) with Fractions | |
| Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions. | |||
| 2 | Algebraic expressions | Directed numbers: addition and subtraction. | |
| Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals. | |||
| 3 | Algebraic expressions | Directed numbers: multiplication and division. | |
| Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer. | |||
| 4 | Decimals | Using decimals – shopping problems | |
| Objective: On completion of the lesson the student will be able to: read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money. | |||
| 5 | Decimals | Rounding decimals | |
| Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number. | |||
| 6 | Decimals | Adding decimals with a different number of decimal places | |
| Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places. | |||
| 7 | Decimals | Subtracting decimals with a different number of places | |
| Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places. | |||
| 8 | Decimals | Multiplying decimals by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers. | |||
| 9 | Decimals | Multiplication of decimals by decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to multiply decimals to two digits. | |||
| 10 | Decimals | Dividing decimal fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. | |||
| 11 | Decimals | Dividing numbers by a decimal fraction | |
| Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction. | |||
| 12 | Fractions | Comparing and ordering fractions | |
| Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts. | |||
| 13 | Fractions | mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one. | |||
| 14 | Fractions | Improper fractions | |
| Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally. | |||
| 15 | Fractions | Finding equivalent fractions | |
| Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines. | |||
| 16 | Fractions | Reducing fractions to lowest equivalent form | |
| Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor. | |||
| 17 | Fractions | Adding and subtracting fractions with different denominators | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other. | |||
| 18 | Fractions | Multiplying fractions | |
| Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form. | |||
| 19 | Fractions | Dividing fractions | |
| Objective: On completion of the lesson the student will be able to divide fractions. | |||
| 20 | Multiplication | Multiples and factors of whole numbers | |
| Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers. | |||
| 21 | Rules for indices/exponents | Adding indices when multiplying terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base. | |||
| 22 | Rules for indices/exponents | Subtracting indices when dividing terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base. | |||
| 23 | Percentages | Calculating Percentages and Fractions of Quantities | |
| Objective: To find percentages and fractions of quantities and solve problems with percentages | |||
| 24 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion. | |||
| 25 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||
| 26 | Time, 24-hour | 24 hour time | |
| Objective: On completion of the lesson the student will be able to: tell the time accurately using twenty-four hour time, change the time from am and pm time to twenty-four hour time, and change the time from twenty-four hour time to am and pm time. | |||
| 27 | Time zones | Time zones | |
| Objective: On completion of the lesson the student will be able to: recognise that there are different time zones, compare time zones, understand daylight saving and adjust times accordingly, and determine the local time in different regions. | |||
| 28 | Area | Finding the area of a triangle and other composite shapes. | |
| Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas. | |||
| 29 | Area | Area of a trapezium. | |
| Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula. | |||
| 30 | Area | Area of a circle. | |
| Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle. | |||
| 31 | Volume | Finding the volume of prisms | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume. | |||
| 32 | Surface area | Surface area of a cube/rectangular prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula. | |||
| 33 | 2-D shapes | Using the prefix to determine polygons | |
| Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides. | |||
| 34 | 3-D shapes | Recognise and name prisms according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties. | |||
| 35 | 3-D shapes | Recognise and name pyramids according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties. | |||
| 36 | 3-D shapes | Recognise nets for prisms, pyramids, cubes and cones | |
| Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones. | |||
| 37 | Geometry-angles | Measuring angles | |
| Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is. | |||
| 38 | Geometry-angles | Adjacent angles | |
| Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems. | |||
| 39 | Geometry-angles | Complementary and supplementary angles | |
| Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems. | |||
| 40 | Geometry-angles | Vertically opposite angles | |
| Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems. | |||
| 41 | Geometry-angles | Angles at a Point. | |
| Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems. | |||
| 42 | Geometry-angles | Parallel Lines. | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. | |||
| 43 | Geometry-triangles | Angle sum of a triangle | |
| Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. | |||
| 44 | Trigonometry-compass | Bearings – the compass. | |
| Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. | |||
| 45 | Geometry-constructions | Geometric constructions | |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. | |||
| 46 | Geometry-locus | Constructions and loci – single condition | |
| Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. | |||
| 47 | 2-D shapes | Recognise and name triangles | |
| Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties. | |||
| 48 | Similar triangles | Similar triangles | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. | |||
| 49 | 2-D shapes | Spatial properties of quadrilaterals | |
| Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals. | |||
| 50 | Tessellating 2-D shapes | Use grids to enlarge/reduce 2D shapes | |
| Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate. | |||
| 51 | Transformations | Special transformations – reflections, rotations and enlargements. | |
| Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable. | |||
| 52 | Translations | Transformations – reflections | |
| Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection. | |||
| 53 | Pythagoras | Find the hypotenuse | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. | |||
| 54 | Sequences and Series | General sequences. | |
| Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula. | |||
| 55 | Sequences and Series | Finding Tn given Sn. | |
| Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term. | |||
| 56 | Algebraic expressions | Algebraic expressions. | |
| Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand. | |||
| 57 | Algebraic expressions | Simplifying algebraic expressions: adding like terms. | |
| Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms. | |||
| 58 | Algebraic expressions | Simplifying algebraic Expressions: subtracting like terms. | |
| Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction. | |||
| 59 | Algebraic expressions | Simplifying Algebraic expressions: combining addition and subtraction. | |
| Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes. | |||
| 60 | Algebraic expressions | Simplifying algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form. | |||
| 61 | Algebraic expressions | Simplifying algebraic expressions: division | |
| Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. | |||
| 62 | Algebraic expressions | Expanding algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step. | |||
| 63 | Algebraic expressions | Expanding and simplifying algebraic expressions | |
| Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. | |||
| 64 | Algebraic equations | Solving equations containing addition and subtraction | |
| Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side. | |||
| 65 | Algebraic equations | Solving equations containing multiplication and division | |
| Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. | |||
| 66 | Algebraic equations | Solving two step equations | |
| Objective: On completion of the lesson the student will be able to solve two step equations. | |||
| 67 | Common fact and diff | Common factor and the difference of two squares | |
| Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. | |||
| 68 | Algebraic expressions | Substitution into algebraic expressions. | |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. | |||
| 69 | Algebra-inequalities | Solving Inequalities. | |
| Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities. | |||
| 70 | Statistics | The range. | |
| Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. | |||
| 71 | Statistic-probability | The mode | |
| Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. | |||
| 72 | Statistic-probability | The mean | |
| Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||
| 73 | Statistic-probability | The median | |
| Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||
| 74 | Statistic-probability | Calculating the median from a frequency distribution | |
| Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. | |||
| 75 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |
| Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. | |||
| 76 | Data | Bar Charts | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||
| 77 | Data | Line graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||
| 78 | Data | Pictograms | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs. | |||
| 79 | Data | Pie and bar graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs. | |||
| 80 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||
| 81 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |
| Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. | |||
| 82 | Statistics | Frequency distribution table | |
| Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. | |||
| 83 | Statistic-probability | Probability of Simple Events | |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||
EdExcel-GCSE Revision Higher Mathematics
| # | TOPIC | TITLE | |
| 1 | Algebra-highest common factor | Highest common factor. | |
| Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression. | |||
| 2 | Fractions | Multiplying mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form. | |||
| 3 | Fractions | Dividing mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals). | |||
| 4 | Rules for indices/exponents | Multiplying indices when raising a power to a power | |
| Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power. | |||
| 5 | Rules for indices/exponents | Multiplying indices when raising to more than one term | |
| Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power. | |||
| 6 | Rules for indices/exponents | Negative Indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices. | |||
| 7 | Fractional indices/exponents | Fractional indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. | |||
| 8 | Fractional indices/exponents | Complex fractions as indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices. | |||
| 9 | Percentages | Calculating Percentages and Fractions of Quantities | |
| Objective: To find percentages and fractions of quantities and solve problems with percentages | |||
| 10 | Percentages | Introduction to percentages, including relating common fractions to percentages | |
| Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage. | |||
| 11 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion. | |||
| 12 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||
| 13 | Percentages | One quantity as a percentage of another | |
| Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another. | |||
| 14 | Sequences and Series-Compound interest | Compound interest | |
| Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods. | |||
| 15 | Significant figures | Significant figures | |
| Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures. | |||
| 16 | Time, distance, speed | Average speed | |
| Objective: On completion of the lesson the student will be able to understand what is meant by the speed of an object, read the instantaneous speed of a vehicle on a speedometer and find the average speed of an object. | |||
| 17 | Scientific notation | Scientific notation with larger numbers | |
| Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation. | |||
| 18 | Scientific notation | Scientific notation with small numbers | |
| Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation. | |||
| 19 | Scientific notation | Changing scientific notation to numerals | |
| Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation. | |||
| 20 | Surds | Introducing surds | |
| Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers. | |||
| 21 | Surds | Some rules for the operations with surds | |
| Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds. | |||
| 22 | Surds | Simplifying surds | |
| Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication. | |||
| 23 | Surds | Expanding surds | |
| Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds. | |||
| 24 | Area | Area of a trapezium. | |
| Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula. | |||
| 25 | Area | Area of a circle. | |
| Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle. | |||
| 26 | Area | Area of regular polygons and composite figures. | |
| Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula. | |||
| 27 | Surface area | Surface area of a cube/rectangular prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula. | |||
| 28 | Surface area | Surface area of a triangular/trapezoidal prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula. | |||
| 29 | Surface area | Surface area of a cylinder and sphere. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula. | |||
| 30 | Surface area | Surface area of pyramids | |
| Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. | |||
| 31 | Surface area | Surface area of cones | |
| Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul | |||
| 32 | Volume | Finding the volume of prisms | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume. | |||
| 33 | Volume | Volume of a cylinder and sphere. | |
| Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume. | |||
| 34 | Volume | Volume of pyramids and cones. | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones. | |||
| 35 | Volume | Composite solids. | |
| Objective: On completion of the lesson the student will be able to: dissect composite solids into simpler shapes so that the volume can be calculated, calculate the volume of a variety of composite solids, and use formulae appropriately. | |||
| 36 | Geometry-triangles | Exterior angle theorem | |
| Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions. | |||
| 37 | Geometry problems | More difficult exercises involving parallel lines | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log | |||
| 38 | Geometry-polygons | Angles of regular polygons | |
| Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees. | |||
| 39 | Trig complementary angles | Complementary angle results. | |
| Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations. | |||
| 40 | Trigonometry-compass | Bearings – the compass. | |
| Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. | |||
| 41 | Circle Geometry | Theorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc. | |
| Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc. | |||
| 42 | Circle Geometry | Theorem – Angles in the same segment of a circle are equal. | |
| Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal. | |||
| 43 | Circle Geometry | Theorem – The angle of a semi-circle is a right angle. | |
| Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’ | |||
| 44 | Circle Geometry | Theorem – The opposite angles of a cyclic quadrilateral are supplementary. | |
| Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary. | |||
| 45 | Circle Geometry | Theorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact. | |
| Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact. | |||
| 46 | Circle Geometry | Theorem – Tangents to a circle from an external point are equal. | |
| Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal. | |||
| 47 | Circle Geometry | Theorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. | |
| Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. | |||
| 48 | Geometry-constructions | Geometric constructions | |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. | |||
| 49 | Geometry-locus | Constructions and loci – multiple conditions | |
| Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. | |||
| 50 | Similar triangles | Similar triangles | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. | |||
| 51 | Similar triangles | Using similar triangles to calculate lengths | |
| Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles. | |||
| 52 | Geometric transformations | Geometry transformations without matrices: reflection (Stage 2) | |
| Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane. | |||
| 53 | Geometric transformations | Geometry transformations without matrices: translation (Stage 2) | |
| Objective: On completion of this lesson the student will perform translations in a number plane. | |||
| 54 | Geometric transformations | Geometry transformations without matrices: rotation (Stage 2) | |
| Objective: On completion of this lesson the student will perform and construct rotations. | |||
| 55 | Geometric transformations | Geometry transformations without matrices: dilation or enlargement (Stage 2) | |
| Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor. | |||
| 56 | Geometry-congruence | Congruent triangles, Test 1 and 2 | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent. | |||
| 57 | Geometry-congruence | Congruent triangles, Test 3 and 4 | |
| Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent. | |||
| 58 | Pythagoras | Find the hypotenuse | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. | |||
| 59 | Pythagoras | Find the hypotenuse Part 2 | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds. | |||
| 60 | Pythagoras | Calculating a leg of a right-angled triangle | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle. | |||
| 61 | Graph sine | Graphing the trigonometric ratios – I Sine curve. | |
| Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period. | |||
| 62 | Graph cosine | Graphing the trigonometric ratios – II Cosine curve. | |
| Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period. | |||
| 63 | Graphs tan curve | Graphing the trigonometric ratios – III Tangent curve. | |
| Objective: On completion of the lesson the student will know how to recognise and draw the tan curve. | |||
| 64 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |
| Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances. | |||
| 65 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |
| Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle. | |||
| 66 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |
| Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle. | |||
| 67 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |
| Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown. | |||
| 68 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |
| Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio. | |||
| 69 | Trigonometry-cosine rule | The cosine rule to find an unknown side. [Case 1 SAS]. | |
| Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle. | |||
| 70 | Trigonometry-cosine rule | The cosine rule to find an unknown angle. [Case 2 SSS]. | |
| Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides. | |||
| 71 | Trigonometry-sine rule | The sine rule to find an unknown side. Case 1. | |
| Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides. | |||
| 72 | Trigonometry-sine rule | The sine rule to find an unknown angle. Case 2. | |
| Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle. | |||
| 73 | Trigonometry-areas | The area formula | |
| Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle. | |||
| 74 | Sequences and Series | General sequences. | |
| Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula. | |||
| 75 | Sequences and Series | Finding Tn given Sn. | |
| Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term. | |||
| 76 | Algebraic expressions-products | Products in simplification of algebraic expressions | |
| Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing. | |||
| 77 | Algebraic expressions-larger expansions | Algebraic Expressions – Larger expansions. | |
| Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. | |||
| 78 | Algebraic fractions | Simplifying algebraic fractions. | |
| Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point. | |||
| 79 | Functions and graphs | Quadratic polynomials of the form y = ax. + bx + c. | |
| Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis. | |||
| 80 | Algebraic equations | Equations involving grouping symbols. | |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||
| 81 | Algebraic equations | Equations involving fractions. | |
| Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||
| 82 | Simultaneous equns | Elimination method | |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. | |||
| 83 | Simultaneous equns | Elimination method part 2 | |
| Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method. | |||
| 84 | Common fact and diff | Common factor and the difference of two squares | |
| Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. | |||
| 85 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. | |
| Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||
| 86 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. | |
| Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||
| 87 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. | |
| Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||
| 88 | Factorising quads | Factorisation of non-monic quadratic trinomials – moon method | |
| Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method. | |||
| 89 | Algebraic expressions | Substitution into algebraic expressions. | |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. | |||
| 90 | Algebra- formulae | Equations resulting from substitution into formulae. | |
| Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. | |||
| 91 | Algebra- formulae | Changing the subject of the formula. | |
| Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously. | |||
| 92 | Algebra-inequalities | Solving Inequalities. | |
| Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities. | |||
| 93 | Absolute value or modulus | Solving and graphing inequalities | |
| Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value. | |||
| 94 | Quadratic equations | Quadratic equations with factorisation. | |
| Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising. | |||
| 95 | Quadratic equations | Solving quadratic equations. | |
| Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations. | |||
| 96 | Quadratic equations | The quadratic formula | |
| Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||
| 97 | Vectors | Vectors | |
| Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram. | |||
| 98 | Statistic-probability | Calculating the median from a frequency distribution | |
| Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. | |||
| 99 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |
| Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. | |||
| 100 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||
| 101 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |
| Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. | |||
| 102 | Statistic-probability | Cumulative frequency | |
| Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. | |||
| 103 | Statistics | Frequency histograms and polygons | |
| Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. | |||
| 104 | Statistic-probability | Rolling a pair of dice | |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. | |||
| 105 | Statistic-probability | Experimental probability | |
| Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||
| 106 | Statistic-probability | Tree diagrams – not depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes. | |||
| 107 | Statistic-probability | Tree diagrams – depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes. | |||
AQA-GCSE Revision Foundation Mathematics
| # | TOPIC | TITLE | |
| 1 | Rules properties | Using Order of Operation procedures (BIDMAS) with Fractions | |
| Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions. | |||
| 2 | Algebraic expressions | Directed numbers: addition and subtraction. | |
| Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals. | |||
| 3 | Algebraic expressions | Directed numbers: multiplication and division. | |
| Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer. | |||
| 4 | Decimals | Using decimals – shopping problems | |
| Objective: On completion of the lesson the student will be able to: read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money. | |||
| 5 | Decimals | Rounding decimals | |
| Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number. | |||
| 6 | Decimals | Adding decimals with a different number of decimal places | |
| Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places. | |||
| 7 | Decimals | Subtracting decimals with a different number of places | |
| Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places. | |||
| 8 | Decimals | Multiplying decimals by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers. | |||
| 9 | Decimals | Multiplication of decimals by decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to multiply decimals to two digits. | |||
| 10 | Decimals | Dividing decimal fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. | |||
| 11 | Decimals | Dividing numbers by a decimal fraction | |
| Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction. | |||
| 12 | Fractions | Comparing and ordering fractions | |
| Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts. | |||
| 13 | Fractions | mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one. | |||
| 14 | Fractions | Improper fractions | |
| Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally. | |||
| 15 | Fractions | Finding equivalent fractions | |
| Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines. | |||
| 16 | Fractions | Reducing fractions to lowest equivalent form | |
| Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor. | |||
| 17 | Fractions | Adding and subtracting fractions with different denominators | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other. | |||
| 18 | Fractions | Multiplying fractions | |
| Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form. | |||
| 19 | Fractions | Dividing fractions | |
| Objective: On completion of the lesson the student will be able to divide fractions. | |||
| 20 | Multiplication | Multiples and factors of whole numbers | |
| Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers. | |||
| 21 | Rules for indices/exponents | Adding indices when multiplying terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base. | |||
| 22 | Rules for indices/exponents | Subtracting indices when dividing terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base. | |||
| 23 | Percentages | Calculating Percentages and Fractions of Quantities | |
| Objective: To find percentages and fractions of quantities and solve problems with percentages | |||
| 24 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion. | |||
| 25 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||
| 26 | Time, 24-hour | 24 hour time | |
| Objective: On completion of the lesson the student will be able to: tell the time accurately using twenty-four hour time, change the time from am and pm time to twenty-four hour time, and change the time from twenty-four hour time to am and pm time. | |||
| 27 | Time zones | Time zones | |
| Objective: On completion of the lesson the student will be able to: recognise that there are different time zones, compare time zones, understand daylight saving and adjust times accordingly, and determine the local time in different regions. | |||
| 28 | Area | Finding the area of a triangle and other composite shapes. | |
| Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas. | |||
| 29 | Area | Area of a trapezium. | |
| Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula. | |||
| 30 | Area | Area of a circle. | |
| Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle. | |||
| 31 | Volume | Finding the volume of prisms | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume. | |||
| 32 | Surface area | Surface area of a cube/rectangular prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula. | |||
| 33 | 2-D shapes | Using the prefix to determine polygons | |
| Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides. | |||
| 34 | 3-D shapes | Recognise and name prisms according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties. | |||
| 35 | 3-D shapes | Recognise and name pyramids according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties. | |||
| 36 | 3-D shapes | Recognise nets for prisms, pyramids, cubes and cones | |
| Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones. | |||
| 37 | Geometry-angles | Measuring angles | |
| Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is. | |||
| 38 | Geometry-angles | Adjacent angles | |
| Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems. | |||
| 39 | Geometry-angles | Complementary and supplementary angles | |
| Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems. | |||
| 40 | Geometry-angles | Vertically opposite angles | |
| Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems. | |||
| 41 | Geometry-angles | Angles at a Point. | |
| Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems. | |||
| 42 | Geometry-angles | Parallel Lines. | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. | |||
| 43 | Geometry-triangles | Angle sum of a triangle | |
| Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. | |||
| 44 | Trigonometry-compass | Bearings – the compass. | |
| Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. | |||
| 45 | Geometry-constructions | Geometric constructions | |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. | |||
| 46 | Geometry-locus | Constructions and loci – single condition | |
| Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. | |||
| 47 | 2-D shapes | Recognise and name triangles | |
| Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties. | |||
| 48 | Similar triangles | Similar triangles | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. | |||
| 49 | 2-D shapes | Spatial properties of quadrilaterals | |
| Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals. | |||
| 50 | Tessellating 2-D shapes | Use grids to enlarge/reduce 2D shapes | |
| Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate. | |||
| 51 | Transformations | Special transformations – reflections, rotations and enlargements. | |
| Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable. | |||
| 52 | Translations | Transformations – reflections | |
| Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection. | |||
| 53 | Pythagoras | Find the hypotenuse | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. | |||
| 54 | Algebraic expressions | Algebraic expressions. | |
| Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand. | |||
| 55 | Algebraic expressions | Simplifying algebraic expressions: adding like terms. | |
| Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms. | |||
| 56 | Algebraic expressions | Simplifying algebraic Expressions: subtracting like terms. | |
| Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction. | |||
| 57 | Algebraic expressions | Simplifying Algebraic expressions: combining addition and subtraction. | |
| Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes. | |||
| 58 | Algebraic expressions | Simplifying algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form. | |||
| 59 | Algebraic expressions | Simplifying algebraic expressions: division | |
| Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. | |||
| 60 | Algebraic expressions | Expanding algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step. | |||
| 61 | Algebraic expressions | Expanding and simplifying algebraic expressions | |
| Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. | |||
| 62 | Algebraic equations | Solving equations containing addition and subtraction | |
| Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side. | |||
| 63 | Algebraic equations | Solving equations containing multiplication and division | |
| Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. | |||
| 64 | Algebraic equations | Solving two step equations | |
| Objective: On completion of the lesson the student will be able to solve two step equations. | |||
| 65 | Common fact and diff | Common factor and the difference of two squares | |
| Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. | |||
| 66 | Algebraic expressions | Substitution into algebraic expressions. | |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. | |||
| 67 | Algebra-inequalities | Solving Inequalities. | |
| Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities. | |||
| 68 | Statistics | The range. | |
| Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. | |||
| 69 | Statistic-probability | The mode | |
| Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. | |||
| 70 | Statistic-probability | The mean | |
| Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||
| 71 | Statistic-probability | The median | |
| Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||
| 72 | Data | Bar Charts | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||
| 73 | Data | Line graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||
| 74 | Data | Pictograms | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs. | |||
| 75 | Data | Pie and bar graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs. | |||
| 76 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||
| 77 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |
| Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. | |||
| 78 | Statistics | Frequency distribution table | |
| Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. | |||
| 79 | Statistic-probability | Probability of Simple Events | |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||
AQA-GCSE Revision Higher Mathematics
| # | TOPIC | TITLE | |
| 1 | Algebra-highest common factor | Highest common factor. | |
| Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression. | |||
| 2 | Fractions | Multiplying mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form. | |||
| 3 | Fractions | Dividing mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals). | |||
| 4 | Rules for indices/exponents | Multiplying indices when raising a power to a power | |
| Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power. | |||
| 5 | Rules for indices/exponents | Multiplying indices when raising to more than one term | |
| Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power. | |||
| 6 | Rules for indices/exponents | Negative Indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices. | |||
| 7 | Fractional indices/exponents | Fractional indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. | |||
| 8 | Fractional indices/exponents | Complex fractions as indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices. | |||
| 9 | Percentages | Calculating Percentages and Fractions of Quantities | |
| Objective: To find percentages and fractions of quantities and solve problems with percentages | |||
| 10 | Percentages | Introduction to percentages, including relating common fractions to percentages | |
| Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage. | |||
| 11 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion. | |||
| 12 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||
| 13 | Percentages | One quantity as a percentage of another | |
| Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another. | |||
| 14 | Sequences and Series-Compound interest | Compound interest | |
| Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods. | |||
| 15 | Significant figures | Significant figures | |
| Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures. | |||
| 16 | Time, distance, speed | Average speed | |
| Objective: On completion of the lesson the student will be able to understand what is meant by the speed of an object, read the instantaneous speed of a vehicle on a speedometer and find the average speed of an object. | |||
| 17 | Scientific notation | Scientific notation with larger numbers | |
| Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation. | |||
| 18 | Scientific notation | Scientific notation with small numbers | |
| Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation. | |||
| 19 | Scientific notation | Changing scientific notation to numerals | |
| Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation. | |||
| 20 | Surds | Introducing surds | |
| Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers. | |||
| 21 | Surds | Some rules for the operations with surds | |
| Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds. | |||
| 22 | Surds | Simplifying surds | |
| Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication. | |||
| 23 | Surds | Expanding surds | |
| Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds. | |||
| 24 | Area | Area of a trapezium. | |
| Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula. | |||
| 25 | Area | Area of a circle. | |
| Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle. | |||
| 26 | Area | Area of regular polygons and composite figures. | |
| Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula. | |||
| 27 | Surface area | Surface area of a cube/rectangular prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula. | |||
| 28 | Surface area | Surface area of a triangular/trapezoidal prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula. | |||
| 29 | Surface area | Surface area of a cylinder and sphere. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula. | |||
| 30 | Surface area | Surface area of pyramids | |
| Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. | |||
| 31 | Surface area | Surface area of cones | |
| Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul | |||
| 32 | Volume | Finding the volume of prisms | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume. | |||
| 33 | Volume | Volume of a cylinder and sphere. | |
| Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume. | |||
| 34 | Volume | Volume of pyramids and cones. | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones. | |||
| 35 | Volume | Composite solids. | |
| Objective: On completion of the lesson the student will be able to: dissect composite solids into simpler shapes so that the volume can be calculated, calculate the volume of a variety of composite solids, and use formulae appropriately. | |||
| 36 | Geometry-triangles | Exterior angle theorem | |
| Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions. | |||
| 37 | Geometry problems | More difficult exercises involving parallel lines | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log | |||
| 38 | Geometry-polygons | Angles of regular polygons | |
| Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees. | |||
| 39 | Trig complementary angles | Complementary angle results. | |
| Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations. | |||
| 40 | Trigonometry-compass | Bearings – the compass. | |
| Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. | |||
| 41 | Circle Geometry | Theorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc. | |
| Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc. | |||
| 42 | Circle Geometry | Theorem – Angles in the same segment of a circle are equal. | |
| Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal. | |||
| 43 | Circle Geometry | Theorem – The angle of a semi-circle is a right angle. | |
| Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’ | |||
| 44 | Circle Geometry | Theorem – The opposite angles of a cyclic quadrilateral are supplementary. | |
| Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary. | |||
| 45 | Circle Geometry | Theorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact. | |
| Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact. | |||
| 46 | Circle Geometry | Theorem – Tangents to a circle from an external point are equal. | |
| Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal. | |||
| 47 | Circle Geometry | Theorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. | |
| Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. | |||
| 48 | Geometry-constructions | Geometric constructions | |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. | |||
| 49 | Geometry-locus | Constructions and loci – multiple conditions | |
| Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. | |||
| 50 | Similar triangles | Similar triangles | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. | |||
| 51 | Similar triangles | Using similar triangles to calculate lengths | |
| Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles. | |||
| 52 | Geometric transformations | Geometry transformations without matrices: reflection (Stage 2) | |
| Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane. | |||
| 53 | Geometric transformations | Geometry transformations without matrices: translation (Stage 2) | |
| Objective: On completion of this lesson the student will perform translations in a number plane. | |||
| 54 | Geometric transformations | Geometry transformations without matrices: rotation (Stage 2) | |
| Objective: On completion of this lesson the student will perform and construct rotations. | |||
| 55 | Geometric transformations | Geometry transformations without matrices: dilation or enlargement (Stage 2) | |
| Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor. | |||
| 56 | Geometry-congruence | Congruent triangles, Test 1 and 2 | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent. | |||
| 57 | Geometry-congruence | Congruent triangles, Test 3 and 4 | |
| Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent. | |||
| 58 | Pythagoras | Find the hypotenuse | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. | |||
| 59 | Pythagoras | Find the hypotenuse Part 2 | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds. | |||
| 60 | Pythagoras | Calculating a leg of a right-angled triangle | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle. | |||
| 61 | Graph sine | Graphing the trigonometric ratios – I Sine curve. | |
| Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period. | |||
| 62 | Graph cosine | Graphing the trigonometric ratios – II Cosine curve. | |
| Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period. | |||
| 63 | Graphs tan curve | Graphing the trigonometric ratios – III Tangent curve. | |
| Objective: On completion of the lesson the student will know how to recognise and draw the tan curve. | |||
| 64 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |
| Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances. | |||
| 65 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |
| Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle. | |||
| 66 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |
| Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle. | |||
| 67 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |
| Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown. | |||
| 68 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |
| Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio. | |||
| 69 | Trigonometry-cosine rule | The cosine rule to find an unknown side. [Case 1 SAS]. | |
| Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle. | |||
| 70 | Trigonometry-cosine rule | The cosine rule to find an unknown angle. [Case 2 SSS]. | |
| Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides. | |||
| 71 | Trigonometry-sine rule | The sine rule to find an unknown side. Case 1. | |
| Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides. | |||
| 72 | Trigonometry-sine rule | The sine rule to find an unknown angle. Case 2. | |
| Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle. | |||
| 73 | Trigonometry-areas | The area formula | |
| Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle. | |||
| 74 | Sequences and Series | General sequences. | |
| Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula. | |||
| 75 | Sequences and Series | Finding Tn given Sn. | |
| Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term. | |||
| 76 | Algebraic expressions-products | Products in simplification of algebraic expressions | |
| Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing. | |||
| 77 | Algebraic expressions-larger expansions | Algebraic Expressions – Larger expansions. | |
| Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. | |||
| 78 | Algebraic fractions | Simplifying algebraic fractions. | |
| Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point. | |||
| 79 | Functions and graphs | Quadratic polynomials of the form y = ax. + bx + c. | |
| Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis. | |||
| 80 | Algebraic equations | Equations involving grouping symbols. | |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||
| 81 | Algebraic equations | Equations involving fractions. | |
| Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||
| 82 | Simultaneous equns | Elimination method | |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. | |||
| 83 | Simultaneous equns | Elimination method part 2 | |
| Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method. | |||
| 84 | Common fact and diff | Common factor and the difference of two squares | |
| Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. | |||
| 85 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. | |
| Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||
| 86 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. | |
| Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||
| 87 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. | |
| Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||
| 88 | Factorising quads | Factorisation of non-monic quadratic trinomials – moon method | |
| Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method. | |||
| 89 | Algebraic expressions | Substitution into algebraic expressions. | |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. | |||
| 90 | Algebra- formulae | Equations resulting from substitution into formulae. | |
| Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. | |||
| 91 | Algebra- formulae | Changing the subject of the formula. | |
| Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously. | |||
| 92 | Algebra-inequalities | Solving Inequalities. | |
| Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities. | |||
| 93 | Absolute value or modulus | Solving and graphing inequalities | |
| Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value. | |||
| 94 | Quadratic equations | Quadratic equations with factorisation. | |
| Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising. | |||
| 95 | Quadratic equations | Solving quadratic equations. | |
| Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations. | |||
| 96 | Quadratic equations | Completing the square | |
| Objective: On completion of the lesson the student will understand the process of completing the square. | |||
| 97 | Quadratic equations | The quadratic formula | |
| Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||
| 98 | Statistic-probability | Calculating the median from a frequency distribution | |
| Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. | |||
| 99 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |
| Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. | |||
| 100 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||
| 101 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |
| Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. | |||
| 102 | Statistic-probability | Cumulative frequency | |
| Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. | |||
| 103 | Statistics | Frequency histograms and polygons | |
| Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. | |||
| 104 | Statistic-probability | Rolling a pair of dice | |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. | |||
| 105 | Statistic-probability | Experimental probability | |
| Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||
| 106 | Statistic-probability | Tree diagrams – not depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes. | |||
| 107 | Statistic-probability | Tree diagrams – depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes. | |||
OCR-GCSE Revision Foundation Mathematics
| # | TOPIC | TITLE | |
| 1 | Rules properties | Using Order of Operation procedures (BIDMAS) with Fractions | |
| Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions.See the sample lesson in action here | |||
| 2 | Algebraic expressions | Directed numbers: addition and subtraction. | |
| Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals.See the sample lesson in action here | |||
| 3 | Algebraic expressions | Directed numbers: multiplication and division. | |
| Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer.See the sample lesson in action here | |||
| 4 | Decimals | Using decimals – shopping problems | |
| Objective: On completion of the lesson the student will be able to: read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money.See the sample lesson in action here | |||
| 5 | Decimals | Rounding decimals | |
| Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number.See the sample lesson in action here | |||
| 6 | Decimals | Adding decimals with a different number of decimal places | |
| Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places.See the sample lesson in action here | |||
| 7 | Decimals | Subtracting decimals with a different number of places | |
| Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places.See the sample lesson in action here | |||
| 8 | Decimals | Multiplying decimals by whole numbers | |
| Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.See the sample lesson in action here | |||
| 9 | Decimals | Multiplication of decimals by decimals to two decimal places | |
| Objective: On completion of the lesson the student will be able to multiply decimals to two digits.See the sample lesson in action here | |||
| 10 | Decimals | Dividing decimal fractions by whole numbers | |
| Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers.See the sample lesson in action here | |||
| 11 | Decimals | Dividing numbers by a decimal fraction | |
| Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction.See the sample lesson in action here | |||
| 12 | Fractions | Comparing and ordering fractions | |
| Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts.See the sample lesson in action here | |||
| 13 | Fractions | mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one.See the sample lesson in action here | |||
| 14 | Fractions | Improper fractions | |
| Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally.See the sample lesson in action here | |||
| 15 | Fractions | Finding equivalent fractions | |
| Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines.See the sample lesson in action here | |||
| 16 | Fractions | Reducing fractions to lowest equivalent form | |
| Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor.See the sample lesson in action here | |||
| 17 | Fractions | Adding and subtracting fractions with different denominators | |
| Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other.See the sample lesson in action here | |||
| 18 | Fractions | Multiplying fractions | |
| Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form.See the sample lesson in action here | |||
| 19 | Fractions | Dividing fractions | |
| Objective: On completion of the lesson the student will be able to divide fractions.See the sample lesson in action here | |||
| 20 | Multiplication | Multiples and factors of whole numbers | |
| Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers.See the sample lesson in action here | |||
| 21 | Rules for indices/exponents | Adding indices when multiplying terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.See the sample lesson in action here | |||
| 22 | Rules for indices/exponents | Subtracting indices when dividing terms with the same base | |
| Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base.See the sample lesson in action here | |||
| 23 | Percentages | Calculating Percentages and Fractions of Quantities | |
| Objective: To find percentages and fractions of quantities and solve problems with percentagesSee the sample lesson in action here | |||
| 24 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion.See the sample lesson in action here | |||
| 25 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.See the sample lesson in action here | |||
| 26 | Time, 24-hour | 24 hour time | |
| Objective: On completion of the lesson the student will be able to: tell the time accurately using twenty-four hour time, change the time from am and pm time to twenty-four hour time, and change the time from twenty-four hour time to am and pm time.See the sample lesson in action here | |||
| 27 | Time zones | Time zones | |
| Objective: On completion of the lesson the student will be able to: recognise that there are different time zones, compare time zones, understand daylight saving and adjust times accordingly, and determine the local time in different regions.See the sample lesson in action here | |||
| 28 | Area | Finding the area of a triangle and other composite shapes. | |
| Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas.See the sample lesson in action here | |||
| 29 | Area | Area of a trapezium. | |
| Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula.See the sample lesson in action here | |||
| 30 | Area | Area of a circle. | |
| Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle.See the sample lesson in action here | |||
| 31 | Volume | Finding the volume of prisms | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.See the sample lesson in action here | |||
| 32 | Surface area | Surface area of a cube/rectangular prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula.See the sample lesson in action here | |||
| 33 | 2-D shapes | Using the prefix to determine polygons | |
| Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides.See the sample lesson in action here | |||
| 34 | 3-D shapes | Recognise and name prisms according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties.See the sample lesson in action here | |||
| 35 | 3-D shapes | Recognise and name pyramids according to spatial properties | |
| Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties.See the sample lesson in action here | |||
| 36 | 3-D shapes | Recognise nets for prisms, pyramids, cubes and cones | |
| Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones.See the sample lesson in action here | |||
| 37 | Geometry-angles | Measuring angles | |
| Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.See the sample lesson in action here | |||
| 38 | Geometry-angles | Adjacent angles | |
| Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.See the sample lesson in action here | |||
| 39 | Geometry-angles | Complementary and supplementary angles | |
| Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.See the sample lesson in action here | |||
| 40 | Geometry-angles | Vertically opposite angles | |
| Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.See the sample lesson in action here | |||
| 41 | Geometry-angles | Angles at a Point. | |
| Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.See the sample lesson in action here | |||
| 42 | Geometry-angles | Parallel Lines. | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.See the sample lesson in action here | |||
| 43 | Geometry-triangles | Angle sum of a triangle | |
| Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.See the sample lesson in action here | |||
| 44 | Trigonometry-compass | Bearings – the compass. | |
| Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north.See the sample lesson in action here | |||
| 45 | Geometry-constructions | Geometric constructions | |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.See the sample lesson in action here | |||
| 46 | Geometry-locus | Constructions and loci – single condition | |
| Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition.See the sample lesson in action here | |||
| 47 | 2-D shapes | Recognise and name triangles | |
| Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties.See the sample lesson in action here | |||
| 48 | Similar triangles | Similar triangles | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar.See the sample lesson in action here | |||
| 49 | 2-D shapes | Spatial properties of quadrilaterals | |
| Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals.See the sample lesson in action here | |||
| 50 | Tessellating 2-D shapes | Use grids to enlarge/reduce 2D shapes | |
| Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate.See the sample lesson in action here | |||
| 51 | Transformations | Special transformations – reflections, rotations and enlargements. | |
| Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.See the sample lesson in action here | |||
| 52 | Translations | Transformations – reflections | |
| Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection.See the sample lesson in action here | |||
| 53 | Pythagoras | Find the hypotenuse | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse.See the sample lesson in action here | |||
| 54 | Sequences and Series | General sequences. | |
| Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.See the sample lesson in action here | |||
| 55 | Sequences and Series | Finding Tn given Sn. | |
| Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term.See the sample lesson in action here | |||
| 56 | Algebraic expressions | Algebraic expressions. | |
| Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand.See the sample lesson in action here | |||
| 57 | Algebraic expressions | Simplifying algebraic expressions: adding like terms. | |
| Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms.See the sample lesson in action here | |||
| 58 | Algebraic expressions | Simplifying algebraic Expressions: subtracting like terms. | |
| Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction.See the sample lesson in action here | |||
| 59 | Algebraic expressions | Simplifying Algebraic expressions: combining addition and subtraction. | |
| Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes.See the sample lesson in action here | |||
| 60 | Algebraic expressions | Simplifying algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form.See the sample lesson in action here | |||
| 61 | Algebraic expressions | Simplifying algebraic expressions: division | |
| Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions.See the sample lesson in action here | |||
| 62 | Algebraic expressions | Expanding algebraic expressions: multiplication | |
| Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step.See the sample lesson in action here | |||
| 63 | Algebraic expressions | Expanding and simplifying algebraic expressions | |
| Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.See the sample lesson in action here | |||
| 64 | Algebraic equations | Solving equations containing addition and subtraction | |
| Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.See the sample lesson in action here | |||
| 65 | Algebraic equations | Solving equations containing multiplication and division | |
| Objective: On completion of the lesson the student will be able to solve simple equations involving all operations.See the sample lesson in action here | |||
| 66 | Algebraic equations | Solving two step equations | |
| Objective: On completion of the lesson the student will be able to solve two step equations.See the sample lesson in action here | |||
| 67 | Common fact and diff | Common factor and the difference of two squares | |
| Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares.See the sample lesson in action here | |||
| 68 | Algebraic expressions | Substitution into algebraic expressions. | |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations.See the sample lesson in action here | |||
| 69 | Algebra-inequalities | Solving Inequalities. | |
| Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.See the sample lesson in action here | |||
| 70 | Statistics | The range. | |
| Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.See the sample lesson in action here | |||
| 71 | Statistic-probability | The mode | |
| Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.See the sample lesson in action here | |||
| 72 | Statistic-probability | The mean | |
| Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.See the sample lesson in action here | |||
| 73 | Statistic-probability | The median | |
| Objective: On completion of the lesson the student will be able to determine the median of a set of raw scoresSee the sample lesson in action here | |||
| 74 | Data | Bar Charts | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.See the sample lesson in action here | |||
| 75 | Data | Line graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.See the sample lesson in action here | |||
| 76 | Data | Pictograms | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.See the sample lesson in action here | |||
| 77 | Data | Pie and bar graphs. | |
| Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs.See the sample lesson in action here | |||
| 78 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.See the sample lesson in action here | |||
| 79 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |
| Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.See the sample lesson in action here | |||
| 80 | Statistics | Frequency distribution table | |
| Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.See the sample lesson in action here | |||
| 81 | Statistic-probability | Probability of Simple Events | |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events.See the sample lesson in action here | |||
OCR-GCSE Revision Higher Mathematics
| # | TOPIC | TITLE | |
| 1 | Algebra-highest common factor | Highest common factor. | |
| Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.See the sample lesson in action here | |||
| 2 | Fractions | Multiplying mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form.See the sample lesson in action here | |||
| 3 | Fractions | Dividing mixed numbers (mixed numerals) | |
| Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).See the sample lesson in action here | |||
| 4 | Rules for indices/exponents | Multiplying indices when raising a power to a power | |
| Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.See the sample lesson in action here | |||
| 5 | Rules for indices/exponents | Multiplying indices when raising to more than one term | |
| Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.See the sample lesson in action here | |||
| 6 | Rules for indices/exponents | Negative Indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices.See the sample lesson in action here | |||
| 7 | Fractional indices/exponents | Fractional indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices.See the sample lesson in action here | |||
| 8 | Fractional indices/exponents | Complex fractions as indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices.See the sample lesson in action here | |||
| 9 | Percentages | Calculating Percentages and Fractions of Quantities | |
| Objective: To find percentages and fractions of quantities and solve problems with percentagesSee the sample lesson in action here | |||
| 10 | Percentages | Introduction to percentages, including relating common fractions to percentages | |
| Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage.See the sample lesson in action here | |||
| 11 | Percentages | Changing fractions and decimals to percentages using tenths and hundredths | |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion.See the sample lesson in action here | |||
| 12 | Percentages | Changing percentages to fractions and decimals | |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.See the sample lesson in action here | |||
| 13 | Percentages | One quantity as a percentage of another | |
| Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another.See the sample lesson in action here | |||
| 14 | Sequences and Series-Compound interest | Compound interest | |
| Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.See the sample lesson in action here | |||
| 15 | Significant figures | Significant figures | |
| Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures.See the sample lesson in action here | |||
| 16 | Time, distance, speed | Average speed | |
| Objective: On completion of the lesson the student will be able to understand what is meant by the speed of an object, read the instantaneous speed of a vehicle on a speedometer and find the average speed of an object.See the sample lesson in action here | |||
| 17 | Scientific notation | Scientific notation with larger numbers | |
| Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation.See the sample lesson in action here | |||
| 18 | Scientific notation | Scientific notation with small numbers | |
| Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.See the sample lesson in action here | |||
| 19 | Scientific notation | Changing scientific notation to numerals | |
| Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation.See the sample lesson in action here | |||
| 20 | Surds | Introducing surds | |
| Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers.See the sample lesson in action here | |||
| 21 | Surds | Some rules for the operations with surds | |
| Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds.See the sample lesson in action here | |||
| 22 | Surds | Simplifying surds | |
| Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication.See the sample lesson in action here | |||
| 23 | Surds | Expanding surds | |
| Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.See the sample lesson in action here | |||
| 24 | Area | Area of a trapezium. | |
| Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula.See the sample lesson in action here | |||
| 25 | Area | Area of a circle. | |
| Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle.See the sample lesson in action here | |||
| 26 | Area | Area of regular polygons and composite figures. | |
| Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula.See the sample lesson in action here | |||
| 27 | Surface area | Surface area of a cube/rectangular prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula.See the sample lesson in action here | |||
| 28 | Surface area | Surface area of a triangular/trapezoidal prism. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula.See the sample lesson in action here | |||
| 29 | Surface area | Surface area of a cylinder and sphere. | |
| Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula.See the sample lesson in action here | |||
| 30 | Surface area | Surface area of pyramids | |
| Objective: On completion of the lesson the student will be able to find the surface areas of pyramids.See the sample lesson in action here | |||
| 31 | Surface area | Surface area of cones | |
| Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendiculSee the sample lesson in action here | |||
| 32 | Volume | Finding the volume of prisms | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.See the sample lesson in action here | |||
| 33 | Volume | Volume of a cylinder and sphere. | |
| Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume.See the sample lesson in action here | |||
| 34 | Volume | Volume of pyramids and cones. | |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones.See the sample lesson in action here | |||
| 35 | Volume | Composite solids. | |
| Objective: On completion of the lesson the student will be able to: dissect composite solids into simpler shapes so that the volume can be calculated, calculate the volume of a variety of composite solids, and use formulae appropriately.See the sample lesson in action here | |||
| 36 | Geometry-triangles | Exterior angle theorem | |
| Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions.See the sample lesson in action here | |||
| 37 | Geometry problems | More difficult exercises involving parallel lines | |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out logSee the sample lesson in action here | |||
| 38 | Geometry-polygons | Angles of regular polygons | |
| Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees.See the sample lesson in action here | |||
| 39 | Trig complementary angles | Complementary angle results. | |
| Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.See the sample lesson in action here | |||
| 40 | Trigonometry-compass | Bearings – the compass. | |
| Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north.See the sample lesson in action here | |||
| 41 | Circle Geometry | Theorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc. | |
| Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc.See the sample lesson in action here | |||
| 42 | Circle Geometry | Theorem – Angles in the same segment of a circle are equal. | |
| Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal.See the sample lesson in action here | |||
| 43 | Circle Geometry | Theorem – The angle of a semi-circle is a right angle. | |
| Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’See the sample lesson in action here | |||
| 44 | Circle Geometry | Theorem – The opposite angles of a cyclic quadrilateral are supplementary. | |
| Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary.See the sample lesson in action here | |||
| 45 | Circle Geometry | Theorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact. | |
| Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact.See the sample lesson in action here | |||
| 46 | Circle Geometry | Theorem – Tangents to a circle from an external point are equal. | |
| Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal.See the sample lesson in action here | |||
| 47 | Circle Geometry | Theorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. | |
| Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.See the sample lesson in action here | |||
| 48 | Geometry-constructions | Geometric constructions | |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.See the sample lesson in action here | |||
| 49 | Geometry-locus | Constructions and loci – multiple conditions | |
| Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane.See the sample lesson in action here | |||
| 50 | Similar triangles | Similar triangles | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar.See the sample lesson in action here | |||
| 51 | Similar triangles | Using similar triangles to calculate lengths | |
| Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles.See the sample lesson in action here | |||
| 52 | Geometric transformations | Geometry transformations without matrices: reflection (Stage 2) | |
| Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane.See the sample lesson in action here | |||
| 53 | Geometric transformations | Geometry transformations without matrices: translation (Stage 2) | |
| Objective: On completion of this lesson the student will perform translations in a number plane.See the sample lesson in action here | |||
| 54 | Geometric transformations | Geometry transformations without matrices: rotation (Stage 2) | |
| Objective: On completion of this lesson the student will perform and construct rotations.See the sample lesson in action here | |||
| 55 | Geometric transformations | Geometry transformations without matrices: dilation or enlargement (Stage 2) | |
| Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor.See the sample lesson in action here | |||
| 56 | Geometry-congruence | Congruent triangles, Test 1 and 2 | |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent.See the sample lesson in action here | |||
| 57 | Geometry-congruence | Congruent triangles, Test 3 and 4 | |
| Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent.See the sample lesson in action here | |||
| 58 | Pythagoras | Find the hypotenuse | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse.See the sample lesson in action here | |||
| 59 | Pythagoras | Find the hypotenuse Part 2 | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds.See the sample lesson in action here | |||
| 60 | Pythagoras | Calculating a leg of a right-angled triangle | |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.See the sample lesson in action here | |||
| 61 | Graph sine | Graphing the trigonometric ratios – I Sine curve. | |
| Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period.See the sample lesson in action here | |||
| 62 | Graph cosine | Graphing the trigonometric ratios – II Cosine curve. | |
| Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period.See the sample lesson in action here | |||
| 63 | Graphs tan curve | Graphing the trigonometric ratios – III Tangent curve. | |
| Objective: On completion of the lesson the student will know how to recognise and draw the tan curve.See the sample lesson in action here | |||
| 64 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |
| Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.See the sample lesson in action here | |||
| 65 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |
| Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.See the sample lesson in action here | |||
| 66 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |
| Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.See the sample lesson in action here | |||
| 67 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |
| Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.See the sample lesson in action here | |||
| 68 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |
| Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.See the sample lesson in action here | |||
| 69 | Trigonometry-cosine rule | The cosine rule to find an unknown side. [Case 1 SAS]. | |
| Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.See the sample lesson in action here | |||
| 70 | Trigonometry-cosine rule | The cosine rule to find an unknown angle. [Case 2 SSS]. | |
| Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.See the sample lesson in action here | |||
| 71 | Trigonometry-sine rule | The sine rule to find an unknown side. Case 1. | |
| Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.See the sample lesson in action here | |||
| 72 | Trigonometry-sine rule | The sine rule to find an unknown angle. Case 2. | |
| Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.See the sample lesson in action here | |||
| 73 | Trigonometry-areas | The area formula | |
| Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.See the sample lesson in action here | |||
| 74 | Sequences and Series | General sequences. | |
| Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.See the sample lesson in action here | |||
| 75 | Sequences and Series | Finding Tn given Sn. | |
| Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term.See the sample lesson in action here | |||
| 76 | Algebraic expressions-products | Products in simplification of algebraic expressions | |
| Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing.See the sample lesson in action here | |||
| 77 | Algebraic expressions-larger expansions | Algebraic Expressions – Larger expansions. | |
| Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions.See the sample lesson in action here | |||
| 78 | Algebraic fractions | Simplifying algebraic fractions. | |
| Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point.See the sample lesson in action here | |||
| 79 | Functions and graphs | Quadratic polynomials of the form y = ax. + bx + c. | |
| Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.See the sample lesson in action here | |||
| 80 | Algebraic equations | Equations involving grouping symbols. | |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbolsSee the sample lesson in action here | |||
| 81 | Algebraic equations | Equations involving fractions. | |
| Objective: On completion of the lesson the student will know how to solve equations using fractions.See the sample lesson in action here | |||
| 82 | Simultaneous equns | Elimination method | |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method.See the sample lesson in action here | |||
| 83 | Simultaneous equns | Elimination method part 2 | |
| Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method.See the sample lesson in action here | |||
| 84 | Common fact and diff | Common factor and the difference of two squares | |
| Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares.See the sample lesson in action here | |||
| 85 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. | |
| Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.See the sample lesson in action here | |||
| 86 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. | |
| Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative.See the sample lesson in action here | |||
| 87 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. | |
| Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative.See the sample lesson in action here | |||
| 88 | Factorising quads | Factorisation of non-monic quadratic trinomials – moon method | |
| Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.See the sample lesson in action here | |||
| 89 | Algebraic expressions | Substitution into algebraic expressions. | |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations.See the sample lesson in action here | |||
| 90 | Algebra- formulae | Equations resulting from substitution into formulae. | |
| Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations.See the sample lesson in action here | |||
| 91 | Algebra- formulae | Changing the subject of the formula. | |
| Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously.See the sample lesson in action here | |||
| 92 | Algebra-inequalities | Solving Inequalities. | |
| Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.See the sample lesson in action here | |||
| 93 | Absolute value or modulus | Solving and graphing inequalities | |
| Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value.See the sample lesson in action here | |||
| 94 | Quadratic equations | Quadratic equations with factorisation. | |
| Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.See the sample lesson in action here | |||
| 95 | Quadratic equations | Solving quadratic equations. | |
| Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.See the sample lesson in action here | |||
| 96 | Quadratic equations | Completing the square | |
| Objective: On completion of the lesson the student will understand the process of completing the square.See the sample lesson in action here | |||
| 97 | Quadratic equations | The quadratic formula | |
| Objective: On completion of the lesson the student will be familiar with the quadratic formula.See the sample lesson in action here | |||
| 98 | Statistic-probability | Calculating the median from a frequency distribution | |
| Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon.See the sample lesson in action here | |||
| 99 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |
| Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values.See the sample lesson in action here | |||
| 100 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.See the sample lesson in action here | |||
| 101 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |
| Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.See the sample lesson in action here | |||
| 102 | Statistic-probability | Cumulative frequency | |
| Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.See the sample lesson in action here | |||
| 103 | Statistics | Frequency histograms and polygons | |
| Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.See the sample lesson in action here | |||
| 104 | Statistic-probability | Rolling a pair of dice | |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.See the sample lesson in action here | |||
| 105 | Statistic-probability | Experimental probability | |
| Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.See the sample lesson in action here | |||
| 106 | Statistic-probability | Tree diagrams – not depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes.See the sample lesson in action here | |||
| 107 | Statistic-probability | Tree diagrams – depending on previous outcomes | |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.See the sample lesson in action here | |||