FOUNDATION CHAPTER 1
UNDERSTANDING WHOLE NUMBERS
SPECIFICATION REFERENCE
 Understanding place value in whole numbers
 Using figures and words for whole numbers and writing numbers in order of size
 Adding, subtracting, multiplying and dividing whole numbers
 Problems in selecting the correct operation from addition, subtraction, multiplication and division
 Writing numbers to the nearest 10, 100 and 1000 and to one significant figure before
approximating and estimating calculations
NA3h/4c
Time: 7–9 hours
NA2a
NA2a
NA3a/g/j/k
NA3a/g/4b
PRIOR KNOWLEDGE
The ability to order numbers
Appreciation of place value
Experience of the four operations using whole numbers
Knowledge of integer complements to 10
Knowledge of multiplication facts to 10  10
Knowledge of strategies for multiplying and dividing whole numbers by 10
OBJECTIVES
By the end of the chapter the student should be able to:
 Understand and order integers
 Add, subtract, multiply and divide integers
 Understand simple instances of BIDMAS, e.g. work out 12  5 – 24  8
 Round whole numbers to the nearest 10, 100, 1000, …
 Multiply and divide whole numbers by a given multiple of 10
 Check their calculations by rounding, e.g. 29  31  30  30
 Check answers by reverse calculation, e.g. If 9  23 = 207 then 207  9 = 23
RESOURCES
Foundation Student book
Foundation Practice book
Chapter/section: 1.1–1.5
Chapter 1
DIFFERENTIATION AND EXTENSION
 More work on long multiplication and division without using a calculator
 Estimating answers to calculations involving the four rules
 Consideration of mental maths problems with negative powers of 10: 2.5  0.01, 0.001
 Directed number work with two or more operations, or with decimals
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
 Present all working clearly with numbers in line; stress that all working is to be shown.
 For non-calculator methods make sure that remainders and carrying are shown.
 Use Exercises 1A–1L for practice. Use Mixed Exercise 1 for consolidation.
FOUNDATION CHAPTER 2
NUMBER FACTS
Time: 6–8 hours
SPECIFICATION REFERENCE
 Understanding negative numbers in context
 Ordering, adding, subtracting, multiplying and dividing positive and negative numbers
 Recognising even, odd and prime numbers and finding factors and multiples of numbers
 Finding squares and cubes of numbers
 Finding squares and square roots of numbers
 Finding cubes and cube roots of numbers
 Finding square roots and cube roots by trial and improvement
 Writing numbers as a product of their prime factors; HCF and LCM
NA2a
NA2a/3a
NA2a
NA2b
NA2b/3o/4d
NA2b/3o
NA2b/3o
NA2a/3a
PRIOR KNOWLEDGE
Number complements to 10 and multiplication/division facts
Use a number line to show how numbers relate to each other
Recognise basic number patterns
Experience of classifying integers
OBJECTIVES
By the end of the chapter the student should be able to:
 Understand and use negative numbers in context, e.g. thermometers
 Find: squares; cubes; square roots; cube roots of numbers, with and without a calculator (including the use of trial and
improvement)
 Understand odd and even numbers, and prime numbers
 Interpret and represent numbers expressed in index form on calculator displays (using the correct notation)
 Find the HCF and the LCM of numbers
 Write a number as a product of its prime factors, e.g. 108 = 2  2  3  3  3
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 2.1–2.8
Chapter 2
Chapter 2
DIFFERENTIATION AND EXTENSION
 Calculator exercise to check factors of larger numbers
 Further work on indices to include negative and/or fractional indices
 Use prime factors to find LCM
 Use a number square to find primes (sieve of Eratosthenes)
 Calculator exercise to find squares, cubes and square roots of larger numbers (using trial and improvement)
ASSESSMENT
Heinemann online assessment tool will be available in 2007
Regular oral work, e.g. a five-minute assessment at the beginning or end of a lesson
Mental test to check knowledge of squares and cubes
Mental test on the recognition of odd and even numbers
Test on performance using a calculator to find squares, cubes and square roots
Test without a calculator on knowledge of squares, cubes and square numbers (keeping the numbers small)
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Investigational tasks leading to number patterns involving powers of numbers.
GCSE past paper questions.
HINTS AND TIPS
 All of the work in this unit is easily reinforced by starter and end activities.
 Oral discussion should be used to ensure:
Recognition of odd and even numbers
Calculators are only used when appropriate.
 Do Exercises 2A–2L for practice. Do Mixed Exercise 2 for consolidation.
FOUNDATION CHAPTER 3A
ESSENTIAL ALGEBRA
Time: 4–6 hours
SPECIFICATION REFERENCE
 Introducing the use of letters
 The meaning of expressions such as 5x
 Simplifying expressions involving one letter only
 Simplifying expressions involving more than one letter
 Omitting the multiplication sign
 Simple algebraic multiplication
 Simple algebraic division
NA5a
NA5a
NA5a
NA5a
NA5a
NA5a/b
NA5a/b
PRIOR KNOWLEDGE
Experience of using a letter to represent a number
Ability to use negative numbers with the four operations
OBJECTIVES
By the end of the chapter the student should be able to:
 Simplify algebraic expressions in one, or more like terms, by adding and subtracting
 Multiply and divide with letters and numbers
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 3.1–3.7
Chapter 3
Chapter 3
DIFFERENTIATION AND EXTENSION
 Further work on collecting like terms, involving negative terms
 Collecting terms where each term may consist of more than one letter, e.g. 3ab + 4ab
 Examples where all the skills above are required
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
 Explanations about mathematical terminology should be tailored to suit the ability of the group.
 Emphasise correct use of symbolic notation, e.g. 3x rather than 3  x.
 Present all work neatly, writing out the questions with the answers to aid revision at a later stage.
 Do Exercises 3A–3G for practice.
FOUNDATION CHAPTER 3B
ESSENTIAL ALGEBRA 2
Time: 6–8 hours
SPECIFICATION REFERENCE
 Using index notation with numbers
 Finding the rules for adding and subtracting indices
 Using index notation in algebra
 Multiplying and dividing using indices
 Using brackets in numerical calculations (BIDMAS)
 Simplifying algebraic expressions involving brackets
 Factorising using a single bracket
NA5c
NA3a
NA5c
NA5c
NA3b
NA3b/5b
NA5b
PRIOR KNOWLEDGE
Experience of using a letter to represent a number
Ability to use negative numbers with the four operations
OBJECTIVES
By the end of the chapter the student should be able to:
 Multiply and divide powers of the same number

Understand and use the index rules to simplify algebraic expressions, e.g. 5 5  52 = 53
 Use brackets to expand and simplify simple algebraic expressions
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 3.8–3.14
Chapter 3
Chapter 3
DIFFERENTIATION AND EXTENSION
 Examples where all the skills above are required
 Factorising where the factor may involve more than one variable
 Use index rules with negative numbers (and fractions)
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
 Emphasise correct use of symbolic notation, e.g. 3x rather than 3  x.
 Present all work neatly, writing out the questions with the answers to aid revision at a later stage.
 Do Exercises 3H–3T for practice. Do Mixed Exercise 3 for consolidation.
FOUNDATION CHAPTER 4
PATTERNS AND SEQUENCES
SPECIFICATION REFERENCE
 Finding the missing numbers in number patterns or sequences
 Investigating number patterns
 Finding the nth term of a number sequence
 Finding whether a number is part of a given sequence
 Using a calculator to produce and generate patterns and sequences
 Using spreadsheets to investigate and to generate number patterns and sequences
Time: 5–7 hours
NA6a
NA6a
NA6a
Na6a
NA3o/p/6a
NA6a/5f
PRIOR KNOWLEDGE
Know about odd and even numbers
Recognise simple number patterns, e.g. 1, 3, 5, ...
Writing simple rules algebraically
Raise numbers to positive whole number powers
OBJECTIVES
By the end of the chapter the student should be able to:
 Find the missing numbers in a number pattern or sequence
 Find the nth term of a number sequence
 Find whether a number is part of a given sequence
 Use a calculator to produce a sequence of numbers
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 4.1–4.6
Chapter 4
Chapter 4
DIFFERENTIATION AND EXTENSION
 Match-stick problems
 Sequences of triangle numbers, Fibonacci numbers, etc
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
Simple investigation of a sequence, using diagrams and number patterns
Use of mental maths in the substitution of simple numbers into expressions
GCSE A01 coursework tasks
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Fibonacci sequence, Pascal’s triangle
Uses of algebra to describe real situation, e.g. n quadrilaterals have 4n sides
HINTS AND TIPS
 Emphasis on good use of notation, e.g. 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.
 The cube (and cube root) function on a calculator may not be the same for all makes.
 Do Exercises 4A–4I for practice. Do Mixed Exercise 4 for consolidation.
FOUNDATION CHAPTER 5
DECIMALS
Time: 5–7 hours
SPECIFICATION REFERENCE
 Putting digits in the correct places
 Writing decimals in ascending and descending order
 Rounding decimal numbers to the nearest whole number and to one decimal place
 Approximating to a given number of decimal places
 Approximating to a given number of significant figures
 Pencil and paper methods for adding and subtracting decimal numbers
 Multiplying decimals by whole numbers and decimals
 Dividing decimals by whole numbers and decimals
NA2a/d
NA2d
NA2a/3h
NA3h
NA3h
NA3i/j
NA3k/i
NA3k/i
PRIOR KNOWLEDGE
Chapter 1: Understanding whole numbers
The concepts of a fraction and a decimal
OBJECTIVES
By the end of the chapter the student should be able to:
 Put digits in the correct place in a decimal number
 Write decimals in ascending order of size
 Approximate decimals to a given number of decimal places or significant figures
 Multiply and divide decimal numbers by whole numbers and decimal numbers (up to two decimal points), e.g. 266.22  0.34
 Know that, for instance 13.5  0.5 = 135  5
 Check their answer by rounding, know that, for instance 2.9  3.1  3.0  3.0
RESOURCES
Foundation Student book
Foundation Practice book
Chapter/section: 5.1–5.8
Chapter 5
DIFFERENTIATION AND EXTENSION
Use decimals 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)
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
 Present all working clearly with decimal points in line; emphasising that all working is to be shown.
 For non-calculator methods make sure that remainders and carrying are shown.
 Amounts of money should always be rounded to the nearest penny where necessary.
 Do Exercises 5A–5J for practice. Do Mixed Exercise 5 for consolidation.
FOUNDATION CHAPTER 6A
ANGLES AND TURNING 1
SPECIFICATION REFERENCE
 An introduction to angles
 Types of angles, estimating the size of angles
 Using vertices to name angles
 Using a protractor to measure angles of all sizes
 Using a protractor to draw angles accurately
 Using the fact that angles on a straight line add to 180
 Using the fact that angles at a point add to 360 and vertically opposite angles are equal
Time: 4–6 hours
SSM2a
SSM2b
SSM2a
SSM4a/d
SSM4d
SSM2a
SSM2a
PRIOR KNOWLEDGE
An understanding of angle as a measure of turning
The ability to use a protractor to measure angles
OBJECTIVES
By the end of the chapter the student should be able to:
 Distinguish between acute, obtuse, reflex and right angles
 Estimate the size of an angle in degrees
 Measure and draw angle to the nearest degree
 Use angle properties on a line and at a point to calculate unknown angles
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 6.1–6.7
Chapter 6
Chapter 6
DIFFERENTIATION AND EXTENSION
 Measuring angles in polygons
 Investigate the angle sum of polygons
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Regular quick test-type homework on angle properties of various shapes.
HINTS AND TIPS
 Make sure that all pencils are sharp and drawings are neat and accurate
 Angles should be within 2 degrees
 Do Exercises 6A–6G for practice.
FOUNDATION CHAPTER 6B
ANGLES AND TURNING 2
SPECIFICATION REFERENCE
 Calculating unknown angles in triangles and quadrilaterals
 Using parallel lines to identify alternate and corresponding angles
 Understanding simple formal proofs in geometry
 Calculating interior and exterior angles in polygons
 Measuring and calculating bearings
Time: 3–5 hours
SSM2d
SSM2c
SSM2c/d
SSM2g
SSM4b
PRIOR KNOWLEDGE
Chapter 6A: Angles and turning 1
Recall the names of special types of triangle, including equilateral, right-angled and isosceles
Know that angles on a straight line sum to 180 degrees
Know that a right angle = 90 degrees
Understand the concept of parallel lines
OBJECTIVES
By the end of the chapter the student should be able to:
 Mark parallel lines in a diagram
 Find missing angles using properties of corresponding angles and alternate angles, giving reasons
 Use angle properties of triangles and quadrilaterals to find missing angles
 Find the three missing angles in a parallelogram when one of them is given
 Calculate and use the sums of the interior angles of convex polygons of sides 3, 4, 5, 6, 8, 10
 Prove that the angle sum of a triangle is 180 degrees
 Explain why the angle sum of a quadrilateral is 360 degrees
 Know, or work out, the relationship between the number of sides of a polygon and the sum of its interior angles
 Measure and calculate bearings
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 6.8–6.12
Chapter 6
Chapter 6
DIFFERENTIATION AND EXTENSION
Harder problems involving multi-step calculations
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
 Generally the diagrams in examinations are not accurately drawn
 Do Exercises 6H–6M for practice. Do Mixed Exercise 6 for consolidation.
FOUNDATION CHAPTER 7
2-D SHAPES
SPECIFICATION REFERENCE
 Basic information about special triangles, quadrilaterals and polygons
 Using square and isometric paper to draw polygons and make patterns
 Recognising when shapes are congruent
 Tessellating with assorted shapes
 Accurate constructions of triangles, quadrilaterals and polygons
 Scale drawings and using scales in maps
 Drawing angles using a ruler and compasses bisecting lines using a pair of compasses
 Constructing loci and regions
Time: 4–6 hours
SSM2d/f
SSM4d
SSM2d
SSM3b/4d
SSM4d/e
SSM3d
SSM4e
SSM4j/e
PRIOR KNOWLEDGE
An ability to use a pair of compasses
Understanding of the terms perpendicular and parallel
OBJECTIVES
By the end of the chapter the student should be able to:
 Use a ruler and compass to draw accurate triangles, and other 2-D shapes, given information about their side lengths and
angles
 Use straight edge and compass to construct: an equilateral triangle; the midpoint and perpendicular bisector of a line
segment; the bisector of an angle
 Find the locus of points, such as the locus of points equidistant to two given points
 Understand, by their experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA
triangles are not
 Recall and use angle properties of equilateral, isosceles and right-angled triangles
 Recall and use the properties of squares, rectangles, parallelograms, trapeziums and rhombuses
 Recall and use properties of circles
 Appreciate why some shapes tessellate and why some shapes do not tessellate
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 7.1–7.8
Chapter 7
Chapter 7
DIFFERENTIATION AND EXTENSION
 Solve loci problems that require a combination of loci
 Construct combinations of 2-D shapes to make nets
 Investigate tessellation
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
 All working should be presented clearly, and accurately.
 A sturdy pair of compasses are essential.
 Have some spare equipment available.
 Do Exercises 7A–7H for practice. Do Mixed Exercise 7 for consolidation.
FOUNDATION CHAPTER 8A
FRACTIONS 1
Time: 5–7 hours
SPECIFICATION REFERENCE
 Understanding parts of a whole
 Writing fractions from everyday situations
 Converting between improper fractions and mixed numbers
 Finding fractions of different quantities
 Cancelling fractions into their lowest terms
 Finding equivalent fractions by cancelling and multiplying
 Using common denominators to compare the size of fractions
 Using common denominators to add fractions
 Using common denominators to subtract fractions
NA3c
NA3c
NA2c
NA3c
NA2c/3c
NA2c
NA2c
NA3c
NA3c
PRIOR KNOWLEDGE
Multiplication facts
Ability to find common factors
A basic understanding of fractions as being ‘parts of a whole unit’
Use of a calculator with fractions
OBJECTIVES
By the end of the chapter the student should be able to:
 Visualise a fraction diagrammatically
 Understand a fraction as part of a whole
 Recognise and write fractions in everyday situations
 Write a fraction in its simplest form and recognise equivalent fractions
 Compare the sizes of fractions using a common denominator
 Add and subtract fractions by using a common denominator
 Write an improper fraction as a mixed fraction
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 8.1–8.9
Chapter 8
Chapter 8
DIFFERENTIATION AND 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
 Solve word problems involving fractions (and in real-life problems, e.g. find perimeter using fractional values)
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
Testing the ability to perform calculations, using simple fractions, without a calculator.
Mental arithmetic test involving simple fractions such as ½, ¼, ...
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
An equivalent fractions worksheet as a preliminary, following on from the initial lesson.
Use the worksheet for comparing fractions, ordering fractions, and adding and subtracting fractions.
Extra examples on a regular basis for revision purposes.
Other work given could have fractional answers as a part of the process.
HINTS AND TIPS
 Understanding of equivalent fractions is the key issue in order to be able to tackle the other content.
 Calculators should only be used when appropriate.
 Constant revision of this aspect is needed.
 All work needs to be presented clearly with the relevant stages of working shown.
 Do Exercises 8A–8I for practice.
FOUNDATION CHAPTER 8B
FRACTIONS 2
Time: 3–5 hours
SPECIFICATION REFERENCE
 Multiplying fractions by cancelling and by using top-heavy fractions
 Dividing fractions by inverting the divisor and multiplying
 Assorted questions using fractions
 Converting between fractions and decimals
 Changing fractions into recurring decimals
 Finding reciprocals of whole numbers, fractions and decimals
NA3d/l
NA3d/l
NA3c/q/4a
NA3c
NA3c/2d
NA3a
PRIOR KNOWLEDGE
ChapterR 8A Fractions 1
OBJECTIVES
By the end of the chapter the student should be able to:
 Multiply and divide a number with a fraction, and a fraction with a fraction (expressing the answer in its simplest form)
 Simplify multiplication of fractions by first cancelling common factors
 Convert a fraction to a decimal, or a decimal to a fraction
 Convert a fraction to a recurring decimal
 Find the reciprocal of whole numbers, fractions, and decimals, e.g. find the reciprocal of 0.4
 Know that 0 does not have reciprocal, and that a number multiplied by its reciprocal is 1
 Use fractions in contextualised problems
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 8.10–8.15
Chapter 8
Chapter 8
DIFFERENTIATION AND EXTENSION
 Using a calculator to find fractions of given quantities
 Working with improper fractions and mixed numbers
 Using the four operations using fractions (and in real-life problems, e.g. find area using fractional values)
 For very able students, cancelling down of algebraic expressions could be considered
ASSESSMENT
Mental testing on a regular basis, of the basic conversions of simple fraction into decimals
Testing the ability to perform calculations, using simple fractions, without a calculator
Mental arithmetic test involving simple fractions such as ½, ¼ ...
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Extra examples on a regular basis for revision purposes.
Other work given could have fractional answers as a part of the process.
HINTS AND TIPS
 Constant revision of this aspect is needed.
 All work needs to be presented clearly with the relevant stages of working shown.
 Non-calculator work with fractions is generally poorly attempted at GCSE. Students may have difficulty with the concept of
dividing by a fraction.
 Do Exercises 8J–8O for practice. Do Mixed Exercise 8 for consolidation.
FOUNDATION CHAPTER 9
ESTIMATING AND USING MEASURES
Time: 7–9 hours
SPECIFICATION REFERENCE
 Making estimates in everyday life
 Making estimates of length using metric and imperial units
 Making estimates of volume and capacity using metric and imperial units
 Making estimates of weights using metric and imperial units
 Using sensible units for measuring
 Reading analogue and digital clocks
 Reading measurements on different types of scales
SSM4a
SSM4a
SSM4a
SSM4a
SSM4a
SSM4a
SSM4a
PRIOR KNOWLEDGE
An awareness of the imperial system of measures
Strategies for multiplying and dividing by 10
Knowledge of the conversion facts for metric lengths, mass and capacity
Knowledge of the conversion facts between seconds, minutes and hours
OBJECTIVES
By the end of the chapter the student should be able to:
 Make estimates of: length; volume and capacity; weights
 Make approximate conversions between metric and imperial units
 Decide on the appropriate units to use in real life problems
 Read measurements from instruments: scales; analogue and digital clocks; thermometers, etc
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 9.1–9.7
Chapter 9
Chapter 9
DIFFERENTIATION AND EXTENSION
 This could be made a practical activity by collecting assorted everyday items for weighing and measuring to check the
estimates of their lengths, weights and volumes
 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
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
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.
Aural questions on dates, times and timetables.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Plan a foreign holiday with dates, timetables to arrive at the airport etc.
HINTS AND TIPS
 Measurement is essentially a practical activity.
 Use a range of everyday objects to make the lesson more real.
 All working should be shown with multiplication or division by powers of 10.
 Do Exercises 9A–9M for practice. Do Mixed Exercise 9 for consolidation.
FOUNDATION CHAPTER 10
COLLECTING AND RECORDING DATA
Time: 4–6 hours
SPECIFICATION REFERENCE
 Ways of collecting data
 Designing questions for a questionnaire
 Random samples and bias
 Designing a data capture sheet
 Using a data capture sheet to collect results from an experiment
 Secondary data and primary data
 Organised collections of information
 Data from the Internet
 Mileage charts
HD3a
HD3a
HD3a
HD3a
HD3a
HD3b
HD3b
HD3b
HD3c
PRIOR KNOWLEDGE
An understanding of why data needs to be collected
Some idea about different types of graphs
OBJECTIVES
By the end of the chapter the student should be able to:
 Design a suitable question for a questionnaire
 Understand the difference between: primary and secondary data; discrete and continuous data
 Design suitable data capture sheets for surveys and experiments
 Understand about bias in sampling
 Use a mileage chart
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 10.1–10.9
Chapter 10
Chapter 10
DIFFERENTIATION AND EXTENSION
Carry out a statistical investigation of their own including- designing an appropriate means of gathering the data
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
Their own statistical investigation.
GCSE coursework – data handling project.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Completion of data collection exercise and statistical project.
HINTS AND TIPS
 Students may need reminding about the correct use of tallies.
 Emphasis the differences between primary and secondary data.
 If students are collecting data as a group they should all use the same procedure.
 Emphasis that continuous data is data that is measured.
 Do Exercises 10A–10H for practice. Do Mixed Exercise 10 for consolidation.
FOUNDATION CHAPTER 11
LINEAR EQUATIONS
SPECIFICATION REFERENCE
 Solving equations with one operation
 Solving equations involving more than one stage
 Solving equations with brackets and more than one operation
Time: 6–8 hours
NA5e
NA5e
NA5e
PRIOR KNOWLEDGE
Experience of finding missing numbers in calculations
The idea that some operations are ‘opposite’ to each other
An understanding of balancing
Experience of using letters to represent quantities
Be able to draw a number line
OBJECTIVES
By the end of the chapter the student should be able to:
 Solve linear equations with one, or more, operations
 Solve linear equations involving a single pair of brackets
 Solve simple equations using inverse operations
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 11.1–11.3
Chapter 11
Chapter 11
DIFFERENTIATION AND EXTENSION
 Use of inverse operations and rounding to one significant figure could be applied to more complex calculations
 Derive equations from practical situations (such as angle calculations)
 Solve equations where manipulation of fractions (including the negative fractions) is required
 Solve linear inequalities where manipulation of fractions is required
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
 Students need to realise that not all linear equations can easily be solved by either observation or trial and improvement, and
hence the use of a formal method is vital.
 Students can leave their answers in fractional form where appropriate.
 Interpreting the direction of an inequality is a problem for many.
 Do Exercises 11A–11O for practice. Do Mixed Exercise 11 for consolidation.
FOUNDATION CHAPTER 12
SORTING AND PRESENTING DATA
SPECIFICATION REFERENCE
 Using tally charts and bar charts to display data
 Using class intervals to record data
 Representing sets of data in a dual bar chart
 Representing information in a dual bar chart
 Discrete and continuous data, and line graphs
 Information that changes with time
 Using a histogram to display continuous data
 Showing the pattern of data in a histogram
Time: 5–7 hours
HD4a/5b
HD3a
HD4a/5b
HD4a/5b
HD4a/5b/c
HD4a/5b/c/k
HD4a/5b
HD4a/5b/c
PRIOR KNOWLEDGE
An understanding of why data needs to be collected and some idea about different types of graphs
Experience of collecting, interpreting, displaying and calculating with data
OBJECTIVES
By the end of the chapter the student should be able to represent data as:
 Bar charts (including dual bar charts)
 Pictograms
 Line graphs
 Histograms (intervals with equal width)
 Frequency polygons
 Time series graphs
 In addition, students should be able to:
 Choose an appropriate way to display discrete, continuous and categorical data
 Identify trends in data over time
 Identify exceptional periods by comparison with similar previous periods
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 12.1–12.8
Chapter 12
Chapter 12
DIFFERENTIATION AND EXTENSION
 Carry out a statistical investigation of their own and use an appropriate means of displaying the results
 Use a spreadsheet to draw different types of graphs
 Collect examples of charts and graphs in the media which have been misused, and discuss the implications
 Make predictions by considering trends of line graphs for time series
 Additional work on making predictions based on current trends, using time series and/or moving averages
 Collect data from the Internet (e.g. RPI) and analyse it for trend
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
Their own statistical investigation.
GCSE coursework – data handling project.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Completion of a simple statistical project.
HINTS AND TIPS
 Clearly label all axes on graphs and use a ruler to draw straight lines.
 Many students enjoy drawing statistical graphs for classroom displays.
 Do Exercises 12A–12G for practice. Do Mixed Exercise 12 for consolidation.
FOUNDATION CHAPTER 13
3-D SHAPES
SPECIFICATION REFERENCE
 Recognising horizontal and vertical surfaces
 Counting the faces, edges and vertices in three-dimensional solids
 3-D shapes in everyday life
 Examples of prisms
 Drawing nets of solids and recognising solids from their nets
 Drawing and interpreting plans and elevations
 Identifying and drawing planes of symmetry in 3-D shapes
Time: 4–6 hours
SSM2j
SSM2j
SSM2k
SSM2k
SSM2j/4d
SSM2k
SSM3b
PRIOR KNOWLEDGE
The names of standard 3-D shapes
Chapter 7: 2-D shapes
OBJECTIVES
By the end of the chapter the student should be able to:
 Count the vertices, faces and edges of 3-D shapes
 Draw nets of solids and recognise solids from their nets
 Draw and interpret plans and elevations
 Draw planes of symmetry in 3-D shapes
 Recognise and name examples of solids, including prisms, in the real world
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 13.1–13.7
Chapter 13
Chapter 13
DIFFERENTIATION AND EXTENSION
 Make solids using equipment such as clixi or multi-link
 Draw shapes made from multi-link on isometric paper
 Build shapes from cubes that are represented in 2-D
 Work out how many small boxes can be packed into a larger box
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Sketch a plan view of your bedroom or an elevation of your house.
HINTS AND TIPS
 Accurate drawing skills need to be reinforced.
 Some students find visualising 3-D objects difficult – simple models will assist.
 Do Exercises 13A–13G for practice. Do Mixed Exercise 13 for consolidation.
FOUNDATION CHAPTER 14
UNITS OF MEASURE
SPECIFICATION REFERENCE
 Changing metric units of length, capacity and weight
 Converting between metric and imperial units used in everyday situations
 Questions involving the use of time in everyday situations
 Questions involving the use of dates in everyday situations
 Reading timetables and working out journey times
Time: 5–7 hours
SSM4a
SSM4a
SSM4a
SSM4a
SSM4a
PRIOR KNOWLEDGE
Chapter 9: Estimating and using measures
OBJECTIVES
By the end of the chapter the student should be able to:
 Change metric units of length, capacity and weight
 Convert between metric and imperial units used in everyday situations
 Do calculations involving time, including the use of time tables and calendars
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 14.1–14.5
Chapter 14
Chapter 14
DIFFERENTIATION AND 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
 Work with “real” timetables and “real” holiday brochures for working out holiday dates
 Use combinations of timetables for multi-stage trips
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
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.
Aural questions on dates, times and timetables.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Plan a foreign holiday with dates, timetables to arrive at the airport etc.
HINTS AND TIPS
 Measurement is essentially a practical activity.
 Use a range of everyday objects to make the lesson more real.
 All working should be shown with multiplication or division by powers of 10.
 Do Exercises 14A–14J for practice. Do Mixed Exercise 14 for consolidation.
FOUNDATION CHAPTER 15A
PERCENTAGES 1
SPECIFICATION REFERENCE
 Introducing percentages
 Writing percentages as decimals and fractions in their lowest terms
 Calculating percentages of different amounts
Time: 3–5 hours
NA2e
NA2c/e/3c
NA3c/m
PRIOR KNOWLEDGE
Four operations of number
The concepts of a fraction and a decimal
Number complements to 10 and multiplication tables
Awareness that percentages are used in everyday life
OBJECTIVES
By the end of the CHAPTER the student should be able to:
 Understand that a percentage is a fraction in hundredths
 Write a percentage as a decimal; or as a fraction in its simplest terms
 Write one number as a percentage of another number
 Calculate the percentage of a given amount
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 15.1–15.3
Chapter 15
Chapter 15
DIFFERENTIATION AND 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%
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
Reinforce equivalence and the connection between percentage, fraction and decimal.
Mental methods of calculating common percentages, e.g. 17.5% using 10%, 5%, 2.5%.
HOMEWORK
This could include 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.
HINTS AND TIPS
 For non-calculator methods make sure that remainders and carrying are shown.
 In preparation for this unit students should be reminded of basic percentages and recognise their fraction and decimal
equivalents.
 Do Exercises 15A–15D for practice.
FOUNDATION CHAPTER 15B
PERCENTAGES 2
SPECIFICATION REFERENCE
 Adding a percentage of an amount
 Reducing an amount by a percentage
 Adding VAT on to an amount
 Using an index to look at increases and decreases over time
 Writing one number as a percentage of another
 Using percentages to compare different fractions and decimals
 Solving numerical problems involving compound interest
Time: 4–6 hours
NA3m
NA3m
NA3m
NA2e/HD5k
NA3e
NA2e
NA3m
PRIOR KNOWLEDGE
Four operations of number
The concepts of a fraction and a decimal
Number complements to 10 and multiplication tables
Awareness that percentages are used in everyday life
OBJECTIVES
By the end of the chapter the student should be able to:
 Find a percentage increase/decrease, of an amount
 Calculate simple and compound interest for two, or more, periods of time
 Calculate an index number
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 15.4–15.10
Chapter 15
Chapter 15
DIFFERENTIATION AND EXTENSION
 Combine multipliers to simplify a series of percentage changes
 Problems which lead to the necessity of rounding to the nearest penny, e.g. real-life contexts
 Comparisons between simple and compound interest calculations
 Formulae in simple interest/compound interest methods
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
Reinforce equivalence and the connection between percentage, fraction and decimal.
Mental methods of calculating common percentages, e.g. 17.5% using 10%, 5%, 2.5%.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
The construction of a VAT ready-reckoner table.
HINTS AND TIPS
 For non-calculator methods make sure that remainders and carrying are shown.
 In preparation for this unit students should be reminded of basic percentages and recognise their fraction and decimal
equivalents.
 Do Exercises 15E–15K for practice. Do Mixed Exercise 15 for consolidation.
FOUNDATION CHAPTER 16
COORDINATES AND GRAPHS
Time: 5–7 hours
SPECIFICATION REFERENCE
 Using coordinates in the first quadrant to draw shapes and find the mid-point of a line segment NA6b/SSM3e
 Drawing linear graphs from tabulated data
NA6c
 Using conversion graphs to convert from one measurement to another
NA6c
 Reading distance–time graphs and calculating speed
NA6c
 Drawing curved graphs for real-life situations
NA6e
 Plotting coordinates that include negative numbers
NA6b/SSM3e
 Drawing the graphs of straight line equations
NA6b
 Using coordinates in 1-D, 2-D and 3-D
SSM3e
PRIOR KNOWLEDGE
Experience at plotting points in all quadrants
OBJECTIVES
By the end of the chapter the student should be able to:
 Draw linear graphs from tabulated data, including real-world examples
 Interpret linear graphs, including conversion graphs and distance-time graphs
 Understand the difference between a line and a line segment
 Solve graphically simultaneous equations, e.g. find when/where the car overtakes the bus
 Plot and reading coordinates on a coordinate grid (in all four quadrants)
 Understand that one coordinate identifies a point on a line, two coordinates identify a point in a plane and three coordinates
identify a point in space, and use the terms ‘1-D’, ‘2-D’ and ‘3-D’
 Find the coordinates of the fourth vertex of a parallelogram
 Identify the coordinates of the vertex of a cuboid on a 3-D grid
 Writing down the coordinates of the midpoint of the line connecting two points
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 16.1–16.8
Chapter 16
Chapter 16
DIFFERENTIATION AND EXTENSION
 Plot graphs of the form y = mx + c where pupil has to generate their own table and set out their own axes
 Use a spreadsheet to generate straight-line graphs, posing questions about the gradient of lines
 More able students could extend to identifying regions relating to straight-line graphs
 Draw quadratic graphs
 Use a graphical calculator to draw straight-line graphs
 Find the coordinates of the point of intersection of two lines
 Shade regions in a linear inequality
 Find the coordinates of the point if intersection of the medians of a triangle, and explore further
 Identify the coordinates of the mid-point of a line segment in 3-D
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
Test ability to join points up in consecutive order
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Drawing shapes using co-ordinates.
Use data collected by students to draw linear graphs.
Consolidation work using conversion graphs.
HINTS AND TIPS
 Clear presentation with axes labelled correctly is vital.
 Recognise linear graphs and hence when data may be incorrect.
 Link to graphs and relationships in other subject areas, i.e. science, geography etc.
 Coordinate axes should be labelled.
 Students often have difficulty visualising 3-D coordinates.
 Do Exercises 16A–16J for practice. Do Mixed Exercise 16 for consolidation.
FOUNDATION CHAPTER 17
RATIO AND PROPORTION
Time: 4–6 hours
SPECIFICATION REFERENCE
 Examples of ratios used in everyday life
 Writing ratios in their lowest terms by cancelling
 Finding and using equivalent ratios
 Ratios as 1:n or n:1
 Sharing in a given ratio
 Examples of direct proportion
 Examples in which increasing one quantity causes another quantity to increase in the same ratio
 Using a scale to convert between map distances and ground distances
NA2f
NA2f
NA2f/3n
NA2f
NA3f
NA3n
NA3n
NA2f
PRIOR KNOWLEDGE
Using the four operations
Ability to recognise common factors
Knowledge of fractions
OBJECTIVES
By the end of the chapter the student should be able to:
 Understand what is meant by ratio
 Write a ratio in its simplest form; and find an equivalent ratio
 Share a quantity in a given ratio
 Understand and use examples in direct proportion
 Interpret map/model scales as a ratio
RESOURCES
Foundation Student book
Foundation Practice book
Chapter/section: 17.1–17.8
Chapter 17
DIFFERENTIATION AND EXTENSION
 Similar triangles
 Share quantities in a ratio involving fractions, and decimals
 Use a map to plan a journey, e.g. how long will the journey take travelling at average speed of 40 kmph (or mixed speeds for
different roads)
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Draw a map, e.g. of a room in your house.
Use a map to work out a distance, e.g. the real distance between two exits on a motorway.
Plan a journey on a map.
HINTS AND TIPS
 Students often cope well with ratios of two quantities.
 They have greater difficulty with ratios of three quantities and particular attention needs to be given to this.
 Do Exercises 17A–17H for practice. Do Mixed Exercise 17 for consolidation.
FOUNDATION CHAPTER 18
SYMMETRY
SPECIFICATION REFERENCE
 Finding lines of symmetry and completing shapes given their lines of symmetry
 Line symmetry in more complicated shapes
 Finding the order of rotational symmetry of various shapes
 Line symmetry and rotational symmetry of regular polygons
Time: 2–4 hours
SSM3a/3b
SSM3a/3b
SSM3a/3b
SSM3a/3b
PRIOR KNOWLEDGE
Chapter 7: 2-D shapes
OBJECTIVES
 Identify reflection and rotation symmetry in 2-D shapes (including shapes with patterns)
 Complete a diagram given one (or two) lines of symmetry
 State the order of rotational symmetry
 For regular polygons, see the relationship between the order of rotational symmetry and the number of lines of symmetry
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 18.1–18.4
Chapter 18
Chapter 18
DIFFERENTIATION AND EXTENSION
 Generate snowflake patterns with paper and scissors
 Investigate symmetry in tessellations
 Investigate symmetry in the natural world
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
Do Exercises 18A–18D for practice. Do Mixed Exercise 18 for consolidation.
FOUNDATION CHAPTER 19
SIMPLE PERIMETER, AREA AND VOLUME
SPECIFICATION REFERENCE
 Perimeters of shapes made up of straight lines and circumferences of circles
 Finding areas by counting squares
 Finding volumes by counting cubes
 Using formulae to find areas of rectangles, triangles and composite shapes
 Using the formulae for the volume of a cuboid
 Finding the surface area of cuboids and prisms
 Division of volumes
 Solving problems involving area and volume
 Changing from one unit to another
 Relationship between speed, time and distance and assorted questions
 Maximising areas using a spreadsheet
Time: 7–9 hours
SSM4f
SSM4f
SSM4g
SSM2e/4f
SSM4g
SSM4f
SSM4g
SSM4f/g
SSM4a/4i
SSM4c
SSM4f/NA5f
PRIOR KNOWLEDGE
Chapter 7: 2-D shapes
Chapter 13: 3-D shapes
Chapter 14: Units of measure
Experience of multiply by powers of 10, e.g. 100  100 = 10 000
OBJECTIVES
By the end of the chapter the student should be able to:
 Find the perimeters, areas and volumes of shapes made up from triangles and rectangles
 Find areas and volumes of shapes by counting squares
 Find the surface area of cuboids and prisms
 Solve a range of problems involving area and volume
 Convert between units of area
 Use the relationship between distance, speed and time to solve problems
 Convert between metric units of speed, e.g. km/h to m/s
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 19.1–19.11
Chapter 19
Chapter 19
DIFFERENTIATION AND EXTENSION
 Calculating areas and volumes using formulae
 Using compound shape methods to investigate areas of other standard shapes such as a trapezium or a kite
 Practical activities , e.g. using estimation and accurate measuring to calculate perimeters and areas of classroom/corridor
floors
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include 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.
A fencing problem, such as finding the smallest/largest area with a fixed perimeter.
HINTS AND TIPS
 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.
 Use a distance, speed, time triangle to help students see the relationship between the variables.
 Do Exercises 19A–19N for practice. Do Mixed Exercise 19 for consolidation.
FOUNDATION CHAPTER 20
PRESENTING AND ANALYSING DATA 1
Time: 4–6 hours
SPECIFICATION REFERENCE
 Finding the most common item in a set of data
 Finding the middle value in a set of data
 Finding the mean
 Using the range of a set of data to compare it with other sets of similar data
 The advantages/disadvantages of each kind of average
 Drawing and using stem and leaf diagrams
 Drawing and using pie charts
HD4b
HD4b
HD4b/j
HD4b/5ad
HD4b/5a
HD4a/5b
HD4a/5b
PRIOR KNOWLEDGE
Some experience of the measures of averages
Ability to order numbers
Measuring and drawing angles
Fractions of simple quantities
OBJECTIVES
By the end of the chapter the student should be able to:
 Find the mode, the median, the mean, and the range for (small) sets of data
 Use a stem and leaf diagram to sort data
 Know the advantages/disadvantages of using the different measure of average
 Represent categorical data in a pie chart
 Interpret categorical data in a pie chart
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 20.1–20.7
Chapter 20
Chapter 20
DIFFERENTIATION AND EXTENSION
 Collect data from class, e.g. children per family etc.
 Find measures of average for data collected in a frequency distribution
 Use stem and leaf diagrams with unusual stems, e.g. 234.1, 234.6, 235.1, ...
 Discuss occasions when one average is more appropriate, and the limitations of each average
 Compare distributions and making inferences, using the shapes of distributions and measures of average and spread, e.g.
‘boys are taller on average but there is a much greater spread in heights’
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
A group work assessment through selected questions and mini-projects.
Data handling project coursework task.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Collect data at home for processing in class.
HINTS AND TIPS
 Students tend to select modal class but identify it by the frequency rather than the class description.
 Explain that the median of grouped data is not necessarily from the middle class interval.
 Accurate drawing skills need to be reinforced.
 Angles should be correct to within 2 degrees.
 Do Exercises 20A–20H for practice. Do Mixed Exercise 20 for consolidation.
FOUNDATION CHAPTER 21
FORMULAE AND INEQUALITES
Time: 8–10 hours
SPECIFICATION REFERENCE
 Using words to state the relationship between different quantities
 Using letters to state the relationship between different quantities
 Substituting into algebraic formulae
 Addition, subtraction and multiplication using negative numbers
 Substituting into formulae which include powers of a variable
 Finding the solution to a problem by writing an equation and solving it
 Solving linear inequalities
NA5f
NA5f
NA5f
NA3a
NA5f
NA5e
NA5d
PRIOR KNOWLEDGE
Understanding of the mathematical meaning of the words: expression, simplifying, formulae and equation
Experience of using letters to represent quantities
Substituting into simple expressions using words
Using brackets in numerical calculations and removing brackets in simple algebraic expressions
OBJECTIVES
By the end of the chapter the student should be able to:
 Use letters or words to state the relationship between different quantities
 Substitute positive and negative numbers into simple algebraic formulae
 Substitute positive and negative numbers into algebraic formulae involving powers
 Find the solution to a problem by writing an equation and solving it

Solve linear inequalities in one variable and present the solution set on a number line
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 21.1–21.7
Chapter 21
Chapter 21
DIFFERENTIATION AND EXTENSION
 Use negative numbers in formulae involving indices
 Change the subject of a formula, e.g. given the formula to convert C to F, what is the formula to convert F to C?
 Develop algebraic skills in the Higher specification
 Various investigations leading to generalisations
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
Discussion of situations that lead to formulae.
Spreadsheet tasks such as ‘guess my rule’.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Uses of algebra to describe real situation, e.g. n quadrilaterals have 4n sides.
HINTS AND TIPS
 Emphasis on good use of notation, e.g. 3ab means 3  a  b.
 Students need to be clear on the meanings of the words expression, equation, word formulae and algebraic formulae as they
can find this confusing.
 Do Exercises 21A–21Q for practice. Do Mixed Exercise 21 for consolidation.
FOUNDATION CHAPTER 22
TRANSFORMATIONS
SPECIFICATION REFERENCE
 Understanding translation as a sliding movement with two components
 Understanding that rotation is a turning motion about an angle and with a centre
 Reflecting various shapes in mirror lines in different positions
 Making various shapes larger using different centres of enlargement and scale factors
Time: 2–4 hours
SSM3b
SSM3b
SSM3b
SSM3c
PRIOR KNOWLEDGE
Recognition of basic shapes
An understanding of the concept of rotation, reflection and enlargement
OBJECTIVES
By the end of the chapter the student should be able to:
 Transform triangles and other shapes by translation, rotation and reflection
 Understand translation as a combination of a horizontal and vertical shift
 Understand rotation as a turn about a given origin
 Reflect shapes in a given mirror line
 Enlarge shapes by a given scale factor from a given point
 Distinguish properties that are preserved under transformations, e.g. write down the angles of a triangle that has been
enlarged
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 22.1–22.4
Chapter 22
Chapter 22
DIFFERENTIATION AND EXTENSION
The tasks set can be extended to include combinations of transformations
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
Practical poster work.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
 Diagrams should be drawn carefully.
 The use of tracing paper is allowed in the examination.
 Do Exercises 22A–22D for practice. Do Mixed Exercise 22 for consolidation.
FOUNDATION CHAPTER 23A
PROBABILITY 1
SPECIFICATION REFERENCE
 Comparing probabilities. How likely is it?
 Finding a number to represent a probability
 Simple probability
Time: 2–4 hours
HD4c/5g
HD4d
HD4c
PRIOR KNOWLEDGE
Some idea of chance and the likelihood of an event happening; and recognition that some events are more likely than others
Experience of using the language of likelihood
OBJECTIVES
By the end of the chapter the student should be able to:
 Use the language of probability to describe the likelihood of an event
 Represent and compare probabilities on a number scale
 List outcomes for single mutually exclusive events and write down their probability
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 23.1–23.3
Chapter 23
Chapter 23
DIFFERENTIATION AND EXTENSION
 Write down probabilities of events that may or may not happen
 Play simple probability games, predicting outcomes , horse race for sum of two dice
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
 Where possible introduce practical work to support the theoretical work.
 Only fractions, decimals or percentages should be used for probability.
 Do Exercises 23A–23C for practice.
FOUNDATION CHAPTER 23B
PROBABILITY 2
Time: 2–4 hours
SPECIFICATION REFERENCE
 Working out the probability that something will not happen if you know the probability that it will happen
 Estimating a probability from the results of an experiment
 Using a diagram to record all the possibilities
 Using the information contained in a two-way table to find an estimate of probability
 Estimating probability by relative frequency
HD4d/5g/h/i/j
HD4f
HD4d/5i/j
HD4e
HD3c/4d
PRIOR KNOWLEDGE
Chapter: 23A Probability 1
Ability to read from a two-way table
OBJECTIVES
By the end of the chapter the student should be able to:
 Write down the theoretical probability for an equally likely event
 Estimate a probability by relative frequency
 Know that a better estimate for a probability is achieved by increasing the number of trials
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 23.4–23.8
Chapter 23
Chapter 23
DIFFERENTIATION AND EXTENSION
The work can be extended to include that of the Higher specification
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS ANDTIPS
 Students can be unsure of the relationship P(not n) = 1 – P(n).
 Only fractions, decimals or percentages should be used for probability.
 Do Exercises 23D–23H for practice. Do Mixed Exercise 23 for consolidation.
FOUNDATION CHAPTER 24A
PRESENTING AND ANALYSING DATA 2A
Time: 2–4 hours
SPECIFICATION REFERENCE
Drawing and using scatter diagrams and lines of best fit; correlation
HD4a/h/5b/f
PRIOR KNOWLEDGE
Plotting coordinates
An understanding of the concept of a variable
Recognition that a change in one variable can affect another
Linear graphs
OBJECTIVES
By the end of the chapter the student should be able to:
 Draw and produce a scatter graph
 Appreciate that correlation is a measure of the strength of association between two variables
 Distinguish between positive, negative and zero correlation using a line of best fit
 Appreciate that zero correlation does not necessarily imply ‘no correlation’ but merely ‘no linear relationship’
 Draw line of best fit by eye and understand what it represents
 Find the equation of the line of best fit and use it to interpolate/extrapolate
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 24.1
Chapter 24
Chapter 24
DIFFERENTIATION AND EXTENSION
 Vary the axes required on a scatter graph to suit the ability of the class.
 Carry out a statistical investigation of their own including; designing an appropriate means of gathering the data, and an
appropriate means of displaying the results.
 Use a spreadsheet, or other software, to produce scatter diagrams/lines of best fit. Investigate how the line of best fit is
affected by the choice of scales on the axes
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
Test a given hypothesis either using data provided or by collecting data from the class.
Their own statistical investigation.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Completion of simple statistical project.
HINTS AND TIPS
 Students should realise that lines of best fit should have the same gradient as the correlation of the data.
 Clearly label all axes on graphs and use a ruler to draw straight lines.
 Do Exercises 24A for practice.
FOUNDATION CHAPTER 24B
PRESENTING AND ANALYSING DATA 2B
Time: 3–5 hours
SPECIFICATION REFERENCE
 Finding the mean, median and mode of a set of data; using appropriate averages
 Finding the mean, mode and median from frequency tables
 Finding the range and interquartile range from a frequency table
 Finding the mean, mode, median from grouped frequency tables
HD4b
HD4g/j
HD4b
HD4g
PRIOR KNOWLEDGE
Chapter 20: Presenting and analysing data 1
Finding the average of two number, i.e. the midpoint
OBJECTIVES
By the end of the chapter the student should be able to:
 Identify the modal class interval in grouped and ungrouped frequency distributions
 Find the class interval containing the median value
 Find the mean of an ungrouped frequency distribution
 Find an estimate for the mean of a grouped frequency distribution by using the mid-interval value
 Use the statistical functions on a calculator or a spreadsheet to calculate the mean for discrete data
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 24.2–24.5
Chapter 24
Chapter 24
DIFFERENTIATION AND EXTENSION
 Find the mean for grouped and continuous data with unequal class intervals
 Collect continuous data and decide on appropriate (equal) class intervals; then find measures of average
 Find the median by cumulative frequency diagram
 Consider other measures of spread, e.g. interquartile range; appreciate advantages/limitations of the range
 Use the statistical functions on a calculator or a spreadsheet to calculate the mean for continuous data
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
Test a given hypothesis either using data provided or by collecting data from the class.
GCSE coursework.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Completion of simple statistical project.
HINTS AND TIPS
 Students should be aware that the actual mean can not be calculated from a grouped frequency distribution; and that using
the midpoint of the class intervals gives the best estimate for the mean.
 The modal class is found for grouped frequency distributions in which the class intervals have an equal.
 Do Exercises 24B–24E for practice. Do Mixed Exercise 24 for consolidation.
FOUNDATION CHAPTER 25
PYTHAGORAS’ THEOREM
SPECIFICATION REFERENCE
 Using Pythagoras’ theorem to calculate the length of the hypotenuse
 Using Pythagoras’ theorem to find one of the shorter sides of a right-angle triangle
Time: 3–5 hours
SSM2h/NA4d
SSM2h/NA4d
PRIOR KNOWLEDGE
Recognise right-angled triangles in different orientations
Be able to square a number with and without a calculator
Be able to rearrange an equation
Be able to use a calculator to taker the square root of a number
Give an answer to one decimal place
OBJECTIVES
 Find the length of the missing side in a right-angled triangle (only 2-D examples)
 Recall and use Pythagoras’ theorem
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 25.1–25.2
Chapter 25
Chapter 25
DIFFERENTIATION AND EXTENSION
 Find the distance of the line segment between two given points on a coordinate grid
 Use Pythagoras’ theorem in multi-step questions involving two right-angled triangles
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
 Students should be encouraged to learn both a linguistic and a mathematical statement of Pythagoras’ theorem.
 Do Exercises 25A–25C for practice. Do Mixed Exercise 25 for consolidation.
FOUNDATION CHAPTER 26A
ADVANCED PERIMETER, AREA AND VOLUME 1
Time: 7–9 hours
SPECIFICATION REFERENCE
 Perimeter and area of triangles and quadrilaterals
 Introducing pi and the formula for the circumference of a circle
 Developing the formula for the area of a circle
 Compound shapes made from circle parts, e.g. semicircles, quadrants
 Surface areas and volumes of prisms
SSM4f
SSM2i/4h
SSM4h
SSM2i/4h
SSM4f/g
PRIOR KNOWLEDGE
The ability to substitute numbers into formulae
OBJECTIVES
By the end of the chapter the student should be able to:
 Use formulae to find the surface area of shapes made up of rectangles and triangles
 Solve problems involving the circumference and area of a circle (and simple fractional parts of a circle)
 Solve problems involving the volume of a cylinder
 Find exact answers by leaving answers in terms of pi
 Understand a formula by considering its dimensions, e.g. identify formulae that represent area from a list
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 26.1–26.5
Chapter 26
Chapter 26
DIFFERENTIATION AND EXTENSION
 Use more complex 2-D shapes, e.g. (harder) sectors of circles
 Use more complex 3-D shapes, e.g. half-cylinders
 Surface area of cylinder/half-cylinder
 Approximate pi as 22
7
 Consider the dimensions of harder formulae, e.g. the surface area of a cone (including base)
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
Need to constantly revise the expressions for area/volume of shapes.
HINTS AND TIPS
 Need to constantly revise the expressions for area/volume of shapes.
 Do Exercises 26A–26M for practice.
FOUNDATION CHAPTER 26B
ADVANCED PERIMETER, AREA AND VOLUME 2
Time: 3–5 hours
SPECIFICATION REFERENCE
 Degrees of accuracy of given measurements
 Using sensible units for various measurements
 Using speed and density formulae
 Converting between units of speed
 Changing units as necessary
SSM4a
SSM4a
SSM4c
SSM4a
SSM4a
PRIOR KNOWLEDGE
Knowledge of metric units, e.g. 1 m = 100 cm, etc.
Know that 1 hour = 60 mins, 1 min = 60 seconds
Experience of multiply by powers of 10, e.g.. 100  100 = 10 000
OBJECTIVES
By the end of the chapter the student should be able to:
 Use the relationship between distance, speed and time to solve problems
 Convert between metric units of speed, e.g. km/h to m/s
 Know that density is found by mass ÷ volume
 Use the relationship between density, mass and volume to solve problems
 Convert between metric units of density, e.g. kg/m to g/cm
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 26.6–26.10
Chapter 26
Chapter 26
DIFFERENTIATION AND EXTENSION
 Perform calculations on a calculator by using standard form
 Convert imperial units to metric units, e.g. mph into kmph
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
 Use a distance, speed and time triangle to help students see the relationship between the variables.
 Do Exercises 26N–26S for practice. Do Mixed Exercise 26 for consolidation.
FOUNDATION CHAPTER 27
DESCRIBING TRANSFORMATIONS
Time: 4 –6 hours
SPECIFICATION REFERENCE
 Describing translations using column vectors
 Describing a reflection by giving the equation of a mirror line
 Describing a rotation by giving the angle, the direction and the centre of rotation
 Describing an enlargement by giving the scale factor and centre
SSM3a/b/f
SSM3a/b
SSM3a/b
SSM3c/3d
PRIOR KNOWLEDGE
Coordinates in four quadrants
Linear equations parallel to the coordinate axes
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 27.1–27.4
Chapter 27
Chapter 27
OBJECTIVES
By the end of the chapter the student should be able to:
 Transform triangles and other shapes by translation, rotation and reflection including combinations of transformations
 Understand translation as a combination of a horizontal and vertical shift including vector notation
 Understand rotation as a clockwise turn about a given origin
 Reflect shapes in a given mirror line. Initially line parallel to the coordinate axes and then y = x or y = –x
 Enlarge shapes by a given scale factor from a given point; using positive whole number scale factors, then positive fractional
scale factors
 Distinguish properties that are preserved under transformations, e.g. write down the angles of a triangle that has been
enlarged
DIFFERENTIATION AND EXTENSION
The tasks set can be extended to include combinations of transformations
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
 Emphasis needs to be placed on ensuring that students do describe the given transformation fully.
 Do Exercises 27A–27F for practice. Do Mixed Exercise 27 for consolidation.
FOUNDATION CHAPTER 28
EXPRESSING, FORMULAE, EQUATIONS AND GRAPHS
Time: 8–10 hours
SPECIFICATION REFERENCE
 Multiplying out brackets
 Graphs of functions y = ax2 + c where a and c can be positive or negative
 Graphs of functions y = ax2 + bx + c
 Using graphs to solve equations such as ax2 + bx + c = d
 Assorted situations treated graphically
 Changing the subject of a formula
 Solving equations of the form ax2 + bx = c or a/x = b
 Solving cubic equations using trial and improvement
 Using a spreadsheet to solve cubic equations by trail and improvement
NA5b
NA6e
NA6e
NA6e
NA6d
NA5f
NA5e
NA5m
NA5m
PRIOR KNOWLEDGE
Substituting numbers into algebraic expressions
Plotting points on a coordinate grid
Experience of dealing with algebraic expression with one pair of brackets
Know ax  bx  (ab) x , where a and b are integers
Substituting numbers into algebraic expressions
Dealing with decimals on a calculator
Ordering decimals
2
OBJECTIVES
By the end of the chapter the student should be able to:
 Substitute values of x into a quadratic function to find the corresponding values of y
 Draw graphs of quadratic functions
 Use quadratic graphs to solve quadratic equations
 Solve quadratic and reciprocal functions
 Expand and simplify expressions with two pairs of brackets
 Solve cubic functions by successive substitution of values of x
RESOURCES
Foundation Student book
Foundation Practice book
Teaching and Learning software
Chapter/section: 28.1–28.9
Chapter 28
Chapter 28
DIFFERENTIATION AND EXTENSION
 Draw simple cubic graphs
 Solve graphically simultaneous equations involving a quadratic graph and a line

Solve functions of the form
1
 x2  5
x
ASSESSMENT
Heinemann online assessment tool will be available in 2007.
HOMEWORK
This could include consolidation of work in class by completion of exercises set, additional work of a similar nature, or extension
work detailed above.
HINTS AND TIPS
 The graphs of quadratic functions should be drawn freehand; and in pencil. Turning the paper often helps.
 Squaring negative integers may be a problem for some.
 Students will often forget the middle term of the expansion- they will need to be reminded later.
 Students should be encouraged to use their calculators efficiently- by using the ‘replay’ function.
 The cube function on a calculator may not be the same for different makes.
 Students should write down all the digits on their calculator display.
 Do Exercises 28A–28M for practice. Do Mixed Exercise 28 for consolidation.