HIGHER UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
HIGHER CHAPTER 1
Integers and powers
SPECIFICATION REFERENCE
Reading, writing and ordering integers and decimals
The operations with negative numbers
Estimating by rounding all numbers in a calculation to 1sf
Rounding whole numbers and decimals to 5sf
Squares, cubes and roots
Evaluating expressions in index form
Simplifying expressions using index laws
BIDMAS
Finding the reciprocal
LCM, HCF and prime factor decomposition
Time: 5 – 7 hours
NA2a
NA2a/3a
NA2a/3h/4a/b
NA3h/4b
NA2b/3g/i
NA3g
NA2b
NA3b
NA3a
NA2a/3a
Prior Knowledge:
For this chapter students are expected to:
Have some notion of place value
Use a number line to show how numbers are related to each other
Use the 4 operations with whole numbers and decimal numbers
Have knowledge of multiplication facts to 10  10
Objectives:
By the end of the chapter the student should be able to:
Understand place value and order positive and negative numbers
Add, subtract, multiply and divide positive and negative integers
Estimate answers by rounding numbers to 1sf
Round whole and decimal numbers up to 5sf
Know the square and square root of number up to 20, and estimate square roots to the nearest whole number
Work out the cube of a number
Use index notation to simplify or evaluate calculations; solve index equations, eg solve 5 x = 125
Use index laws to multiply/divide numbers with the same base (not power of power)
Perform multi-step calculations in the correct order (bidmas)
Work out the reciprocal of whole numbers, decimals and fractions
Find the HCF and LCM of numbers; express a number as a product if prime factors
Differentiation & Extension
More work on long multiplication and division with/without a calculator (combinations of the 4 rules)
Use a number square to find the prime numbers to 100 (sieve of Eratosthenes)
Use prime factors to find LCM
Calculator/ spreadsheet exercise to find prime factors of large numbers
Investigate cube roots
Resources
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Higher
Chapter/section: 1.1 – 1.10
See the Teaching and Learning Software for the activities linking to this chapter.
Assessment Issues
Written testing to assess knowledge of content
Homework
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of
a similar nature, or extension work detailed above.
Notes
Present all working clearly with numbers in line; emphasising that all working is to be shown
For non-calculator methods make sure that remainders and carrying are shown
Factor trees should not contain the number 1
Do exercises 1A – 1J for practice. Do Mixed exercise 1 for consolidation.
HIGHER UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
HIGHER CHAPTER 2 (Part A)
Fractions, decimals and percentages
SPECIFICATION REFERENCE
Converting improper fractions to mixed numbers and vice versa
Simplifying fractions by dividing the HCF of the numerator and denominator
Ordering fractions by converting them to equivalent fractions with the same number
Adding, subtracting, multiply and divide fractions and mixed numbers
Time: 3 – 5 hours
NA2c
NA2c
NA2c
NA3i
PRIOR KNOWLEDGE:
Chapter 1- Integers and powers
Understand fractions as being ‘parts of a whole unit’
OBJECTIVES
By the end of the chapter the student should be able to:
Change improper fractions to mixed numbers and vice versa
Express a fraction as an equivalent fraction
Order fractions by first expressing them as equivalent fractions with the same denominator (including practical
examples)
Add, subtract, multiply and divide fractions and mixed numbers (including practical examples)
DIFFERENTIATION & EXTENSION
Careful differentiation is essential for this topic dependent upon the student’s ability
Relating simple fractions to remembered percentages and vice-versa
Using a calculator to change fractions into decimals and looking for patterns
Working with improper fractions and mixed numbers
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Higher
Chapter/section: 2.1 – 2.5
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Testing ability to simplify fractions without a calculator
Mental arithmetic test involving fractions and mixed numbers
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of
a similar nature, or extension work detailed above
Worksheet for the four rules with fractions; Worksheet for the four rules with decimals
Extra examples on a regular basis for revision purposes
NOTES
An understanding of equivalent fractions is key to this section
Calculators should be used only when appropriate
All work needs to be presented clearly with the relevant stages of working shown
Do exercises 2A – 2E for practice.
HIGHER UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
HIGHER CHAPTER 2 (Part B) Fractions, decimals and percentages
Time: 4 – 6 hours
SPECIFICATION REFERENCE
Multiplying and dividing decimals by 10, 100, 1000
Ordering decimals and fractions
Adding, subtracting, multiplying and dividing decimal numbers
Round numbers to an appropriate degree of accuracy
Using a calculator to evaluate expressions
NA3i
NA2d/3c
NA3i/k/4a
NA3o/p/4a/b
NA30/p
PRIOR KNOWLEDGE:
Number 1
The concepts of a fraction and a decimal
OBJECTIVES
By the end of the chapter the student should be able to:
Multiply and divide decimal numbers by 10, 100 and 1000 (moving the decimal point)
Understand place value in decimal numbers; order decimal numbers
Add, subtract, multiply and divide decimal numbers (including practical examples)
Convert between decimal numbers and fractions (including converting a recurring number to a fraction)
Order decimal numbers and fractions
Give the answer to a calculation to an appropriate degree of accuracy, i.e. within the context of the problem
Use a calculator for calculations involving bidmas
DIFFERENTIATION & EXTENSION
Use harder decimal numbers in real-life problems
Use standard form for vary large/small numbers
Money calculations that require rounding answers to the nearest penny
Multiply and divide decimals by decimals (more than 2 dp)
Research the earliest use of decimals in the history of mathematics
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Higher
Chapter/section: 2.6 – 2.13
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of
a similar nature, or extension work detailed above.
NOTES
Present all working clearly with decimal points in line (all working should be shown)
Amounts of money should always be rounded to the nearest penny where necessary
Do exercises 2F – 2M for practice.
HIGHER UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
HIGHER CHAPTER 2 (Part C)
Fractions, decimals and percentages
SPECIFICATION REFERENCE
Percentages, fractions and decimals
Finding the percentage of a quantity
Time: 1 – 3 hours
NA2e
NA2e
PRIOR KNOWLEDGE:
4 operations of number
The concepts of a fraction and a decimal
Number complements to 10 and multiplication tables to 10  10
Awareness that percentages are used in everyday life
OBJECTIVES
By the end of the chapter the student should be able to:
Convert between decimals, fractions and percentages
Find the percentage of a quantity (including practical examples)
DIFFERENTIATION & EXTENSION
Fractional percentages of amounts
Percentages which convert to recurring decimals (e.g. 33 13 %), and situations which lead to percentages of more than
100%
Simple interest calculations
Discuss why reducing a quantity by 10%, and than by 10% again, is not the same as reducing a quantity by 20%
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Higher
Chapter/section: 2.14 – 2.15
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Reinforce equivalence and the connection between percentage, fraction and decimal.
Mental methods for calculating common percentages (e.g. 17.5% using 10%, 5%, 2.5%)
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of
a similar nature, or extension work detailed above
Independent research into the many uses made of percentages, particularly in the media
NOTES
For non-calculator methods make sure that remainders and carries are shown
In preparation for this unit students should be reminded of basic percentages and recognise their fraction and decimal
equivalents
Do exercises 2N – 2O for practice. Do Mixed exercise 2 for consolidation of whole chapter
HIGHER UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
HIGHER CHAPTER 3
Powers, indices and calculations
SPECIFICATION REFERENCE
Zero, negative and fractional indices
Standard form
Calculations using standard form
Estimating and checking with standard form
Time: 3 – 5 hours
NA2b/3g
NA2b/3i/p
NA3i/m/4b
NA3m/4a/b
PRIOR KNOWLEDGE:
Chapter 2 (Part B) Fractions, decimals and percentages
OBJECTIVES
By the end of the chapter the student should be able to:
Find the value of a number with zero, negative or fractional index
Write an ordinary number in standard form and vice versa
Calculate with numbers in standard form with/without a calculator (including practical examples)
Round numbers in standard form to 1sf to estimate/check calculations (without calculator)
DIFFERENTIATION & EXTENSION
Practical examples involving very large and/or very small numbers (eg. examples in astronomy and biology)
Compare the relative sizes of things using standard form. How much bigger is an elephant compared to an ant?
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Higher
Chapter/section: 3.1 – 3.4
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Regular oral work – e.g. a five-minute assessment at the beginning or end of a lesson
Test standard form with/without a calculator
GCSE past paper questions
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of
a similar nature, or extension work detailed above
NOTES
All of the work in this unit is easily reinforced by starter and end activities
Calculators should be used only when appropriate
Do exercises 3A – 3D for practice. Do Mixed Exercise 3 for consolidation
HIGHER UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
HIGHER CHAPTER 4
Time: 5 – 7 hours
Essential algebra
SPECIFICATION REFERENCE
Simplifying terms, products and sums
Expanding and factorising brackets
Simplifying algebraic fractions
NA5a/b
NA5b
NA5b
PRIOR KNOWLEDGE:
Know that a letter can be used to represent a number
Ability to use negative numbers with the four operations
Experience of using BIDMAS in calculations without a calculator
OBJECTIVES
By the end of the chapter the student should be able to:
Simplify expressions with like terms, eg x2 + 3x2; 3ab + 5ab +2c2
Expand and factorise expressions with one pair of brackets, eg expand x(2x +3y); factorise 3xy2  6x2y
Expand and simplify expressions involving more than one pair of brackets, eg 3(x + 4) – 2 (x – 3); (2x + 3)(3x – 4)
Factorise quadratic expression (including the difference of two squares)
Simplify algebraic fractions, eg
8a  28
4
,
2  x  3
2
6  x  3
2 x  32
2
,
x  3x  4
2
DIFFERENTIATION & EXTENSION
Further work on factorising quadratic expressions involving negative terms and non-unitary coefficient of x2
Simplify algebraic fractions with harder factorisations
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Higher
Chapter/section: 4.1 – 4.9
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
5 minutes mini-test at the start/end of each lesson
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of
a similar nature, or extension work detailed above
NOTES
Explanations about mathematical terminology should be tailored to suit the ability of the group
Emphasise correct use of symbolic notation (e.g. x2 rather than x  x)
Present all work neatly, writing out the questions with the answers to aid revision at a later stage
Do exercises 4A – 4I for practice. Do Mixed Exercise 4 for consolidation
HIGHER UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
HIGHER CHAPTER 5
Coordinates and graphs
SPECIFICATION REFERENCE
Reading and plotting coordinates in all four quadrants
Finding the coordinates of the final point to make a given shape
Using the formula to find the mid-point of line segments
Identifying 2-D and 3-D shapes; 3-D coordinates
The graphs of straight lines
Time: 3 – 5 hours
NA6b/S3e
S3e
S2a/3e
S3e
NA6b
PRIOR KNOWLEDGE:
Using positive and negative integers on a number line
Experience of drawing simple 2-D shapes, eg triangles, squares, parallelograms, etc
OBJECTIVES
By the end of the chapter the student should be able to:
Write down and plot the coordinates of points in all four quadrants
Add a point to a coordinate grid to complete a given shape (parallelogram; rhombus; trapezium; square)
Use the formula to calculate the mid-point of a line segment
Understand how to represent points in 1-D, 2-D and 3-D
Write down an equation for a line parallel to the coordinate axes; Draw a line parallel to the coordinate axes given the
equation
Find the value of a in y = ax from the graph of in y = ax (by considering number pattern in the coordinates)
Produce a table of values for a linear relation and plot the points on a grid (including fractional coefficients of x)
DIFFERENTIATION & EXTENSION
Use non-integer coordinates
Find the coordinates of the point of intersection of the medians of a triangle
Identify the coordinates of the mid-point of a line segment in 3-D
Examples of linear equations in real-life situations (using different letters for x and y)
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Higher
Chapter/section: 5.1 – 5.7
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
5 minutes mini-test at the start/end of each lesson
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of
a similar nature, or extension work detailed above
NOTES
Clear presentation with axes labelled correctly is vital.
Students often have difficulty visualising 3-D coordinates; 3-D models are useful
Do exercises 5A – 5G for practice. Do Mixed Exercise 5 for consolidation
HIGHER UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
HIGHER CHAPTER 6
Sequences
SPECIFICATION REFERENCE
Generating sequences and finding term to term rules
Finding the nth term of an arithmetic series
Finding the nth term and number of matchsticks, tiles, etc for shapes in a sequence
Time: 2 – 4 hours
NA6a
NA6a
NA6a
PRIOR KNOWLEDGE:
Know about odd and even numbers
Recognise simple number patterns, eg 1, 3, 5, ...
Writing simple rules algebraically
OBJECTIVES
By the end of the chapter the student should be able to:
Generate a sequence from a rule, eg given first term = 25, and rule = subtract 5
Find the rule and continue the number pattern or sequence
Relate the term in a sequence to its position, eg multiply term number by 2 and add 1
Continue a sequence when the sequence is a pattern of shapes
Find and use the nth term of a sequence of numbers/shapes
Find whether a number is part of a given sequence
DIFFERENTIATION & EXTENSION
Investigate the number patterns in Pascal’s triangle
Investigate sequences of triangle numbers, Fibonacci numbers, etc
Generate sequences on a spreadsheet
Use algebra to describe real situation, e.g. n quadrilaterals have 4n sides
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Higher
Chapter/section: 6.1 – 6.3
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Simple investigation of a sequence, using diagrams and number patterns
Use of mental maths in the substitution of simple numbers into expressions
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of
a similar nature, or extension work detailed above
NOTES
Emphasis on good use of notation 3n means 3  n
When investigating linear sequences, students should be clear on the description of the pattern in words, the difference
between the terms and the algebraic description of the nth term
Calculators may be used to generate simple sequences, eg using the “ans” function (or similar)
Do exercises 6A – 6C for practice. Do Mixed Exercise 6 for consolidation.
HIGHER UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
HIGHER CHAPTER 7
Properties of shapes
SPECIFICATION REFERENCE
Definitions and names of polygons
Properties of triangles and quadrilaterals
Geometric proof
Parallel lines
Bearings
Time: 3 – 5 hours
S2b/c/e
S2a
S2a
S4a
PRIOR KNOWLEDGE:
The concept of parallel lines
The concept of vertical and horizontal
The concept of an angle between two lines
Experience in drawing triangles, quadrilaterals and circles
OBJECTIVES
By the end of the chapter the student should be able to:
Name a polygon with 3, 4, ..., 10 sides
Identify triangles by their properties (scalene, isosceles, equilateral, right-angled, obtuse, and acute)
Use the angle properties of triangle to find missing angles
Prove the exterior angle of a triangle is equal to the sum of the two opposite interior angles
Identify quadrilaterals by their properties (trapezium, parallelogram, rhombus, rectangle, square, kite and arrowhead)
Use alternate and corresponding angles in parallel lines to find missing angles
Know that a bearing is an angle measured clockwise from North
Work out the bearing of B from A given the bearing of A from B
DIFFERENTIATION & EXTENSION
Use triangles to find the angle sums of polygons
Use the angle properties of triangles to find missing angles in combinations of triangles
Prove the angle sum in a triangle is 180
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Higher
Chapter/section: 7.1 – 7.6
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Incorporate this work in regular mini-tests
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of
a similar nature, or extension work detailed above.
NOTES
All working should be presented clearly, and accurately
Draw lines using a ruler and an HB pencil
Do exercises 7A – 7F for practice. Do Mixed Exercise 7 for consolidation.
HIGHER UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
HIGHER CHAPTER 8
Properties of circles
SPECIFICATION REFERENCE
Names and definitions of parts of a circle
Solving geometric problems using tangent(s)
Using circles to draw regular polygons
Time: 2 – 4 hours
S2h
S2h
S2h
PRIOR KNOWLEDGE:
Chapter 7- Properties of shapes
Ability to draw a circle with compasses
OBJECTIVES
By the end of the chapter the student should be able to:
Identify and name the various parts of a circle (centre, radius, diameter, circumference, sector, segment, arc and chord)
Use the angle properties of tangents to find missing angles (tangent at a point, tangents from a point)
Draw a regular polygon inside a circle using 360/n, eg draw a regular nonagon inside a circle
DIFFERENTIATION & EXTENSION
Investigate other circle theorems by accurately measuring angles
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Higher
Chapter/section: 8.1 – 8.3
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Incorporate this work in regular mini-tests
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of
a similar nature, or extension work detailed above.
NOTES
All working should be presented clearly, and accurately
Draw lines using an HB pencil
A sturdy pair of compasses are essential- spare equipment is advisable
Do exercises 8A – 8C for practice. Do Mixed Exercise 8 for consolidation.
HIGHER UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
HIGHER CHAPTER 9
Measures
SPECIFICATION REFERENCE
Converting units
Estimating answers
Maximum and minimum possible values and possible error
Using the formulae for speed and density
Changing units in compound measures
Time: 5 – 7 hours
NA4a/b/S4a
NA4b/S4a
NA4b/S4a
NA4a/b/S4a
NA4a/S4a
PRIOR KNOWLEDGE:
Know that: 1 hour = 60 minutes; 1 day = 24 hours
Some experience of metric/imperial measures
OBJECTIVES
By the end of the chapter the student should be able to:
Convert measurements to the same unit before doing a calculation, eg 3m  12cm  10mm
Use common metric/imperial equivalents to convert between units
Round measurements to 1sf to find an estimate for a calculation
Understand that measurements can not be precise, and write down the maximum and minimum possible values
Work out the maximum/minimum possible error in a calculation involving measures
Use speed = distance/time to work out speed, distance or time
Use density = mass/volume to work out density, mass or volume
Change the units of speed between metric/metric units or metric/imperial units
Compare quantities by converting to the same units, eg grams/p, kg/m3
DIFFERENTIATION & EXTENSION
Use ICT and reference books to find the weights, volumes and heights of large structures such as buildings, aeroplanes
and ships
Work with more difficult examples, eg with quantities in standard form
Use uncommon units, eg Astronomical Units, speed of light, etc
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Higher
Chapter/section: 9.1 – 9.8
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Mental testing to check for knowledge of everyday measures, and estimation
Mental test questions on changing units, changing between metric and imperial units
Mental questions to test knowledge of common conversion factors
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of
a similar nature, or extension work detailed above
NOTES
Measurement is essentially a practical activity
All working should be shown with multiplication or division by powers of 10
Use a distance/speed/time triangle and a density/mass/volume triangle to assist calculations
Do exercises 9A – 9G for practice. Do Mixed Exercise 9 for consolidation.
HIGHER UNIT 2 (OLD UNIT 3) SCHEMES OF WORK
HIGHER CHAPTER 10
Perimeter, area and volume
SPECIFICATION REFERENCE
Using formulae to find the area of triangles, parallelograms, and trapeziums
Calculating the surface area and volume of cuboids
Using the formula to calculate the volume of a prism
Time: 3 – 4 hours
S4d
S4d
S4d
PRIOR KNOWLEDGE:
The names of quadrilaterals
Ability to substitute numbers into a formula
Some notion of the difference between length, area and volume
OBJECTIVES
By the end of the chapter the student should be able to:
Use the area formulae for triangles, parallelograms and trapeziums
Work out the surface area of 3-D shapes based on rectangles and triangles (by working out the area of each face)
Use v = l  w  h to solve problems involving the volume and dimensions of a cuboid
Work out how many small boxes fit into a large box
Use volume = cross-section  length to find the volume of a regular prism, eg with trapezium cross-section
DIFFERENTIATION & EXTENSION
Further problems involving combinations of shapes
Using compound shape methods to investigate the area of other standard shapes, eg kites
Practical activities e.g. using estimation and accurate measuring to calculate perimeters and areas of classroom/corridor
floors
RESOURCES
Heinemann GCSE Modular Mathematics Unit 2 (old Unit 3) Higher
Chapter/section: 10.1 – 10.5
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Regular quick tests on perimeters, areas and volumes of standard shapes
HOMEWORK
Homework at each stage could comprise consolidation of work in class by completion of exercises set, additional work of
a similar nature, or extension work detailed above
Find the perimeter and area of the floor of a room at home, eg carpet tiles
A fencing problem – find the smallest/largest area with a fixed perimeter
NOTES
Discuss the correct use of language and units
Ensure that pupils can distinguish between perimeter, area and volume
Many students have little real understanding of perimeter, area and volume. Practical experience is essential to clarify
these concepts
Do exercises 10A – 10E for practice. Do Mixed Exercise 10 for consolidation.