AQA GCSE Maths Schemes of Work – writing brief D R A F...

Longman AQA GCSE Mathematics Two-year Modular Scheme of Work – Starting with Unit 1 – for Foundation sets

OVERVIEWNotes to Teacher:1. At a minimum, aim for completion of Chapters 1–3 by the end of Year 9.2. At a minimum, aim for completion of Chapters 4–9 by the October half-term of Year 10.3. The assumption is that the March and June exams are at the beginning of March and June respectively.4. Unit 2 revision will need to include the earlier work on ratio (Chapters 4 and 10).

Chapter Teaching hours

Grades AQA Modular specification reference

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UNIT 1: Statistics and Number1. Data collection 5 F, E, D, C The Data Handling Cycle: S1

Data Collection: S2.1, S2.2, S2.3, S2.4Data presentation and analysis: S3.1

2. Interpreting and representing data 1

3 G, F, C Data presentation and analysis: S3.2Data Interpretation: S4.1, S4.4

3. Number skills 1 4 G, F, E, D Working with numbers and the number system: N1.1, N1.2, N1.3, N1.4, N1.5, N1.14Fractions, Decimals and Percentages: N2.1, N2.3, N2.7Measures and Construction: G3.4

4. Fractions, decimals, percentages and ratio

5 G, F, E, D, C Fractions, Decimals and Percentages: N2.5, N2.6, N2.7Ratio and Proportion: N3.1, N3.3

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5. Interpreting and representing data 2

5 F, E, D, C Data presentation and analysis: S3.2Data Interpretation S4.1, S4.2, S4.3

6. Range and averages 4 G, F, E Data presentation and analysis: S3.3Data Interpretation: S4.1

7. Probability 1 4 G, F, E, D Probability: S5.1, S5.2, S5.3, S5.48. Probability 2 4 E, D, C Data Collection: S2.5

Data presentation and analysis: S3.1, S3.2Probability: S5.2, S5.5h, S5.7, S5.8, S5.9

9. Range, averages and conclusions

4 F, E, D, C Data presentation and analysis: S3.3Data Interpretation: S4.1, S4.4

10. Ratio and proportion 4 D, C Ratio and Proportion: N3.1, N3.2, N3.3UNIT 2: Number and Algebra

11. Number skills 2 5 G, F, E, D, C Working with numbers and the number system: N1.2, N1.3, N1.4, N1.512. Multiples, factors, powers and roots

6 G, F, E, D, C Working with numbers and the number system: N1.6, N1.7, N1.8, N1.9

13. Basic rules of algebra

6 F, E, D, C The Language of Algebra: N4.1Expressions and Equations: N5.1

© Pearson Education Limited 2010 1


14. Fractions 7 G, F, E, D, C Working with numbers and the number system: N1.3Fractions, Decimals and Percentages: N2.1, N2.2, N2.7

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15. Decimals 5 F, E, D, C Working with numbers and the number system: N1.2Fractions, Decimals and Percentages: N2.3, N2.4

16. Equations and inequalities

5 F, E, D, C Expressions and Equations: N5.4, N5.7

UNIT 1 REVISION FOR MARCH EXAM (6 HOURS)17. Indices and formulae 6 G, F, E, D, C Working with numbers and the number system: N1.8, N1.9

The Language of Algebra: N4.2Expressions and Equations: N5.6

18. Percentages 5 E, D, C Fractions, Decimals and Percentages: N2.5, N2.7, N2.7h19. Sequences and proof

6 G, F, E, D, C Expressions and Equations: N5.9Sequences, Functions and Graphs: N6.1, N6.2

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20. Coordinates and linear graphs

7 G, F, E, D, C Sequences, Functions and Graphs: N6.3, N6.4, N6.11, N6.12

UNIT 2 REVISION FOR JUNE EXAM (8 HOURS)

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UNIT 3: Geometry and Algebra21. Number skills revisited

3 Working with numbers and the number system: N1.3, N1.4, N1.14Fractions, decimals and Percentages: N2.1, N2.5, N2.7Ratio and Proportion: N3.1

22. Angles 5 G, F, E, D, C Properties of angles and shapes: G1.1, G1.2Measures and Construction: G3.6, G3.8

23. Measurement 1 4 G, F, E Working with numbers and the number system: N1.3Measures and Construction: G3.3, G3.5

24. Triangles and constructions

4 G, E, D, C Properties of angles and shapes: G1.2, G1.8Measures and Construction: G3.9, G3.10

25. Equations, formulae and proof

3 D, C The Language of Algebra: N4.2Expressions and Equations: N5.1, N5.4, N5.6Geometrical reasoning and calculation: G2.3

U1/U2 REVISION FOR NOVEMBER RE-SITS (5 HOURS)26. Quadrilaterals and other polygons

6 G, F, E, D, C Expressions and Equations: N5.4Sequences, Functions and Graphs: N6.3Properties of angles and shapes: G1.2, G1.3, G1.4, G1.6

27. Units and scale 2 E Measures and Construction: G3.1, G3.428. Perimeter, area and volume

6 F, E, D, C Mensuration: G4.1, G4.4

29. 3-D objects 2 G, F, E, D Geometrical reasoning and calculation: G2.4



30. Reflection, translation and rotation

5 G, F, E, D, C Properties of angles and shapes: G1.7Vectors: G5.1

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31. Circles and cylinders 7 G, D, C Properties of angles and shapes: G1.5Mensuration: G4.1h, G4.3, G4.4

32. Measurement 2 3 D, C Working with numbers and the number system: N1.4, N1.13hMeasures and Construction: G3.4, G3.7

33. Enlargement 3 F, E, D Properties of angles and shapes: G1.7Measures and Construction: G3.2

34. Trial and improvement

2 D, C Working with numbers and the number system: N1.14Expressions and Equations: N5.8

U1/U2 REVISION FOR MARCH RE-SITS (5 HOURS)35. Quadratic graphs 5 D, C Sequences, Functions and Graphs: N6.12, N6.1336. Constructions and loci

4 C Measures and Construction: G3.10, G3.11

37. Pythagoras’ theorem 6 C Geometrical reasoning and calculation: G2.1

UNIT 3 REVISION FOR JUNE EXAM (19 HOURS)Y11 SUMMER TERM

[Full detail begins on next page]



Chapter 1 Data collection Time: 5 hours

S1 Understand and use the statistical problem solving process which involves specifying the problem and planning collecting data processing and presenting the data interpreting and discussing the results.

S2.1 Types of data: qualitative, discrete, continuous. Use of grouped and ungrouped data.S2.2 Identify possible sources of bias.S2.3 Design an experiment or survey.S2.4 Design data collection sheets distinguishing between different types of data.S3.1 Design and use two-way tables for grouped and ungrouped data.

Learning objectives

Grade Resource Common mistakes and misconceptions Support and homework Extra support

AQA Modular specification reference

AQA GCSE Maths Foundation sets Student Book; Foundation sets Teacher Guide

Foundation sets Teacher Guide

Foundation sets Practice Book

G-F Practice Book

S1 Learn about the data handling cycleKnow how to write a hypothesis

D Section 1.1 Formulating a hypothesis that cannot be tested.Thinking that a hypothesis is not valuable if it is eventually proved false.

Section 1.1

S2.3, S2.4 Know where to look for information

D Section 1.2 Not realising that data collected by a third party (even if the results of a survey or experiment) is classed as secondary data.

Section 1.2

S2.1 Be able to identify different types of data

D Section 1.3 Not appreciating that some data can be treated as either discrete or continuous depending on the context (e.g. age – this is really continuous, but is often treated as discrete, such as when buying child or adult tickets).

GPW 1.3 Section 1.3



S2.4 Work out methods for gathering data efficiently

F, E Section 1.4 Using shortcuts in the tallying process – counting up the items in each class, rather than tallying items one by one.

Section 1.4 Section 1.1

S2.4 Work out methods for gathering data that can take a wide range of values

D Section 1.5 Using overlapping class intervals.Recording data which is on the boundary of a class interval in the wrong class.

Section 1.5

S3.1 Work out methods for recording related data

D Section 1.6 Not checking that the totals in two-way tables add up.

Section 1.6

S2.3, S2.4 Learn how to write good questions to find out information

C Section 1.7 Using overlapping classes, or gaps between classes, for response options.

Section 1.7

S2.2, S2.3, S2.4

Know the techniques to use to get a reliable sample

C Section 1.8 Mistaking biased samples for random samples.

Section 1.8



Chapter 2 Interpreting and representing data 1 Time: 3 hours

S3.2 Produce charts and diagrams for various data types. Scatter graphs, stem-and-leaf, tally charts, pictograms, bar charts, dual bar charts, pie charts, line graphs, frequency polygons, histograms with equal class intervals.S4.1 Interpret a wide range of graphs and diagrams and draw conclusions.S4.4 Compare distributions and make inferences.

Learning objectives






G-F Practice Book

S3.2, S4.1 Draw a pictogramInterpret a pictogram

G Section 2.1 Forgetting to include a key when drawing a pictogram.Not drawing parts of the shape accurately.


S3.2, S4.1 Draw bar chart for ungrouped dataInterpret a bar chartDraw and interpret vertical line graphsDraw dual and compound bar chartsUse dual and compound bar charts to make comparisons

G, F Section 2.2 Confusing the two axes when the data is numerical. Drawing bars which are not equal in width.

GPW 2.2 Section 2.2 Section 2.2

S3.2, S4.1, S4.4

Draw frequency polygons for grouped data

C Section 2.3 Using a grouped label on the horizontal axis rather than a continuous scale.

GPW 2.3 Section 2.3



Chapter 3 Number skills 1 Time: 4 hours

N1.1 Understand integers and place value to deal with arbitrarily large positive numbers.N1.2 Add, subtract, multiply and divide any number.N1.3 Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.N1.4 Approximate to a given power of 10, up to three decimal places and one significant figure.N1.5 Order rational numbers.N1.14 Use calculators effectively and efficiently, including statistical functions.N2.1 Understand equivalent fractions, simplifying a fraction by cancelling all common factors.N2.3 Use decimal notation and recognise that each terminating decimal is a fraction.N2.7 Calculate with fractions, decimals and percentages.G3.4 Convert measurements from one unit to another.

Learning objectives






G-F Practice Book

N1.1, N1.5 Read and write whole numbers in figures and wordsUse place valueCompare and order whole numbers

G Section 3.1 Failing to understand the concept of place value and so reading 204 as 24 (20, 4 twenty-four).


N1.5, N2.3 Read and write decimal numbers in figures and in wordsUse decimal notation and place value

F, E Section 3.2 Thinking that the more digits in a number, the greater the value of the number.




Compare and order decimal numbers

N1.4 Round positive numbers to the nearest 10, 100 or 1000Round decimals to the nearest whole numberRound decimals to a given number of decimal placesRound numbers to one significant figure

G, F, E Section 3.3 Treating the digits on each side of the decimal point as separate whole numbers, so giving 0.95 rounded to 1 d.p. as 0.1.


G3.4 Convert between different metric units of length, mass and capacity

F Section 3.4 Ignoring the different units when comparing measurements.


N2.1, N2.7 Use fraction notationIdentify equivalent factionsSimplify fractionsFind fractions of quantities and measurements

G, F Section 3.5 Not understanding that the denominator of a fraction represents the ‘number of parts in the whole’.


N1.2, N1.3, N1.14

Understand and use the order of operationsUse the four rules with whole numbers, decimals and fractionsDevelop calculator

G, F, E, D

Section 3.6 Forgetting to use BIDMAS when using calculators to perform calculations.




skills and use a calculator effectively



Chapter 4 Fractions, decimals, percentages and ratio Time: 5 hours

N2.5 Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.N2.6 Interpret fractions, decimals and percentages as operators.N2.7 Calculate with fractions, decimals and percentages.N3.1 Use ratio notation, including reduction to its simplest form and its various links to fraction notation.N3.3 Solve problems involving ratio and proportion, including the unitary method of solution.

Learning objectives






G-F Practice Book

N2.5, N2.6, N2.7

Find a percentage of an amount without using a calculatorFind a percentage of an amount with a calculatorFind percentages of amounts in more complex situations

F, E, D Section 4.1 Thinking that percentages over 100% cannot exist.Treating a percentage such as 0.05% as though it were 5%.Adding the percentage to the cost when finding a percentage increase (e.g. £315 + 15% VAT = £330).


N2.7 Write one quantity as a percentage of anotherWrite one quantity as a percentage of another in more complex situations

D, C Section 4.2 Not using the original amount as the denominator, when finding a percentage difference.Working with quantities in different units.

Section 4.2

N2.7 Convert between G Section 4.3 Incorrectly multiplying numbers with one GPW 4.3 Section 4.3 Section 4.2



fractions, decimals and percentages

decimal place by 10, rather than 100, when converting a decimal to a percentage.

N2.7 Understand and use a retail prices indexUnderstand and use a retail prices index in more complex situations

D, C Section 4.4 Using a previously found price instead of the base year price.

Section 4.4

N3.1, N3.3 Simplify a ratio to its lowest termsUse a ratio when comparing a scale model to the real-life objectUse a ratio in practical situations

E, D Section 4.5 Swapping over the numbers in the ratio (e.g. 2 : 5 becomes 5 : 2). Simplifying ratios without ensuring the quantities are in the same units.

GPW 4.5 Section 4.5

N3.1 Write a ratio as a fractionUse a ratio to find one quantity when the other is known

D, C Section 4.6 Turning a ratio into a fraction (e.g. the ratio 4 : 5 becomes ).Failing to find the value of the unit fraction in more complex problems.

GPW 4.6 Section 4.6

N3.3 Write a ratio in the form 1 : n or n : 1

C Section 4.7 Ignoring different units in a ratio (e.g. simplifying 2 days : 15 hours to 1 : 7½) .

GPW 4.7 Section 4.7



Chapter 5 Interpreting and representing data 2 Time: 5 hours

S3.2 Produce charts and diagrams for various data types. Scatter graphs, stem-and-leaf, tally charts, pictograms, bar charts, dual bar charts, pie charts, line graphs, frequency polygons, histograms with equal class intervals.S4.1 Interpret a wide range of graphs and diagrams and draw conclusions.S4.2 Look at data to find patterns and exceptions.S4.3 Recognise correlation and draw and/or use lines of best fit by eye, understanding what they represent.

Learning objectives






G-F Practice Book

S3.2, S4.1 Interpret a pie chart

F Section 5.1 Looking at the angle in a pie chart and ignoring the fact that the pie chart can represent a different number of people.


S3.2, S4.1 Draw a pie chart E Section 5.2 Not drawing the angles in the pie chart accurately or using the appropriate scale on the protractor.Measuring each angle from the same starting point.

GPW 5.2 Section 5.2

S3.2 Draw a stem-and-leaf diagram

D Section 5.3 Forgetting to put a key and order the leaves. Forgetting to recombine the stem and leaf and just giving the leaf as the value.

Section 5.3

S3.2, S4.2, S4.3

Draw a scatter diagram on a given gridInterpret points on a scatter diagram

D Section 5.4 Assuming that all the plotted points must be joined with a line. Drawing the diagram without spending time working out the best scale.

Section 5.4

S3.2, S4.2, S4.3

Draw a line of best fit on a scatter

D, C Section 5.5 Trying to make the line of best fit go through the origin, rather than drawing it

Section 5.5



diagramDescribe types of correlationUse the line of best fit

appropriately.

S3.2 Draw a frequency diagram for grouped data

D Section 5.6 Using grouped labels on the data axes (e.g. 15–20, rather than the ends of the bar being clearly marked with a 15 at one end and a 20 at the other end).

Section 5.6



Chapter 6 Range and averages Time: 4 hours

S3.3 Calculate median, mean, range, mode and modal class.S4.1 Interpret a wide range of graphs and diagrams and draw conclusions.

Learning objectives






G-F Practice Book

S3.3 Calculate the range of a set of data

F Section 6.1 Failing to spot the largest or smallest values.Not checking that all the data values are given in the same unit before calculating the range.

GPW 6.1-6.4


S3.3 Find the mode of a set of data

G Section 6.2 Writing down the number of times the modal value occurs and not the data value itself.Omitting units when writing the mode.

GPW 6.1-6.4


S3.3 Find the median of an odd number of pieces of dataFind the median of an even number of pieces of data

G, F Section 6.3 Choosing one of the two middle values when finding the median of an even number of data values.

GPW 6.1-6.4


S3.3 Calculate the mean of a set of data

F, E Section 6.4 Not pressing the = key to find the total of the data values before dividing, when using a calculator.

GPW 6.1-6.4


S3.3 Find the mode and range from a frequency table.Calculate the total frequency from a

F Section 6.5 Confusing the frequencies and the data values.

GPW 6.5/6.6




frequency table.Find the median from a frequency table

S3.3, S4.1 Write down the mode from a bar chart or pie chartFind the range from a bar chartFind the mean, median and range from a stem-and-leaf diagram

G, F, E Section 6.6 Writing the frequency rather than the data value when finding the mode.

GPW 6.5/6.6




Chapter 7 Probability 1 Time: 4 hours

S5.1 Understand and use the vocabulary of probability and the probability scale.S5.2 Understand and use estimates or measures of probability from theoretical models (including equally likely outcomes), or from relative frequency.S5.3 List all outcomes for single events, and for two successive events, in a systematic way and derive related probabilities.S5.4 Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1.

Learning objectives






G-F Practice Book

S5.1 Understand and use some of the basic language of probability

G Section 7.1 Incorrectly interpreting the event. Section 7.1 Section 7.1

S5.3 List all possible outcomes for an experimentList all possible outcomes for a combined event

G, F Section 7.2 Working in a haphazard way when giving possible combinations, thus missing one or more combinations.


S5.1 Understand and use the basic language of probabilityUnderstand, draw and use a probability scale from 0 to 1

G, F Section 7.3 Not considering all the conditions that may affect an event.


S5.2 Find the probability F Section 7.4 Incorrectly giving the probability of, for GPW 7.4 Section 7.4 Section



of an outcome example, rolling a 2 on a dice as: P(rolling a

2) = .

Not realising that = .

7.3

S5.1, S5.2 Work out the probability of an event that can happen in more than one way

F Section 7.5 Not understanding the language of, for example, ‘greater than 4’ and ‘at least 4’.


S5.4 Work out the probability of an event not happening when you know the probability that it will happen

E Section 7.6 Incorrectly subtracting decimals from 1. Section 7.6

S5.4 Understand and use the fact that the sum of the probabilities of all mutually exclusive outcomes is 1

D Section 7.7 Not reading questions carefully enough and so adding or subtracting incorrect values.

GPW 7.7 Section 7.7



Chapter 8 Probability 2 Time: 4 hours

S2.5 Extract data from printed tables and lists.S3.1 Design and use two-way tables for grouped and ungrouped data.S3.2 Produce charts and diagrams for various data types. Scatter graphs, stem-and-leaf, tally charts, pictograms, bar charts, dual bar charts, pie charts, line graphs, frequency polygons, histograms with equal class intervals.S5.2 Understand and use estimates or measures of probability from theoretical models (including equally likely outcomes), or from relative frequency.S5.5h Know when to add or multiply two probabilities: if A and B are mutually exclusive, then the probability of A or B occurring is P(A) + P(B), whereas if A and B are independent events, the probability of A and B occurring is P(A) × P(B). [Note: Listing events in a sample space diagram can be used instead of multiplying individual probabilities. (Multiplying will only be expected at Higher tier.)] S5.7 Compare experimental data and theoretical probabilities.S5.8 Understand that if an experiment is repeated, this may – and usually will – result in different outcomes.S5.9 Understand that increasing sample size generally leads to better estimates of probability and population characteristics.

Learning objectives






G-F Practice Book

S3.2, S5.2 Work out probabilities from a variety of frequency diagrams

E Section 8.1 Incorrectly reading the vertical axis of bar charts.Not understanding a grouped frequency table.


S2.5, S3.1 Draw and use two-way tables and sample space diagrams

E, D Section 8.2 Not considering each cell in the sample space diagram individually, but often completing one or two cells correctly, then following a perceived, but often wrong, pattern.Not reading a question carefully and so giving information not requested.

GPW 8.2 Section 8.2

S5.2 Predict the likely D Section 8.3 Incorrectly finding fractions of an amount. GPW 8.3 Section 8.3



number of successful events given the probability of any outcome and the number of trials or experiments

S5.2, S5.7, S5.8, S5.9

Estimate probabilities from experimental data

C Section 8.4 Trying to plot decimals worked out to three decimal places or more. Comparing theoretical probability with relative frequency without taking into account the number of trials carried out.

Section 8.4

S5.5h Calculate the probability of two independent events happening at the same time

C Section 8.5 Not recognising when a question involves independent events and so adding rather than multiplying the fractions.

GPW 8.5 Section 8.5



Chapter 9 Range, averages and conclusions Time: 4 hours

S3.3 Calculate median, mean, range, mode and modal class.S4.1 Interpret a wide range of graphs and diagrams and draw conclusions.S4.4 Compare distributions and make inferences.

Learning objectives






G-F Practice Book

S3.3, S4.1 Calculate the total frequency from a frequency tableCalculate the mean from an ungrouped frequency table

F, D, C Section 9.1 Dividing by the number of rows in the frequency table (i.e. the number of different data values) and not by the sum of the frequencies.


S3.3, S4.1 Find the modal class from a grouped frequency tableEstimate the range from a grouped frequency tableWork out which class interval contains the median from data given in a grouped frequency tableEstimate the mean

D, C Section 9.2 Incorrectly calculating the mid-points of class intervals for grouped discrete data (e.g. the mid-point of the class interval 10–19 is 14.5, not 15).Interpreting ‘find an estimate for the mean’ as ‘guess the mean’.

GPW 9.2 Section 9.2



of data given in a grouped frequency table

S3.3, S4.1 Draw conclusions from statistics and from data given in tables and diagramsExplain why a sample may not be representative of a whole population

E, D Section 9.3 Failing to provide evidence for conclusions. Section 9.3

S4.4 Compare two sets of data using the mean, median and rangeCompare two sets of data given in frequency tables or diagrams

E, D Section 9.4 Not appreciating that similarities as well as differences can be talked about when comparing two sets of data.

Section 9.4



Chapter 10 Ratio and proportion Time: 4 hours

N3.1 Use ratio notation, including reduction to its simplest form and its various links to fraction notation.N3.2 Divide a quantity in a given ratio.N3.3 Solve problems involving ratio and proportion, including the unitary method of solution.

Learning objectives






G-F Practice Book

Number skills: ratio (N3.1, N3.3) Section 10.1

N3.1, N3.2, N3.3

Share a quantity in a given ratio

D, C Section 10.1 Converting a ratio to a fraction, e.g. using

for a ratio of 2 : 3.

GPW 10.1 Section 10.1

N3.1, N3.3 Solve word problems involving ratio

C Section 10.2 Not multiplying both sides of the ratio by the same number.Giving an answer without considering the context.

Section 10.2

N3.3 Understand direct proportionSolve proportion problems using the unitary method

D Section 10.3 Not always seeing the relationships between numbers (e.g. if the cost of 4 items is given, and the price of 8 is asked for).


N3.3 Work out which product is the better buy

D Section 10.4 Not making the units the same for each item.Comparing unlike unit rates (e.g. price per gram for one item but amount for 1p for the other).

Section 10.4

N3.3 Solve word D, C Section 10.5 Dividing by the wrong quantity in conversion GPW 10.5 Section



problems involving direct and inverse proportionUnderstand inverse proportion

problems. 10.5



Chapter 11 Number skills 2 Time: 5 hours

N1.2 Add, subtract, multiply and divide any number.N1.3 Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.N1.4 Approximate to a given power of 10, up to three decimal places and one significant number.N1.5 Order rational numbers.

Learning objectives






G-F Practice Book

N1.2 Add and subtract mentallyRecall positive integer complementsUse standard column procedures to add and subtract whole numbers

G, F Section 11.1 Forgetting to ‘reduce’ a number when borrowing from it.

Section 11.1

Section 11.1

N1.2 Multiply whole numbers by 10, 100 and 1000Remember and use multiplication facts up to 10 × 10Multiply mentallyMultiply whole numbers using written methods

G, F, E Section 11.2 Forgetting to add the numbers to find the final answer when using the grid method.Forgetting the ‘zero’ when multiplying by tens when using the standard method.


Section 11.2



N1.2 Divide whole numbers by 10, 100 and 1000Derive division facts from multiplication factsUse repeated subtraction for division of whole numbers

G, F, E Section 11.3 Incorrectly writing 3.6 for an answer of 3 remainder 6.Not giving an answer in the context of the problem.


Section 11.3

N1.3, N1.4 Check a result by working the problem backwardsMake estimates and approximations of calculations

G, F, E, D, C

Section 11.4 Finding an approximate value independent of the context in which it is set.Giving an answer without reading the question carefully.

Section 11.4

Section 11.4

N1.2, N1.5 Calculate a temperature rise and fallOrder negative numbersAdd and subtract negative numbersMultiply and divide negative numbers

G, F, E Section 11.5 Ignoring the ‘negative’ sign in front of a number when adding/subtracting a negative number.

Section 11.5

Section 11.5



Chapter 12 Multiples, factors, powers and roots Time: 6 hours

N1.6 The concepts and vocabulary of factor (divisor), multiple, common factor, highest common factor, least common multiple, prime number and prime factor decomposition.N1.7 The terms square, positive and negative square root, cube and cube root.N1.8 Index notation for squares, cubes and powers of 10.N1.9 Index laws for multiplication and division of integer powers.

Learning objectives






G-F Practice Book

N1.6, N1.7 Identify and use integers, square numbers and cube numbersRecall the squares of integers up to 15 and the cubes of 2, 3, 4, 5 and 10

G, F, E Section 12.1 Incorrectly thinking that ‘taking a square’ means multiplying by 2 and a cube as multiplying by 3.

Section 12.1

Section 12.1

N1.6 Solve problems involving multiples Find lowest common multiples

E, C Section 12.2 Confusing factors and multiples.Assuming that the LCM of two numbers is the product of the numbers.

Section 12.2

Section 12.2

N1.6 Solve problems involving factorsRecognise two-digit prime numbersFind highest

E, C Section 12.3 Missing out 1 as a factor.Confusing HCFs and LCMs.Thinking that 1 is a prime number.Failing to recognise that a number is not prime, when finding prime factors.

Section 12.3



common factorsN1.7 Calculate squares

and cubesCalculate square roots and cube rootsUnderstand the difference between positive and negative square rootsEvaluate expressions involving squares, cubes and roots

E, D, C Section 12.4 Multiplying by 2 instead of squaring.Writing = –6 or = ±6 when finding the negative square root. Forgetting that square roots of positive numbers can be negative.

Section 12.4

Section 12.3

N1.8 Understand and use index notation in calculations

E Section 12.5 Working out 27 as 2 × 7. GPW 12.5/12.6

Section 12.5

N1.6 Write a number as a product of prime factors using index notationUse prime factors to find HCFs and LCMs

C Section 12.6 Mistaking non-primes for primes. GPW 12.5/12.6

Section 12.6

N1.9 Use laws of indices to multiply and divide numbers written in index notation

C Section 12.7 Multiplying and dividing powers instead of adding and subtracting.

Section 12.7



Chapter 13 Basic rules of algebra Time: 6 hours

N4.1 Distinguish the different roles played by letter symbols in algebra, using the correct notation.N5.1 Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors.

Learning objectives






G-F Practice Book

N4.1 Write simple expressions using letters to represent unknown numbersUse the correct notation in algebra

F, E, D Section 13.1 Writing m × 3 = m3. Section 13.1

Section 13.1

N5.1 Simplify algebraic expressions with only one letterSimplify algebraic expressions by collecting like terms

F, E Section 13.2 Failing to comprehend that x = 1x.Combining unlike terms.

Section 13.2

Section 13.2

N5.1 Multiply together two simple algebraic expressions

E Section 13.3 Treating terms in m2 and in m as like terms (e.g. simplifying 3m2 + m wrongly to 4m2).


N5.1 Multiply terms in a bracket by a number outside the bracket

D Section 13.4 Forgetting to multiply the second term in the bracket by the term outside (e.g. expanding 2(x + 3) as 2x + 3), or ignoring minus signs (e.g. writing 3(m – 2) as 3m + 6).




Multiply terms in a bracket by a term that includes a letter

N5.1 Simplify expressions involving brackets

D, C Section 13.5 Forgetting to multiply the second term in the bracket by the term outside.Getting the wrong signs when multiplying negative values.

Section 13.5

N5.1 Recognise factors of algebraic termsSimplify algebraic expressions by taking out common factors

D Section 13.6 Not realising that x is a factor of x and x2.Not taking out the highest common factor.Identifying the common factor but forgetting to work out one of the terms inside the bracket.


N5.1 Multiply together two algebraic expressions with bracketsSquare a linear expression

C Section 13.7 Confusing methods.Forgetting to multiply pairs of terms.




Chapter 14 Fractions Time: 7 hours

N1.3 Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.N2.1 Understand equivalent fractions, simplifying a fraction by cancelling all common factors.N2.2 Add and subtract fractions.N2.7 Calculate with fractions, decimals and percentages.

Learning objectives






G-F Practice Book

Number skills: equivalent fractions (N2.1) Section 14.1

N2.1 Compare fractions with different denominators

F, E, D Section 14.1 Multiplying the denominator but not the numerator when finding equivalent fractions.


Section 14.2

N2.1 Change an improper fraction into a mixed numberChange a mixed number into an improper fraction

F Section 14.2 Giving the answer in the wrong form.

Writing, for example, and as

or .


Section 14.3

N2.2 Add and subtract fractions with the same denominatorAdd fractions and change the answer to a mixed number

G, F, E, D

Section 14.3 Adding/subtracting the denominators as well as the numerators.

Not converting to equivalent fractions to make the denominators the same.

Section 14.3

Section 14.4



Add and subtract fractions when one denominator is a multiple of the otherAdd and subtract fractions when both denominators have to be changed

N2.2 Add and subtract mixed numbers

C Section 14.4 Incorrectly converting a mixed number to an improper fraction.Not converting the final answer back to a mixed number.


N2.7 Multiply a fraction by a whole numberMultiply a fraction by a fraction

E Section 14.5 Multiplying both the numerator and the

denominator by the whole number (e.g. ×

20 = ).

Multiplying diagonally as though ‘cross-multiplying’ is being done (e.g. × = ).

Section 14.5

Section 14.5

N2.7 Multiply a whole number by a mixed numberMultiply a fraction by a mixed number

D, C Section 14.6 Multiplying both the numerator and the denominator by the whole number (e.g. 3 ×

= ).

Section 14.6

N1.3 Find the reciprocal of a whole number, a decimal or a fraction

C Section 14.7 Leaving denominators as decimal numbers.Not simplifying answers when asked to do so.


N2.7 Divide a whole number or a fraction by a fractionDivide mixed numbers by whole

D, C Section 14.8 Finding the reciprocal of the wrong fraction, or finding the reciprocal of both fractions.

Section 14.8



numbers



Chapter 15 Decimals Time: 5 hours

N1.2 Add, subtract, multiply and divide any number. N2.3 Use decimal notation and recognise that each terminating decimal is a fraction.N2.4 Recognise that recurring decimals are exact fractions, and that some exact fractions are recurring decimals.

Learning objectives






G-F Practice Book

N1.2 Understand how decimals workMultiply or divide any number by a power of ten

F Section 15.1 Incorrectly adding the number of zeros as and when appropriate.Not counting decimal places correctly when multiplying or dividing by higher powers of 10.

Section 15.1

Section 15.1

N1.2 Add and subtract decimal numbers

E Section 15.2 Not lining up the decimal points.Not recording the ‘carry over’ and forgetting to add it on.Not reducing a number during an exchange.


N2.3 Convert decimals to fractions

D Section 15.3 Working with the incorrect power of 10.Not giving answers in the simplest form.Being confused by place holding zeros in the middle of a number.


N1.2 Multiply and divide decimal numbers

D, C Section 15.4 Working out the equivalent whole-number multiplication but forgetting to return to the decimal calculation at the end.

Confusing multiplication with the rules for addition, writing a long multiplication with




decimal points underneath each other.

‘Moving the decimal point back’ at the end of a decimal division.

N2.4 Convert fractions to decimalsRecognise recurring decimals

D, C Section 15.5 Confusing 0.3 with .Not understanding that recurring decimals are a form of exact maths and therefore rounding answers.




Chapter 16 Equations and inequalities Time: 5 hours

N5.4 Set up and solve simple linear equations.N5.7 Solve linear inequalities in one variable and represent the solution set on a number line.

Learning objectives






G-F Practice Book

N5.4 Solve equations involving addition or subtractionSolve equations involving multiplication and division

F, E Section 16.1 Not appreciating that an equation can be written in different but equivalent formats (e.g. 2a + 7 = 9 → 7 + 2a = 9 → 9 = 2a + 7).

GPW 16.1a-16.5a, 16.1b-16.5b

Section 16.1

Section 16.1

N5.4 Solve two-step equations

E, D Section 16.2 Not appreciating that an equation can be written in different but equivalent formats (e.g. 2a + 7 = 9 → 7 + 2a = 9 → 9 = 2a + 7). Incorrectly combining number work involving fractions and decimals with equation solving.

GPW 16.1a-16.5a, 16.1b-16.5b

Section 16.2

N5.4 Write and solve equations

E, D Section 16.3 Not appreciating that an equation can be written in different but equivalent formats (e.g. 2a + 7 = 9 → 7 + 2a = 9 → 9 = 2a + 7). Not following a question carefully when writing an equation to represent a problem.

GPW 16.1a-16.5a, 16.1b-16.5b

Section 16.3

N5.4 Solve equations involving brackets

D, C Section 16.4 Forgetting to multiply the second term in the bracket by the term outside.Getting the wrong signs when multiplying

GPW 16.1a-16.5a,

Section 16.4



negative numbers.Incorrectly simplifying after expanding the bracket.

16.1b-16.5b

N5.4 Solve equations with an unknown on both sides

D, C Section 16.5 Introducing errors when there are a negative number of unknowns on either side of the equation.

GPW 16.1a-16.5a, 16.1b-16.5b

Section 16.5

N5.7 Show inequalities on number linesWrite down whole number values for unknowns in an inequality

E, D Section 16.6 Confusing the convention of an open circle for a strict inequality and a closed circle for an included boundary.Not remembering how to use inequality symbols.

Section 16.6

N5.7 Solve simple inequalities

C Section 16.7 Not reversing the sign when multiplying or dividing by a negative.

Section 16.7



Chapter 17 Indices and formulae Time: 6 hours

N1.8 Index notation for squares, cubes and powers of 10.N1.9 Index laws for multiplication and division of integer powers.N4.2 Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’.N5.6 Derive a formula, substitute numbers into a formula and change the subject of a formula.

Learning objectives






G-F Practice Book

N4.2, N5.6 Substitute numbers into a simple formula written in wordsUse simple formulae that are written using letters

G, F Section 17.1 Substituting the wrong values for letters. Section 17.1

Section 17.1

N4.2, N5.6 Use algebra to derive formulae

E, D Section 17.2 Not seeing the ‘general’ case. Section 17.2

N1.8, N4.2 Use index notation in algebra Use index notation when multiplying or dividing algebraic

E, D, C

Section 17.3 Not realising that x means x1, or that a number divided by 1 gives the number itself (e.g. 6 ÷ 1 = 6).

Section 17.3



termsN1.9 Use index laws to

multiply and divide powers in algebra

C Section 17.4 Forgetting that a letter on its own in a calculation, such as p in p2 × p, is raised to the power 1.


N4.2, N5.6 Substitute numbers to work out the value of simple algebraic expressionsSubstitute numbers into expressions involving brackets and powers

F, E, D Section 17.5 Incorrectly substituting values into expressions (e.g. substituting a = 6 into the expression 4a, writing 46 and assuming it is forty-six). Ignoring BIDMAS.


Section 17.2

N4.2, N5.6 Substitute numbers into a variety of formulae

E, D Section 17.6 Not realising that means n ÷ 10, or that × 6 means of 6 = 3.


N5.6 Changing the subject of a formula

C Section 17.7 Not using brackets or a clear division (e.g. rewriting c = 2a + 5 as a = c − 5 ÷ 2).Not using the inverse operation (e.g. x + y = z becomes x = z + y).




Chapter 18 Percentages Time: 5 hours

N2.5 Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.N2.7 Calculate with fractions, decimals and percentages.N2.7h Including reverse percentage calculations. [Note: At Foundation tier, no more than two-step calculations will be required; percentages will be e.g. 10%, 20%.]

Learning objectives






G-F Practice Book

Number skills: fractions, decimals and percentages (N2.7); calculating with percentages (N2.7) Section 18.1, 18.2

N2.7 Calculate a percentage increase or decrease

D Section 18.1 Giving the actual increase/decrease as the answer when the amount after the increase/decrease is what is required.Using the multiplier as 1.5 rather than 1.05 for an increase of 5%.Writing ‘=’ between quantities that are not equal, because the ‘=’ sign is used as a shorthand for ‘then I do this’.


N2.5, N2.7 Perform calculations involving creditPerform simple interest calculationsPerform calculations involving VAT

E, D Section 18.2 Not seeing that 17.5% = 10% + 5% + 2.5%.Forgetting to add on the initial deposit in credit calculations.

GPW 18.2a, b

Section 18.2



N2.7 Calculate a percentage profit or loss

C Section 18.3 Confusing cost price and selling price. GPW 18.3 Section 18.3

N2.7h Perform calculations involving repeated percentage changes

C Section 18.4 Not understanding when the multiplier should be greater than or less than 1.Using the multiplier as 1.5 rather than 1.05 for an increase of 5%.




Chapter 19 Sequences and proof Time: 6 hours

N5.9 Use algebra to support and construct arguments.N6.1 Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence.N6.2 Use linear expressions to describe the nth term of an arithmetic sequence.

Learning objectives






G-F Practice Book

N6.1 Find the next term in a sequenceDescribe the term-to-term rule for continuing a sequenceFind the next term in a sequence including negative values

G, F, E Section 19.1 Expecting all sequences to ascend.Looking at the first two numbers and assuming that the rest follow this pattern.

Section 19.1

Section 19.1

N6.1 Continue sequences by finding differences between consecutive termsExplain the term-to-term rule

E Section 19.2 Expecting all sequences to have common differences.Looking at the first two numbers and assuming that the rest follow this pattern.


N6.2 Find any term in a sequence given the nth term

E, D, C Section 19.3 Mistaking x2 for 2x. GPW 19.3 Section 19.3



Find the nth term of a linear sequence

N6.2 Draw the next pattern in a sequenceFind the nth term for pattern sequences

G, F, E, C

Section 19.4 Not making the connection between the structure of the physical pattern and the form the nth term takes.

Section 19.4

Section 19.2

N5.9 Show step-by-step deduction when solving problemsUse notation and symbols correctly

E, D Section 19.5 Not appreciating that a proof shows something works for all values.

Section 19.5

N5.9 Show something is false using a counter-example

C Section 19.6 Assuming that ‘number’ means positive whole number.Not identifying an appropriate counter-example.




Chapter 20 Coordinates and linear graphs Time: 7 hours

N6.3 Use the conventions for coordinates in the plane and plot points in all four quadrants, including using geometric information.N6.4 Recognise and plot equations that correspond to straight-line graphs in the coordinate plane, including finding their gradients.N6.11 Construct linear functions from real-life problems and plot their corresponding graphs.N6.12 Discuss, plot and interpret graphs (which may be non-linear) modelling real situations.

Learning objectives






G-F Practice Book

N6.3 Read and plot coordinates in the first quadrantRead and plot coordinates in all four quadrantsFind the mid-point of a line segment

G, F, D, C

Section 20.1 Swapping the position of the x- and y-coordinates.


Section 20.1

N6.4 Recognise straight-line graphs parallel to the x- or y-axisPlot graphs of linear functionsWork out coordinates of points of intersection when two graphs cross

E, D Section 20.2 Incorrectly calibrating the coordinate axes. Not using a third point as a check when drawing a straight line.


N6.4 Plot straight-line D, C, Section 20.3 Forgetting the negative on the gradient. GPW 20.3 Section



graphsFind the gradient of a straight-line graph

20.3

N6.11 Plot and use conversion graphs

F, E Section 20.4 Inaccurately reading from one value on a conversion graph to find another value.

Section 20.4

Section 20.2

N6.11, N6.12 Draw, read and interpret distance–time graphsSketch and interpret real-life graphs

E, D, C Section 20.5 Drawing and labelling axes before working out the axes range appropriate to the problem.

Section 20.5



Chapter 21 Number skills revisited Time: 3 hrs

N1.3 Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.N1.4 Approximate to a given power of 10, up to three decimal places and one significant figure.N1.14 Use calculators effectively and efficiently.N2.1 Understand equivalent fractions, simplifying a fraction by cancelling all common factors.N2.5 Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.N2.7 Calculate with fractions, decimals and percentages.N3.1 Use ratio notation, including reduction to its simplest form and its various links to fraction notation.

Learning objectives






G-F Practice Book

Understand equivalent fractionsSimplify a fraction by cancelling all common factorsRecognise that each terminating decimal is a fractionConvert simple fractions to percentages and vice versaUse percentages to compare proportions

G, F, E, D

Chapter 21 Chapter 21 Section 21.1



Understand ‘reciprocal’ as multiplicative inverseUse ratio notationUse brackets and the hierarchy of operationsAdd, subtract, multiply and divide integersUse calculators effectively and efficiently; use function keys for squaresUse inverse operationsRound to the nearest integer, to one significant figure and to one, two or three decimal placesGive solutions in the context of the problem to an appropriate degree of accuracy



Chapter 22 Angles Time: 5 hours

G1.1 Recall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines, and opposite angles at a vertex.G1.2 Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals.G3.6 Understand and use bearings.G3.8 Measure and draw lines and angles.

Learning objectives






G-F Practice Book

G1.1, G3.6 Describe angles as turns and in degreesUnderstand clockwise and anticlockwiseKnow and use compass directions

G Section 22.1 Confusing clockwise and anticlockwise. Section 22.1

Section 22.1

G1.1, G3.8 Use letters to name anglesRecognise and name types of anglesDraw angles using a protractorMeasure angles using a protractorEstimate the size of

G, F Section 22.2 Using the wrong scale on the protractor. Section 22.2

Section 22.2



an angle in degreesG1.1 Calculate angles on

a straight line and angles around a pointRecognise vertically opposite angles

F, E Section 22.3 Not realising that angles marked with the same letter are equal.Measuring rather than calculating angles.


Section 22.3

G1.2 Recognise corresponding and alternate anglesCalculate angles in diagrams with parallel lines

D Section 22.4 Confusing alternate and corresponding angles.


G3.6 Use three-figure bearing notationMeasure the bearing from one place to anotherPlot a bearingCalculate bearings in diagrams

E, D, C Section 22.5 Confusing which angles need to be found.Not realising that some of the angles asked for can simply be read off the diagram.




Chapter 23 Measurement 1 Time: 4 hours

N1.3 Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.G3.3 Interpret scales on a range of measuring instruments and recognise the inaccuracy of measurements.G3.5 Make sensible estimates of a range of measures.

Learning objectives






G-F Practice Book

G3.5 Choose the most appropriate metric units for measurementMake sensible estimates of length, volume and mass in everyday situations

G, F Section 23.1 Overestimating quantities when dealing with larger units (i.e. m rather than cm).

GPW 23.1/23.2

Section 23.1

Section 23.1

G3.3 Interpret scales on a range of measuring instruments

G, F Section 23.2 Counting small divisions in simple units (e.g. 1 or 0.1) regardless of the number of subdivisions.

GPW 23.1/23.2

Section 23.2

Section 23.2

N1.3 Understand time using the 12-hour and 24-hour clockSolve problems involving time and dates

G, F Section 23.3 Subtracting or adding 10 rather than 12 to convert between 12- and 24-hour times (e.g. recording 14.30 as 4.30 pm).

GPW 23.3/23.4

Section 23.3

Section 23.3

N1.3 Solve problems F, E Section 23.4 Confusing the decimal parts of an hour with GPW Section Section



involving time and datesWork out the time taken for a journey from a timetable

hours and minutes (e.g. writing 1.25 hours as 1 hour 25 minutes) and vice versa.

23.3/23.4 23.4 23.3



Chapter 24 Triangles and constructions Time: 4 hours

G1.2 Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals.G1.8 Understand congruence and similarity.G3.9 Draw triangles and other 2D shapes using a ruler and protractor. G3.10 Use straight edge and a pair of compasses to do constructions.

Learning objectives






G-F Practice Book

G1.2 Recognise and draw the four main types of triangleSolve angle problems in trianglesSolve angle problems in triangles involving algebra

G, E, D

Section 24.1 Not realising when a triangle is isosceles and thinking that the problem cannot be solved. Trying to do too many steps in one go when answering algebra-based questions.


Section 24.1

G3.9, G3.10 Draw triangles accurately when given the length of all three sidesDraw triangles accurately when at least one angle is given

E, D Section 24.2 Inaccurately using a protractor or compasses.Not completing the triangle by drawing the third side. Rubbing out construction lines.

Section 24.2

G1.8 Recognise and C Section 24.3 Thinking that two triangles are congruent Section



explain how triangles are congruent

when they are not (due to the relative positions of side lengths or angles being in different positions).

24.3



Chapter 25 Equations, formulae and proof Time: 3 hours

N4.2 Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’.N5.1 Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors.N5.4 Set up and solve simple linear equations.N5.6 Derive a formula, substitute numbers into a formula.G2.3 Justify simple geometrical properties.

Learning objectives






G-F Practice Book

Algebra skills: expressions (N4.2, N5.1); brackets (N5.1); solving equations (N5.4); formulae (N5.6)Section 25.1, 25.2, 25.3

N5.4, N5.6 Write your own formulae and equationsSet up and solve equationsSubstitute into a formula to solve problemsChange the subject of a formula

D, C Section 25.1 Failing to consider the different terms of an expression when changing the subject of a formula (e.g. W = x + 3 2W = x + 3). Not using brackets or a clear division (e.g. rewriting c = 2a + 5 as a = c − 5 ÷ 2).Not using the inverse operation (e.g. x + y = z becomes x = z + y).


G2.3 Prove simple results from geometry

C Section 25.2 Not laying out answers in an organised way.Not providing reasons for each stage of the working.

Section 25.2



Chapter 26 Quadrilaterals and other polygons Time: 6 hours

N5.4 Set up and solve simple linear equations.N6.3 Use the conventions for coordinates in the plane and plot points in all four quadrants, including geometric information.G1.2 Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals.G1.3 Calculate and use the sums of the interior and exterior angles of polygons.G1.4 Recall the properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus.G1.6 Recognise reflection and rotation symmetry of 2D shapes.

Learning objectives






G-F Practice Book

G1.2, N5.4 Calculate interior angles of quadrilateralsSolve angle problems in quadrilaterals involving algebra

E, D Section 26.1 Working things out mentally without writing down the calculations.Not showing full working for the algebra questions.


G1.2, G1.4 Identify quadrilaterals given their propertiesMake quadrilaterals from two trianglesUse parallel lines and other angle properties in quadrilaterals

F, E, D Section 26.2 Giving correct answers but not explaining the properties used.

Section 26.2

Section 26.1

G1.3 Use the exterior D, C Section 26.3 Forgetting the formula for the exterior angles GPW 26.3 Section



angles of polygons to solve problems

of a polygon and how to apply it. 26.3

G1.3 Calculate interior angles of polygonsSolve more complex angle problems involving exterior and interior angles of polygons

D, C Section 26.4 Incorrectly splitting the polygon into triangles.


N6.3 Plot all points of a quadrilateral given geometric informationFind the mid-point of a line segment

E Section 26.5 Plotting the numbers on the x- and y-axes the wrong way round.Not recognising, or be able to name, some of the less common quadrilaterals (e.g. the kite and trapezium).Averaging only the x- or y-coordinate and not both when finding the mid-point.

Section 26.5

G1.6 Recognise and draw lines of symmetry in simple shapesRecognise rotational symmetry in 2-D shapes

G, F Section 26.6 Incorrectly thinking that, for example, a rectangle has 4 lines of symmetry, a kite has 2 lines of symmetry, and a parallelogram has 2 lines of symmetry.

Section 26.6

Section 26.2



Chapter 27 Units and scale Time: 2 hours

G3.1 Use and interpret maps and scale drawings.G3.4 Convert measurements from one unit to another.

Learning objectives






G-F Practice Book

G3.4 Know and use approximate metric equivalents of pounds, feet, miles, pints and gallons

E Section 27.1 Not considering the relative size of units when deciding whether to multiply or divide.

GPW 27.1/27.2

Section 27.1

Section 27.1

G3.1 Use and interpret maps and scale drawings

E Section 27.2 Missing out steps when converting between (for example) km and cm.Not making allowances when measurements are given in a variety of units.

GPW 27.1/27.2

Section 27.2

Section 27.1



Chapter 28 Perimeter, area and volume Time: 6 hours

G4.1 Calculate perimeters and areas of shapes made from triangles and rectangles.G4.4 Calculate volumes of right prisms and of shapes made from cubes and cuboids.

Learning objectives






G-F Practice Book

G4.1 Find the perimeter and area of rectangles, parallelograms, triangles and trapezia

F, E, D Section 28.1 Not making rough estimates of areas as a check to avoid arithmetical errors.Incorrectly converting between units.Using measurements in different units.


Section 28.1, 28.2

G4.1 Find the perimeter and area of compound shapes

D Section 28.2 Incorrectly calculating missing lengths.Adding areas instead of subtracting.

Section 28.2

G4.4 Find the volume and surface area of a prism

E, D, C Section 28.3 Confusing volume and surface area. GPW 28.3 Section 28.3

Section 28.3



Chapter 29 3-D objects Time: 2 hours

G2.4 Use 2D representations of 3D shapes.

Learning objectives






G-F Practice Book

G2.4 Recognise the net of a 3-D objectDraw the net of a 3-D object

G, F Section 29.1 Incorrectly visualising 3-D objects in 2-D. Section 29.1

Section 29.1

Section 29.1

G2.4 Make a drawing of a 3-D object on isometric paperDraw plans and elevations of 3-D objectsIdentify planes of symmetry of 3-D objects

E, D Section 29.2 Missing out hidden cubes when converting from a 3-D view to a plan or elevation.Using isometric paper in landscape not in portrait.

Section 29.2



Chapter 30 Reflection, translation and rotation Time: 5 hours

G1.7 Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations.G5.1 Understand and use vector notation for translations.

Learning objectives






G-F Practice Book

G1.7 Draw a reflection of a shape in a mirror lineDraw reflections on a coordinate gridDescribe reflections on a coordinate grid

G, F, E, D, C

Section 30.1 Drawing the image a different distance from the mirror line than the object.Incorrectly identifying mirror lines parallel to the x- or y-axis.


Section 30.1

G1.7, G5.1 Translate a shape on a gridUse column vectors to describe translations

D, C Section 30.2 Forgetting what the two values in the column vector mean. Using coordinate notation instead of vector notation.Confusing the terms ‘transformation’ and ‘translation’.

Section 30.2

G1.7 Draw the position of a shape after rotation about a centreDescribe a rotation fully giving the size

D, C Section 30.3 Working out the angle of rotation incorrectly.Turning in the wrong direction.




and direction of turn and the centre of rotation



Chapter 31 Circles and cylinders Time: 7 hours

G1.5 Distinguish between centre, radius, chord, diameter, circumference, tangent, arc, sector and segment.G4.1h Extend to other compound shapes. [Note: Extending work on circumference and area of circles to include semicircles, quadrants, etc. will help Foundation tier students attempt C-grade questions towards the end of a Foundation paper.]G4.3 Calculate circumferences and areas of circles.G4.4 Calculate volumes of right prisms and of shapes made from cubes and cuboids.

Learning objectives






G-F Practice Book

G1.5 Recall the definition of a circle and the meaning of related terms

G Section 31.1 Forgetting to divide by 2 when the diameter is given and the radius is needed.

Section 31.1

Section 31.1

G1.5, G4.1h, G4.3

Calculate the circumference of a circleCalculate the perimeters of compound shapes involving circles or parts of circles

D, C Section 31.2 Not multiplying by 2 when the radius is given and the diameter is needed.


G1.5, G4.1h, G4.3

Calculate the area of a circleCalculate the areas of compound shapes involving circles or parts of

D, C Section 31.3 Multiplying by p before squaring. Section 31.3



circlesG4.3, G4.4 Calculate the

volume of a cylinderSolve problems involving the surface area of cylinders

C Section 31.4 Multiplying by p before squaring. Section 31.4



Chapter 32 Measurement 2 Time: 3 hours

N1.4 Approximate to a given power of 10, up to three decimal places and one significant figure.N1.13h Calculate and use upper and lower bounds. [Note: It is reasonable to expect a Foundation candidate to understand that measures given to the nearest whole number can be inaccurate by up to half a unit either way. This also links to the concept of rounding (N1.4).]G3.4 Convert measurements from one unit to another.G3.7 Understand and use compound measures.

Learning objectives






G-F Practice Book

G3.4, G3.7 Convert between different units of areaConvert between different units of volume

D, C Section 32.1 Multiplying by 100 when converting from m3 to cm3.

GPW 32.1/32.2

Section 32.1

Section 32.1

N1.4, N1.13h Recognise that measurements given to the nearest whole unit may be inaccurate by up to one half unit in either direction

C Section 32.2 Difficulty comprehending the definition of the upper bound, since, for example, 146.5 rounds to 147.

GPW 32.1/32.2

Section 32.2

Section 32.1

G3.7 Calculate average speeds

D Section 32.3 Not remembering the formulae.Confusing the decimal parts of an hour with hours and minutes (e.g. using 1 hour 45 minutes as 1.45 hours).


Section 32.2



Chapter 33 Enlargement Time: 3 hours

G1.7 Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations.G3.2 Understand the effect of enlargement for perimeter, area and volume of shapes and solids.

Learning objectives






G-F Practice Book

G1.7, G3.2 Identify the scale factor of an enlargementEnlarge a shape on a gridEnlarge a shape using a centre of enlargement

F, E, D Section 33.1 Inaccurately counting squares.Adding the scale factor instead of multiplying by the scale factor.Not using the centre of enlargement.

GPW 33.1a, 33.1b

Section 33.1

Section 33.1



Chapter 34 Trial and improvement Time: 2 hours

N1.14 Use calculators effectively and efficiently.N5.8 Use systematic trail and improvement to find approximate solutions of equations where there is no simple analytical method of solving them.

Learning objectives






G-F Practice Book

N1.14 Use a calculator efficiently

D Section 34.1 Including brackets unnecessarily in calculations.Not giving answers as decimals when questions do not ask for an alternative.

GPW 34.1/34.2

Section 34.1

Section 34.1

N5.8 Use trial and improvement to find solutions to equations

C Section 34.2 Not checking the mid-point to determine which of two values is correct (e.g. choosing between x = 3.3 and x = 3.4 based on the value of the function and the desired output). Using the value of the equation as the answer rather than the value of the variable.

GPW 34.1/34.2

Section 34.2

Section 34.1



Chapter 35 Quadratic graphs Time: 5 hours

N6.12 Discuss, plot and interpret graphs (which may be non-linear) modelling real situations.N6.13 Generate points and plot graphs of simple quadratic functions, and use these to find approximate solutions.

Learning objectives






G-F Practice Book

N6.12, N6.13 Draw quadratic graphsIdentify the line of symmetry of a quadratic graphDraw and interpret quadratic graphs in real-life contexts

D, C Section 35.1 Drawing the bottom of the graph flat when a graph has its vertex between two plotted points.


Section 35.1

N6.13 Use a graph to solve quadratic equations

C Section 35.2 Forgetting to write down all the solutions. Section 35.2



Chapter 36 Constructions and loci Time: 4 hours

G3.10 Use straight edge and a pair of compasses to do constructions.G3.11 Construct loci.

Learning objectives






G-F Practice Book

G3.10 Construct the perpendicular bisector of a line segmentConstruct the bisector of an angle

C Section 36.1 Failing to keep the settings of compasses constant.Rubbing out construction lines.Not using compasses.


Section 36.1

G3.11 Construct lociSolve locus problems, including the use of bearings

C Section 36.2 Confusing a distance from a point with the distance from a line.Making inaccurate constructions.Shading the wrong region.

Section 36.2



Chapter 37 Pythagoras’ theorem Time: 6 hours

G2.1 Use Pythagoras’ theorem.

Learning objectives






G-F Practice Book

G2.1 Understand Pythagoras’ theorem

C Section 37.1 Forgetting that x2 means x × x, not x × 2. Section 37.1

Section 37.1

G2.1 Calculate the hypotenuse of a right-angled triangleSolve problems using Pythagoras’ theorem

C Section 37.2 Forgetting to take the square root to find the final answer. Not correctly identifying the hypotenuse.Drawing a scale diagram to ‘calculate’ the length of a hypotenuse.


G2.1 Calculate the length of a shorter side in a right-angled triangleSolve problems using Pythagoras’ theorem

C Section 37.3 Not correctly identifying the hypotenuse.Forgetting to take the square root to find the final answer. Forgetting that Pythagoras’ theorem only applies to right-angled triangles. Not identifying the appropriate information when problems are set in context.Not being able to identify the position of the right angle.


G2.1 Calculate the length of a line segment AB

C Section 37.4 Subtracting instead of adding the two pairs of coordinates.

Section 37.4




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