SUPPORT - Pearson Education€¦ · Web viewSample medium term plans for maths using Impact Maths. Year 7 Contents. Planning with the Framework 1. Year 7 planning chart 2. ... Y5

Key Stage 3Sample medium term plans for maths using Impact MathsYear 7

ContentsPlanning with the Framework 1

Year 7 planning chart 2

Autumn term 3Algebra 1 3Number 1 4Shape, space and measures 1 5Number 2 6Handling data 1 7Algebra 2 8Shape, space and measures 2 9

Spring term 11Handling data 2 11Number and measures 3 12Algebra 3 14Shape, space and measures 3 15Number 4 16Algebra 4 16

Summer term 18Shape, space and measures 4 18Handling data 3 19Number 5 21Algebra 5 22Shape, space and measures 5 23

Working with the Impact guideThe Impact maths KS3 scheme has been used in schools since 1998. It has been continually updated to meet the requirements of the Framework for Teaching Mathematics. This document provides a detailed guide of how to deliver the framework using Impact materials.

Heinemann Educational has the permission of the DfES to reproduce their objectives in this matching guide. We have retained all the elements of the DfES sample plans to make it very easy for you to plan your schemes of work for Year 7 using Impact. For example:0Core objectives are in bold as in the medium-term plans.

1We have given references to the sections in 1G and 1R.2For ease of reference, the layout is very similar to the DfES sample medium-term plans, with the Impact sections in the column(s) alongside. 3We have repeated the DfES’s columns of ‘support’, ‘core’ and ‘extension’ to help with differentiation across sets.4We have also retained the dependencies between topics as the DfES sample plans.

How to use this documentThis is a reproduction of the sample medium-term plans produced by the National Numeracy Strategy, reproduced with permission and acknowledgement to the DfES.

Details of how these charts can be used for planning are given on p1. In addition to the material provided by the NNS, detailed cross-references in the teaching objectives for the main activities refer to the Impact maths student books and pupil performance packs. The cross-references in the teaching objectives for the oral and mental activities refer to the lesson starters in the 1R pupil performance pack. There is also a short narrative for each topic of work, giving advice on using Impact and other resources.

All cross-references refer to material in 1G and 1R. Not all of the extension objectives are covered in Impact 1R, and you may need to use resources from higher years to provide extension material.

Matching guides for Years 8 and 9 will be available in the autumn and spring terms, respectively.

Notes on tables(in part) section covers point in part.(part) part of section covers point.

About the authorDerek Huby is an experienced primary and secondary numeracy consultant, as well as being an experienced maths teacher and head of department.

AcknowledgementWe would like to thank Derek Huby and Jim Newall for their work in the preparation of this document.

Impact maths sample medium-term plans for mathematics

Planning with the Framework[The text of this page is reproduced with permission from the Department for Education and Skills.]

The Framework for teaching mathematics: Years 7, 8 & 9 provides teachers with guidance on meeting the National Curriculum requirements for mathematics. It sets out yearly teaching programmes showing how objectives for teaching mathematics can be planned from Year 7 to Year 9. A key task in developing medium-term plans for Key Stage 3 mathematics is to identify the objectives for the units of work that are going to be taught. In doing this, schools may choose to start from their existing schemes of work, or alternatively, may find that these sample plans provide a useful starting point.

The sample plans are designed to continue the progression and expectations established in the yearly teaching programmes up to Year 6. They are based on the examples of planning charts in the Framework. There are many other ways to organise the mathematics curriculum in Key Stage 3. The planning charts indicate dependencies between topics but the order and content of the units can be adjusted.

Each sample plan identifies core objectives that define a minimum expectation for the majority of pupils in a particular year group. Plans for particular year groups are designed to show:5Progression in the teaching objectives for each strand of the curriculum;6Links between the teaching objectives, bringing together related ideas across the strands;7Opportunities to revisit topics during the year (the pitch of the second and subsequent units of a topic need careful adjusting in the light of teachers’ assessment of pupils’ progress);8How objectives for using and applying mathematics can be incorporated into units.

For each term, suggested objectives for oral and mental mathematics are also identified. Oral and mental work can both support the main teaching programme as well as providing a means of regularly revisiting important elements.

Many schools set pupils for mathematics. Teachers of higher sets may well base their pupils’ work on the programme for a later year group, while teachers of lower sets may need to draw on objectives in the teaching programmes from a previous year group. As always, the success of setting depends on teachers in the mathematics department being involved in careful monitoring, close teamwork and co-operative planning to make sure that expectations for all pupils are suitably high and that lower expectations are not justified simply because pupils are in a lower set.

There are some secondary schools where, at present, relatively few pupils attain level 5 or above at the end of Key Stage 3. Pupils may lack a secure understanding

of some of the work they have been taught earlier. To begin with, these schools should look carefully at the programmes for Year 5 and Year 6 and draw suitable teaching objectives from them when they are planning work for Year 7, making corresponding adjustments for Years 8 and 9. A decision like this would need to be reviewed before the start of the next school year to allow for improving standards over time.

How the plans are set outTeaching objectives for oral and mental activities are placed at the beginning of the plan for each term. Objectives for the main activities are set out in four main columns: 9The first identifies the areas of mathematics studied in the unit and identifies links to the supplement of examples in the Framework.10The second identifies support objectives from previous yearly teaching programmes, as in Springboard 7. These are linked to the core objectives for each unit.11The third column sets out the core objectives for the year group, the ones you would expect to focus on for the majority of pupils.12The fourth provides extension objectives, to stretch able pupils, drawn from the next year’s teaching programme. These are linked to the core objectives for the unit.

Impact maths sample medium-term plans for mathematics Page 1

Key Stage 3 National Strategy

YEAR 7 PLANNING CHARTAutumn36 hours Number 1

Place value Algebra 1Integers Sequences and SSM 1Calculations functions Mensuration6 hours 6 hours (perimeter and area)

4 hoursNumber 2

HD1 FDPRP Algebra 2 SSM 2Handling data, 6 hours Equations and formulae Coordinatesincluding probability 5 hours Geometrical reasoning:6 hours lines, angles and shapes

3 hours

Spring33 hours Number and measures 3 Algebra 3

Place value Integers, powers and rootsCalculations Sequences, functionsCalculator methods and graphs

HD2 Measures 6 hoursHandling data 8 hours5 hours

Number 4FDPRP SSM 35 hours Algebra 4 Geometrical reasoning: lines

Equations and angles and shapesformulae Construction4 hours 5 hours

Summer36 hours SSM 4

Algebra 5 TransformationsNumber 5 Sequences, functions and graphs 6 hours

HD 3 Place value Equations and formulaeHandling data, Calculations, including calculator methods 8 hours SSM 5including probablity FDPRP Geometrical reasoning: lines8 hours Solving problems angles and shapes

8 hours Construction6 hours

35 weeks ------------------------------------------------------------------------------------------------------------------------ 105 hours ---------------------------------------------------------------------------------------------------------------------------------------

Impact maths sample medium-term plans for mathematics Page 2

Key Stage 3 National Strategy Year 7: Autumn termNumbers in the LH column refer to the supplement of examples for the core teaching programme

YEAR 7 – AUTUMN TERMTeaching objectives for the oral and mental activities

1R 1R13Read and write whole numbers in figures and words.14Multiply and divide whole numbers by 10, 100, 1000.15Count on and back in steps of 0.1, 0.2, 0.25, ½, ¼, …16Round whole numbers to the nearest 10 or 100.17Order, add and subtract positive and negative numbers in context.18Recognise multiples and use simple tests of divisibility.19Know pairs of factors of numbers to 100.20Know or derive quickly prime numbers less than 30.21Know or derive quickly squares to a least 12 ´ 12 and the corresponding roots.22Convert between fractions, decimals and percentages.23Find simple fractions of quantities.

24Know addition and subtraction facts to 20 and whole number complements of 100.25Find two decimals (one decimal place) with a sum of 1.26Add and subtract several small numbers or several multiples of 10, e.g. 50 – 40 + 80 – 100.

2.46.4

2.16, 2.172.45.4, 5.55.55.55.1

8.88.3, 8.4

27Add and subtract pairs of numbers, e.g. 76 ± 38, 760 ± 380.28Find doubles and halves of numbers, e.g. 670, 5.6.29Recall multiplication facts to 10 ´ 10 and derive associated division facts.30Multiply and divide a two-digit number by a one-digit number.

31Visualise, describe and sketch 2-D shapes in different orientations.32Estimate and order acute and obtuse angles.

33Use metric units (length, mass, capacity) and units of time for calculations.34Use metric units for estimation (length, mass capacity).35Convert between m, cm and mm, km and m, kg and g, litres and ml.36Know rough metric equivalents of common imperial units.

37Apply mental skills to solve problems.38

5.1

14.114.4

7.9, 10.1, 10.27.17.3

Teaching objectives for the main activities

Algebra 1 (6 hours)

SUPPORT from the Y5 and Y6 teaching programmes

1G CORE from the Y7 teaching programme 1G 1R EXTENSION from the Y8 teaching programme

1R

Sequences and functions(144-163)

39Recognise and extend number sequences formed by counting on from any number in steps of constant size, extending beyond zero when counting back.

3.4 40Generate and describe simple integer sequences.

3.13.23.417.5

3.13.2

41Know squares to at least 10x10.

3.6 (part)5.15.417.1

42Generate terms of a simple sequence, given a rule (e.g. finding a term from the previous term, finding a term given its position in the sequence).

3.33.43.53.6

3.33.43.5

43Generate terms of a linear sequence using term-to-term and position-to-term definitions of the sequence, on paper and using a spreadsheet or graphical calculator.

3.6

44Generate sequences from practical contexts and describe the general term in simple cases.

3.13.2

3.13.23.6

45Begin to use linear expressions to describe the nth term of an arithmetic sequence.

3.6

46Express simple functions in words, then using symbols.47Represent them in mappings.

3.310.110.2

3.311.1

48Represent mappings expressed algebraically.

—

Formulae & Identities

49Use letter symbols to represent unknown numbers or variables.

— 9.1–9.3


(112-113)Solving Problems(32-35)

50Suggest extensions to problems by asking ‘What if…?’; begin to generalise and to understand the significance of a counter-example.

— —

NOTES (1G)51Chapter 3 of book 1G covers the objectives in the support programme, as well as introducing pupils to the majority of the core objectives.52The work on mappings is of an introductory nature; compare section 3.3 with p160 in the Framework examples.

NOTES (1R)53Chapter 3 of book 1R covers the majority of the core and extension objectives in this unit. The use of letter symbols to represent unknown numbers or variables is introduced in chapter 9. Section 3.6 presents some quite challenging work on finding rules; compare this section with the Framework’s examples, on pp156–157.

Number 1 (6 hours)

SUPPORT from the Y5 and Y6 teaching programme


1R

Place Value(36-41)

54Read and write whole numbers in figures and words.

2.12.22.32.4

55Understand and use decimal notation and place value.56Multiply and divide integers and decimals by 10, 100, 1000, and explain the effect.

6.1 (in part)5.5 (in part)

6.1–6.2

5.6–5.86.4–6.5

57Use decimal notation for tenths and hundredths.58Know what each digit represents in numbers with up to two decimal places.

6.16.2

59Compare and order decimals in different contexts.60Know that when comparing measurements they must be in the same units.

— 6.3

7.4

Integers(48-51)

61Calculate a temperature rise and fall across 0ºC.

11.1– 11.5

62Understand negative numbers as positions on a number line.63Order, add and subtract positive and negative integers in context.

11.6

—

12.4–12.712.1–12.3

64Add, subtract, multiply and divide integers.

5.9, 12.6, 12.7

Calculations(88-91, 102-105)

65Know squares to at least 10x10.

3.6 (part)5.15.417.1

66Consolidate the rapid recall of number facts, including positive integer complements to 100 and multiplication facts to 10 x 10, and quickly derive associated division facts.

5.1, 5.2, 5.5, 5.6 (in part)

2.1–2.12, 5.1, 5.2 (part),5.9

67Recall known facts, including fraction to decimal conversions.68Use known facts to derive unknown facts, including products such as 0.7 and 6, and 0.03 and 8.

6.66.76.8

69Use informal pencil and paper methods to support, record or explain additions & subtractions.

See notes below

70Make and justify estimates and approximations of calculations.71Use standard column procedures to add and subtract whole numbers and decimals with up to two places.

—

2.11 2.12 6.4

2.19

2.152.166.2

Calculator methods(108-109)

72Develop calculator skills and use a calculator effectively.

17.1–17.5

73Enter numbers and interpret the display in different contexts (decimals, money).

17.1–17.5

5.10, 20.3–20.5

Solving Problems(2-11)

74Solve word problems and investigate in a range of contexts: (number).75Compare and evaluate solutions.

See notes below

See notes below


1G NOTES76There are exercises to practice ‘Solving word problems’ throughout the text, especially in Chapters 5, 6, and 8. Chapter 2 revises many aspects of whole number work. This will need to be approached selectively, taking account of previous learning. The early part of chapter 6 can be used to reinforce the idea of decimal fractions as an extension of the base-10 system used for whole number notation. Directed number is introduced in chapter 11; it may be possible to omit some of the earlier material, and proceed to section 11.4, which deals with ‘bridging through zero’. The first two sections in chapter 17 give the opportunity to revise square numbers, and develop calculator skills. Informal methods for addition and subtraction are not covered in the book, although formal column methods are dealt with in chapter 2. You will need to assess pupils’ readiness for such methods; see the QCA booklet Teaching Written Calculation Methods.77Positive integer complements not dealt with in 1G.

1R NOTES78There are exercises to practice ‘Solving word problems’ throughout the text. It will be necessary to use the materials in this unit selectively, taking into account what is likely to be a wide range of previous learning. Chapter 2 contains a large amount of material revising basic number skills. I t will probably not be appropriate to cover all of this material with the whole class; assessments made during the mental and oral starter will give a good indication of what is required. Chapters 5 and 6 cover multiplication and division, and decimal notation. Again, a selective approach is necessary. Chapter 12 deals with directed numbers, which pupils should have encountered in their primary work – the earlier material in the chapter could be reviewed quickly, as an oral exercise, before moving on to the sections indicated. The efficient use of the calculator is covered in chapter 20.

Shape, space and measures 1 (4 hours)



1R

Mensuration(198-201, 228-231, 234-241)

79Identify different nets for an open cube.

See notes below

80Use 2-D representations to visualise 3-D shapes and deduce some of their properties.

1.81.9 (in part)

1.91.10 (in part)

81Measure and draw lines to the nearest millimetre.82Record estimates and readings from scales to a suitable degree of accuracy.

7.1, 7.2

7.7

83Use names and abbreviations of units of measurement to measure, estimate, calculate and solve problems in everyday contexts involving length, area

7.37.49.6–9.9

7.1–7.410.3, 10.4, 10.8

84Make simple scale drawings. —

85Understand that area is measured in square centimetres (cm2)86Understand, measure and calculate perimeters of rectangles and regular polygons.

9.69.7

9.1–9.39.5

87Know and use the formula for the area of a rectangle.88Calculate the perimeter and area of shapes made from rectangles.

— 10.5

10.1, 10.2, 10.5

89Deduce and use formulae for the area of a triangle, parallelogram and trapezium.

10.610.7(D only)

90Calculate the surface area of cubes and cuboids.

— 10.12 91Know and use the formula for the volume of a cuboid.

10.1010.11

92Solve word problems and investigate in a range of contexts: length, perimeter and area.

— —

1G NOTES93Sections 7.1 and 7.2 go as far as measuring in centimetres; this would need to be extended to millimetre accuracy to meet the learning objective. This is covered in the corresponding section in book 1R. Section 7.7 deals with reading from scales – a topic which often causes difficulty. Chapter 9 deals with area and perimeter, and can be taught in the ‘correct’ order. The first objective, ‘Identify different nets for an open cube’, forms the basis for a good visualisation activity, perhaps in a lesson starter. Draw various arrangements of 5 squares, and ask the class whether they would fold to make an open cube.

1R NOTES94Activities relating to most of the learning objectives in this short unit will be found in chapters 1, 7 and 10. The whole of chapter 10 could be used, selectively, with pupils following the core programme. Although sections 10.8 and 10.9 are not explicitly referenced in the table, the material contained in them provides a useful summary of area problems, and a good introduction to the work on volume. When planning the delivery of this unit, you will need to bear in mind that the time available is limited; it will be important to use any available assessment information, and your own judgements of pupils’ abilities, to decide which material needs to be covered, and in what depth.


Number 2 (6 hours)



1R

Fractions, decimals, percentages (60-77)

95Change an improper fraction to a mixed number.96Recognise when two simple fractions are equivalent, including relating hundredths to tenths.97Use decimal notation for tenths and hundredths.

See note below

6.1, 6.2

98Use fraction notation to describe parts of shapes and to express a smaller whole number as a fraction of a larger one.99Simplify fractions by cancelling all common factors and identify equivalent fractions.100Convert terminating decimals to fractions, e.g. 0.23 = 23/100.101Use a diagram to compare two or more simple fractions.

8.18.2(part)

—

15.4

8.4

8.1, 8.11

8.5

16.3

8.9

102Know that a recurring decimal is a fraction.103Use division to convert a fraction to a decimal.104Order fractions by converting them to decimals.

—

8.8

6.3

105Begin to add and subtract simple fractions and those with common denominators.106Calculate simple fractions of quantities and measurements (whole-number answers).107Multiply a fraction by an integer.

8.5

8.3 (part)

—

8.6

8.3, 8.4

8.4

108Calculate fractions of quantities and measurements (fraction answers).109Multiply and divide an integer by a fraction.

—

8.10

110Understand percentage as the ‘number of parts per 100’.111Recognise the equivalence of percentages, fractions and decimals.112Calculate simple percentages.

15.1, 15.215.3, 15.415.1–15.4

16.1, 16.216.3, 16.416.5

113Find the outcome of a given percentage increase or decrease.

16.6


114Find a difference by counting up through the next multiple of 10, 100 or 1000.115Add and subtract mentally pairs of two-digit numbers.

—

2.6–2.9

116Consolidate and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings.117Solve simple word problems mentally.

6.6 6.4, 6.5 6.6 (part)

118Recall fraction to decimal conversions.

8.8

119Check a result by considering whether it is of the right order of magnitude and by working the problem backwards.

See notes below

See notes below

Solving problems(28-31)

120Break a complex calculation into simpler steps, choosing and using appropriate and efficient operations, methods and resources, including ICT.

See notes below

See notes below

121Present and interpret solutions in the context of the original problem.122Explain and justify methods and conclusions, orally and in writing.

See notes below

See notes below


1G Notes123The first set of objectives in the ‘support’ column are covered in book 1G; see sections 8.2 and 8.5. The mental calculation skills listed in this column can be revised and practised in the mental and oral starter.

1R Notes124Chapters 6, 8 and 16 provide a considerable amount of material for this unit. In planning a series of lessons within this unit, it will be necessary to be selective about selection and presentation of the work involved; it may be possible to omit some of the exercises, or to present them orally. When solving problems, aim to reinforce the skills outlined at the bottom of the core column in the table.

Handling Data 1 (6 hours)



1R

Handling Data(256-261, 268-271)

125Calculate statistics for small sets of discrete data:

§ find the mode, median and range, and the modal class for grouped data;

§ calculate the mean, including from a simple frequency table, using a calculator for a larger number of items.

17.1–17.4

17.5

126Recognise when it is appropriate to use the range, mean, median and mode.127Calculate a mean using an assumed mean.

—

—

128Solve a problem by representing, extracting and interpreting data in tables, graphs, charts and diagrams; e.g.

§ line graphs;§ frequency tables and bar

charts.

14.1–14.9

—14.7, 14.8

§ Interpret diagrams and graphs (including pie charts), and draw simple conclusions based on the shape of graphs and simple statistics for a single distribution.

14.5, 14.6, 14.8

15.3, 15.5, 15.6

Probability(276-283)

§ Use vocabulary and ideas of probability, drawing on experience.

4.1–4.5 4.1–4.4

§ Understand and use the probability scale from 0 to 1.

§ Find and justify probabilities based on equally likely outcomes in simple contexts.

§ Identify all the possible mutually exclusive outcomes of a single event.

4.6

4.6

—

4.5–4.6

4.6–4.7

4.8

129Know that if the probability of an event occurring is p, then the probability of it not occurring is 1–p.130Find and record all possible mutually exclusive outcomes for two successive events in a systematic way, using diagrams and tables.

4.9 (in part)

—

§ Collect data from a simple experiment and record in a frequency table

§ Estimate probabilities based on this data.

—

—

4.10

4.10

1G Notes131Chapters 4 and 14 provide good coverage of the material required in this chapter. You may wish to aim to cover all of the material in chapter 14 first, moving on to consider the work on probability in chapter 4 with pupils who cope well with the work in

1R Notes§ The references given above are those required to move pupils forward in their

learning, if they are secure in their grasp of topics covered at primary level. For example, references to work on simple bar charts and bar line charts are not given


chapter 14. Do bear in mind that the majority of pupils will have covered the topics in chapter 14 at primary level, and you will be revisiting these; do so selectively. In chapter 4, pupils may be used to the idea of probability as a qualitative measure of likelihood, although the use of the numerical scale for probability is likely to be new to them.132Pie charts are only covered in passing.

in the table, although this material is presented in the book. It may be useful to refer to this introductory material, in order to remind the pupils of work they have already done; less confident pupils may benefit from doing some of the material in these earlier sections as written exercises.

Algebra 2 (5 hours)



1R

Equations, formulae and identities(112-119, 138-143)

133Use letter symbols to represent unknown numbers or variables.134Know the meanings of the words term, expression and equation.

9.19.29.3, 11.1, 11.7

135Begin to distinguish the different roles played by letter symbols in equations, formulae and functions.136Know the meanings of the words formula and function.

—

11.1 (in part)

137Understand and use the relationships between the four operations, and the principles (not the names) of the arithmetic laws.138Use brackets.

2.10, 5.1, 5.6, 5.7, 5.8

—

139Understand that algebraic operations follow the same conventions and order as arithmetic operations.

9.59.611.4

140Know that algebraic operations follow the same conventions and order as arithmetic operations; use index notation for small positive integer powers.

9.9

141Simplify linear algebraic expressions by collecting like terms.142Begin to multiply a single term over a bracket (integer coefficients).

—

—

9.3, 9.4

9.7

143Simplify or transform linear expressions by collecting like terms.144Multiply a single term over a bracket.

9.4

9.7

145Use simple formulae from mathematics and other subjects.146Substitute positive integers into simple linear expressions and formulae and, in simple cases, derive a formula.

10.1, 10.2

11.1, 11.3 11.5, 11.6

147Substitute integers into simple formulae, including examples that lead to an equation to solve, and positive integers into expressions involving small powers (e.g. 3x2 + 4 or 2x3).

11.7–11.9

Solving Problems (26-27)

148Identify the necessary information to solve a problem.149Represent problems mathematically, making correct use of symbols, words, diagrams, tables and graphs.

11.2,11.911.9

1G Notes150Chapter 10 provides material relating to using simple formulae. Most pupils should be able to tackle at least some of the core activities in this unit.

1R Notes151Chapters 9 and 11 cover all of the material need in this unit. The later material in these chapters cover most of the requirements of the extension sections.





1R

152Recognise positions. 12.1 153Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes.

1.2, 13.8

13.5, 13.6, 14.11, 1.2

Geometrical reasoning: line, angles and shapes(178-189)

154Identify parallel and perpendicular lines.155Know the sum of angles at a point, on a straight line and in a triangle and recognise vertically opposite angles.

—

13.5

1.814.6 to 14.8

156Identify alternate angles and corresponding angles157Understand a proof that:

§ the sum of the angles of a triangle is 180 and of a quadrilateral is 360;

§ the exterior angle of a triangle is equal to the sum of the two interior opposite angles.

—

14.7 (part), 14.8 (in part)—

158Recognise properties of rectangles.159Classify triangles (isosceles, equilateral, scalene), using criteria such as equal sides, equal angles, lines of symmetry.

1.7

1.6

160Begin to identify and use angle, side and symmetry properties of triangles and quadrilaterals.

1.3–1.7 1.3–1.7 § Classify quadrilaterals by their geometric properties.

1.7

Coordinates(218-219)

161Read and plot coordinates in the first quadrant.

12.112.2

162Use conventions and notation for 2-D coordinates in all four quadrants.163Find coordinates of points determined by geometric information.

—

—

13.1–13.413.7

Mensuration(232-233)

164Use angle measure.

165Distinguish between and estimate the size of acute, obtuse and reflex angles.

13.5, 13.613.7–13.9

14.1–14.314.4, 14.5

1G Notes166Many pupils using book 1G will need plenty of opportunity to practise the vocabulary related to shape. Another important aspect is visualisation; many lower-attaining pupils will continue to benefit from activities designed to help them to visualise shapes and their properties.167This can be tackled effectively as a starter activity. For example, pairs of pupils sit back-to-back. One pupil is given a geometrical diagram, and they have to describe it to their partner, whose task is to reproduce the diagram purely from the spoken instructions provided.168Reflex angles not covered.

1R Notes169Pupils need to be introduced to the notation and conventions for labelling angles and shapes. This could be done in the mental and oral starter; for example, you could draw a polygon on the board, with the vertices labelled; now call out a three-letter ‘code’ for one of the angles, and ask the class to estimate its size.170The extension materials require proofs for geometric properties, which are partially covered in the book. You may wish to explore these proofs with more able pupils. The emphasis should, of course, be on understanding the principles, rather than memorising the proof!171Corresponding and alternate angles are not covered in 1R.

Key Stage 3 National Strategy Year 7: Spring termNumbers in the LH column refer to the supplement of examples for the core teaching programme

YEAR 7 – SPRING TERMTeaching objectives for the oral and mental activities

1R 1R172Read and write whole numbers in figures and words.173Multiply and divide decimals by 10, 100, 1000.174Count back in steps of 0.4, 0.75, ¾ …175Order decimals in different contexts.176Round decimals to the nearest whole number.177Order, add and subtract integers.178Recognise multiples and use tests of divisibility.179Know pairs of numbers up to 100.180Know or derive quickly prime numbers less than 30.181Know or derive quickly squares to at least 12 ´ 12 and the corresponding roots.182Find simple equivalent fractions.

183Know whole-number complements of 50 and 100.184Find two decimals with a sum of 1 or 0.1 (two decimal places).185Add several small numbers and find their mean.186Add and subtract pair of numbers, e.g. 7.6 ± 3.8, 760 ± 380.

6.4

2.16, 2.172.45.4, 5.55.55.55.5

8.5

17.1

187Find doubles and halves of numbers, e.g. 6500, 0.76, ¾.188Recall multiplication and division facts to 10 ´ 10.189Derive answers to calculations, e.g. 60 ´ 80, 0.4 ´ 0.9.190Multiply and divide a two-digit number by a one-digit number.

191Visualise, describe and sketch 2-D shapes.192Estimate and order acute and obtuse angles.

193Use metric units (length and area) and units of time for calculations.

194Convert between m, cm and mm, km and m.195Calculate perimeter and area of rectangles.

196Discuss and interpret graphs.

197Apply mental skills to solve simple problems.

5.1

14.114.4

7.9, 10.1, 10.27.310.1, 10.2

13.8, 13.9





1R

Handling Data(248-255, 262-265, 268-271)

198Solve a problem by representing, extracting and interpreting data in tables, graphs, charts and diagrams.

14.1–14.9

199Given a problem that can be addressed by statistical methods, suggest possible answers.

— —

200Decide which data would be relevant to an enquiry and possible sources.

— — 201Decide the degree of accuracy needed for the data.

—

202Plan how to collect and organise small sets of data.203Design a data collection sheet or questionnaire to use in a simple survey; construct frequency tables for discrete data, grouped where appropriate in equal class intervals.

14.1, 14.214.3, 14.4

15.1

15.1, 15.2

204Plan how to collect the data, including sample size205Construct frequency tables with given equal class intervals for sets of continuous data.

—

—

206Collect small sets of data from surveys and experiments, as planned.

— —

207Construct, on paper and using ICT, graphs and diagrams to represent data, including:

208Construct on paper and using ICT:

§ pie charts for categorical 15.6,


§ bar-line graphs; § frequency diagrams for grouped

discrete data;§ Use ICT to generate pie charts.

14.7 15.815.3–15.515.6

data;

§ simple line graphs for time series.

15.820.11

209Solve problems by representing data in a bar chart and line graph.

14.7 § Interpret diagrams and graphs (including pie charts), and draw simple conclusions based on the shape of graphs.

14.8 15.6

§ Solve word problems and investigate in a range of contexts: handling data.

1G Notes210This unit references the same materials as ‘Handling Data 1’. You will need to decide which sections will be covered in each unit. One approach would be to cover as many of the sections as possible in Handling Data 1, and to use this unit for revision and some project work. See the guidance given on page 18 of the introduction to the Framework.211Pie charts are not covered in 1G.

1R Notes212This unit lends itself particularly well to project work. It will probably be worth reviewing the earlier material in chapter 15 at this stage, and to make sure that pupils are given the opportunity to engage in a purposeful and relevant statistical investigation. Although some pupils may wish to use the idea of correlation in their project work, this material is not actually required until Year 9.

Numbers and Measures 3 (8 hours)


1G CORE from the Y7 teaching programme 1G 1R EXTENSION from the from the Y8 teaching programme

1R

Place Value(42-45)

213Round positive whole numbers to the nearest 10, 100 or 1000 and decimals to the nearest whole number or one decimal place.

2.172.186.11

214Round positive numbers to any given power of 10.215Round decimals to the nearest whole number or to one or two decimal places.

6.11

6.11

Calculations(82-87, 92-103, 104-107, 110-111)

216Understand and use the relationships between the four operations, and the principles (not the names) of the arithmetic laws.

217Understand addition, subtraction, multiplication and division as they apply to whole numbers and decimals.218Know how to use the laws of arithmetic and inverse operations.

2.15, 2.16

5.1, 5.2 5.6–5.13, 6.2, 6.4–6.9

219Know multiplication facts up to 10 x 10.

5.1, 5.2 220Know and use the order of operations, including brackets.

11.4 (in part)

221Recall products such as 0.7 and 6, and 0.03 and 8.

6.8

222Add several numbers.223Use doubling and halving.

224Partition to mentally multiply TU x U.

2.5, 2.82.11 (part)5.11

225Consolidate and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings.

6.4–6.9


226Solve simple word problems mentally.227Make and justify estimates and approximations of calculations.

2.12

2.19, 6.12

228Extend written methods to:§ HTU x U and U.t x U;§ TU x TU§ HTU ÷ U

§ Divide £.p by a two-digit number to give £.p.

§ Round up or down after divi-sion, depending on the context.

—5.95.76.9 (part)—

229Multiply and divide three-digit by two-digit whole numbers.230Extend to multiplying and dividing decimals with one or two places by single-digit whole numbers.

—

—

5.12, 5.136.8, 6.9

231Multiply and divide integers and decimals including by decimals such as 0.6 and 0.06.232Understand where to position the decimal point by considering equivalent calculations.

6.8, 6.9 (in part)

—


— 6.12


§ Develop calculator skills and use a calculator effectively.

17.117.2

234Carry out calculations with more than one step using brackets and the memory235Use the square root and sign change keys.

17.1–17.5

—

20.120.220.75.3 (in part)

Measures(228-231)

§ Use, read and write standard metric units and measuring equipment to estimate or measure length, mass or capacity.

§ Suggest suitable units and measuring equipment to estimate or measure length, mass or capacity.

7.1–7.7

7.1

236Use names and abbreviations of units of measurement to measure, estimate, calculate and solve problems in everyday contexts involving length, area, mass, capacity, time and angle.237Convert one metric unit to another (e.g. grams to kilograms).238Read and interpret scales on a range of measuring instruments.

7.1–7.6 7.8–7.11

7.3, 7.4 7.67.7

7.1–7.7 7.9–7.11, 14.3, 20.47.3, 7.6

7.8

239Know rough metric equivalents of imperial measures in daily use.

—


§ Use all four operations to solve word problems, including time.

2.10, 5.5 (part), 5.6, 5.7 (part), 5.8, 5.9 7.8–7.11


— —

241Present and interpret solutions in the context of the original problem242Explain and justify methods and conclusions, orally and in writing.

— — 243Give solutions to an appropriate degree of accuracy in the context of the problem.

—

1G Notes244The work on extending written methods for multiplication and division can use the material in chapters 5 and 6 as a starting point.

1R Notes§ The use of the sign change key is not covered in chapter 20, and reference to it

should be made if it is to be included in this unit. The work on multiplying & dividing


245Section 2.5 covers adding two numbers only. decimals and whole numbers in chapter 6 goes up to a level between the core and extension requirements in this unit. Extension work on imperial and metric units is provided in book 2B.

Algebra 3 (6 hours)



1R

Integers, powers and roots (52-59)

246Recognise multiples up to 10 x 10.

247Know and apply simple tests of divisibility.

5.1–5.3

5.8, 17.4

248Recognise and use multiples, factors (divisors), common factor, highest common factor and lowest common multiple in simple cases, and primes (less than 100).249Use simple tests of divisibility.

5.10

—

5.1, 5.2 5.4, 5.5 (in part)

5.4

250Find the prime factor decomposition of a number.

5.5

251Identify factors of two-digit numbers.

5.10 252Recognise the first few triangular numbers, squares of numbers to at least 12 x12 and the corresponding roots.

3.2 (part), 3.6

3.75.3

253Use squares, and positive and negative square roots.


254Use a calculator to square numbers.

17.2 255Use the square root key. — 5.3 256Use the function keys for sign change, powers and roots.

20.2 (in part)

Sequences, functions and graphs(148-167)

257Recognise and extend number sequences.

3.1–3.4 258Generate terms of a simple sequence, given a rule (e.g. finding a term from the previous term, finding a term given its position in the sequence).

— 3.4–3.6 259Generate terms of a linear sequence using term-to-term and position-to-term definitions of the sequence, on paper and using a spreadsheet or graphical calculator.

3.6, 20.9


— 3.1–3.3 261Begin to use linear expressions to describe the nth term of an arithmetic sequence.

3.6

262Express simple functions in words, then using symbols.263Represent them in mappings.

3.3 3.3 264Express simple functions in symbols265Represent mappings expressed algebraically.

11.2

266Read and plot co-ordinates in the first quadrant.267Represent and interpret data in a graph (e.g. for a multiplication table.)

12.1, 12.212.3

268Generate coordinate pairs that satisfy a simple linear rule.269Plot the graphs of simple linear functions, where y is given explicitly in terms of x, on paper and using ICT.

270Recognise straight-line graphs parallel to the x-axis or y-axis.

—

—

—

13.4

13.7

13.5

271Generate points in all four quadrants and plot the graphs of linear functions.272Recognise that equations of the form y = mx + c correspond to straight-line graphs.

13.2, 13.6, 13.713.6

Solving problems(2-13, 26-27)

273Solve mathematical problems, explaining patterns and relationships.

Ch. 16 274Solve word problems and investigate in a range of contexts: number and algebra.

10.1–10.3

11.1–11.6

275Solve more complex problems by breaking them into smaller steps.

—

276Identify the necessary information to solve a problem.277Represent problems mathematically,

—

—

11.7–11.9

278Represent problems and interpret solutions in algebraic or graphical form, using correct

11.7to11.9


making correct use of symbols, words, diagrams, tables and graphs.

notation.

1G Notes 1R Notes279There are several sections which have been included in both the core and extension columns above. These sections (for example, 3.6) provide harder material which may be accessible to some pupils following the core programme.




1R

Geometrical reasoning: lines, angles and shapes(184-189, 198-201)

280Recognise reflection symmetry.281Recognise where a shape will be after reflection.282Recognise where a shape will be after a translation.283Calculate angles on a straight line.284Calculate angles in a triangle or around a point.

1.3, 1.4

1.5 (in part)—

—

—

285Begin to identify and use angle, side and symmetry properties of triangles and quadrilaterals.286Solve geometrical problems involving these properties, using step-by-step deduction and explaining reasoning with diagrams and text.

1.6, 1.7

—

1.6, 1.7

14.8 (in part)

287Solve geometrical problems using side and angle properties of equilateral, isosceles and right-angled triangles and special quadrilaterals.

14.8 (in part), 14.9 (in part)

288Use 2-D representations to visualise 3-D shapes and deduce some of their properties.

1.81.9

1.91.10

Construction(220-223)

289Use a protractor to measure and draw acute and obtuse angles to the nearest degree.

13.6 290Use a ruler and protractor to: § measure and draw lines to the

nearest millimetre and angles, including reflex angles, to the nearest degree;

§ construct a triangle given two sides and the included angle (SAS) or two angles and the included side (ASA)

§ Explore these constructions using ICT.

13.8 (in part)

13.8 (in part)

—

7.2, 14.3, 14.10

14.3, 14.11

—

291Use straight edge and compasses to construct:

§ the mid-point and perpendicular bisector of a line segment;

§ the bisector of an angle.§ Construct a triangle, given three

sides (SSS).

—

——

1G Notes292The required material on angles is covered in chapter 14 of book 1R. The work on translation and rotation is in chapter 18 of book 1R.

1R Notes293The angles work in this work is introductory; there is a lot more advanced work in book 2B.

Number 4 (5 hours)



1R

FDPRP(70-81)

294Relate fractions to division.295Find simple fractions of whole-number quantities.296Find simple percentages of whole-number quantities.

8.38.1, 8.2

—

297Recognise the equivalence of percentages, fractions and decimals.

298Calculate simple percentages and use percentages to compare simple proportions.

15.3, 15.4

—

8.8, 16.2–16.416.5–16.6

299Express one given number as a percentage of another.300Use the equivalence of fractions, decimals and percentages to compare proportions.

—

8.11 (in part)


301Solve simple problems using ideas of ratio and proportion (‘one for every…’ and ‘one in every…’)

— 302Understand the relationship between ratio and proportion.303Use direct proportion in simple contexts.304Use ratio notation, reduce a ratio to its simplest form and divide a quantity into two parts in a given ratio.305Solve simple problems about ratio and proportion using informal strategies.

—

—

—

—

8.11

8.11

8.12

8.13

306Divide a quantity into two or more parts in a given ratio.307Use the unitary method to solve simple word problems involving ratio and direct proportion.

8.13

—

Calculations(110-111)


— 2.19 (in part)

1G Notes 1R Notes

Algebra 4 (4 hours)


1G CORE from the Y7 teaching programmes

1G 1R EXTENSION from the Y8 teaching programme

1R

Equations, formulae and identities(112-125)

309Use letter symbols to represent unknown numbers or variables.310Know the meanings of the words term, expression and equation.

— 9.1–9.3

11.2, 11.7

311Begin to distinguish the different roles played by letter symbols in equations, formulae and functions.312Know the meanings of the words formula and function.

11.1, 11.3, 11.611.7


2.105.75.85.9

—

315Understand that algebraic operations follow the same conventions and order as arithmetic operations.

— 11.411.5

316Simplify linear algebraic expressions by collecting like terms.317Begin to multiply a single term over a bracket (integer coefficients.)

— 9.3–9.4

9.5–9.7

318Construct and solve simple linear equations with integer coefficients (unknown on one side only) using an appropriate method (e.g. inverse operations).

— 11.7 319Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (e.g. inverse operations, transforming both sides in same way.)

11.811.9

1G notes 1R notes


Key Stage 3 National Strategy Year 7: Summer termNumbers in the LH column refer to the supplement of examples for the core teaching programme

YEAR 7 – SUMMER TERMTeaching objectives for the oral and mental activities

1R 1R320Multiply and divide decimals by 10, 100 and 1000 and small multiples of 10.321Round numbers, including to one or two decimal places.322Order decimals and simple fractions in different contexts.323Recognise and use tests of divisibility.324Know pairs of factors of numbers to 100.325Know or derive quickly prime numbers less than 30.326Know or derive squares to at least 12 ´ 12, multiples of 10, 0.1 to 0.9 and corresponding to square roots.327Convert between fractions, decimals and percentages.328Find fractions and percentages of quantities.

329Know complements of 0.1, 1, 10, 50, 100.330Add and subtract pairs of numbers, e.g. 0.65 + 3.8, 765 + 47.331Use jottings to support addition and subtraction of whole numbers and decimals.332Find doubles and halves of decimals and fractions.333Recall multiplication and division facts to 10 ´ 10.334Use doubling and halving to calculate, e.g. 6 ´ 4.5, 1.38 ´ 50.

6.4

2.16, 2.17

5.4, 5.55.55.5

8.88.3, 8.4

5.1

335Use factors to multiply and divide mentally, e.g. 35 ´ 12, 144 ¸36, 3.2 ´ 30.336Derive answers to calculations, e.g. 0.4 ´ 9, 0.7 ´ 0.9.337Multiply and divide a two-digit number by a one-digit number.338Use approximations to estimate the answers to calculations, e.g. 39 ´ 2.8.

339Solve equations such as 100 = x + 37.

340Visualise and describe 2-D and 3-D shapes.341Estimate and order acute, obtuse and reflex angles.

342Use metric units (length, mass, capacity) and units of time for calculations.343Convert between m, cm and mm, km and m, kg and g, litres and ml.344Convert between metric and common imperial units.

345Discuss and interpret graphs.

346Apply mental skills to solve simple problems.

14.114.4

7.9, 10.1, 10.27.3

13.8, 13.9





1R

Transformations(202-212)

347Understand and use the language and notation associated with reflections, translations and rotations.

— 18.1–18.3

348Recognise reflection symmetry.349Recognise where a shape will be after reflection.350Recognise where a shape will be after a translation.

1.31.41.5 (in part)—

351Recognise and visualise the transformation and symmetry of a 2-D shape:

§ reflection in given mirror lines, and line symmetry;

§ rotation about a given point, and rotation symmetry;

§ translation.§ Explore these transformations and

symmetries using ICT.

—

—

——

18.1

18.2

18.3—

352Transform 2-D shapes by simple combinations of rotations, reflections and translations, on paper and using ICT353Identify all the symmetries of 2-D shapes.

—

1.3, 1.4

354Understand and use the language and notation associated

—


with enlargement.355Enlarge 2-D shapes, given a centre of enlargement and a positive whole-number scale factor.

—

Solving problems(14-17, 32-35)

§ Solve word problems and investigate in a range of contexts: shape & space.

§ Suggest extensions to problems by asking ‘What if…?’; begin to generalise and to understand the significance of a counter-example.

—

—

—

—

1G Notes356For translation, see book 1R, section 18.3.

1R Notes357Enlargement is covered in book 2R, chapter 11, along with the other plane transformations.




1R

Handling Data(250-273)

358Decide which data would be relevant to an enquiry and possible sources.

— 15.1 (in part)

359Plan how to collect and organise small sets of data360Design a data collection sheet or questionnaire to use in a simple survey.361Construct frequency tables for discrete data, grouped where appropriate in equal class intervals.

—

—

—

15.1

15.1

15.2, 15.7

362Find the mode and range of a set of data. Begin to find the median and mean of a set of data.

— 363Calculate statistics for small sets of discrete data:

§ find the mode, median and range, and the modal class for grouped data;

§ calculate the mean, including from a simple frequency table, using a calculator for a larger number of items.

17.2–17.417.1, 17.5, 20.12

364Recognise when it is appropriate to use the range, mean, median and mode and, for grouped data, the modal class.365Calculate a mean using an assumed mean.

—

—

§ Construct, on paper and using ICT, graphs and diagrams to represent data, including:

§ bar-line graphs; 14.7 15.4, 15.5,

366Construct, on paper and using ICT:

§ pie charts for categorical data;

§ simple line graphs for time

15.615.8


§ frequency diagrams for grouped discrete data

§ Use ICT to generate pie charts.

—

17.8

15.815.2–15.320.11 (in part)

series.

367Solve a problem by representing, extracting and interpreting data in tables, graphs and charts.

14.1–14.9

§ Interpret diagrams and graphs (including pie charts), and draw simple conclusions based on the shape of graphs and simple statistics for a single distribution.

— 15.6 § Interpret tables, graphs and diagrams for both discrete and continuous data.

15.7 (in part)

§ Compare two simple distributions using the range and one of the mode, median or mean.

— 17.6

§ Write a short report of a statistical enquiry and illustrate with appropriate diagrams, graphs and charts, using ICT as appropriate.

§ Justify the choice of what is presented.

—

—

—

—

Probability(278-285)

§ Understand and use the probability scale from 0 to 1.

§ Find and justify probabilities based on equally likely outcomes in simple contexts.

§ Identify all the possible mutually exclusive outcomes of a singe event.

4.6

4.6

—

4.5–4.6

4.6, 4.7

4.8

§ Know that if the probability of an event occurring is p, then the probability of it not occurring is 1 – p.

§ Find and record all possible mutually exclusive outcomes for single events and two successive events in a systematic way, using diagrams and tables.

4.9 (in part)

—

§ Collect data from a simple experiment and record in a frequency table.

§ Estimate probabilities based on this data.

—

—

4.10

4.10

§ Understand that: § if an experiment is repeated

there may be, and usually will be, different outcomes;

§ increasing the number of times an experiment is repeated generally leads to better estimates of probability.

—

—

§ Compare experimental and theoretical probabilities in simple contexts.

— 4.10

1G Notes 1R Notes


Number 5 (8 hours)



1R

Place Value(52-55)

368Recognise multiples up to 10 x 10.369Know simple tests of divisibility.370Identify factors of two-digit numbers.

5.1

5.4

5.4

371Recognise and use multiples, factors (divisors), common factor, highest common factor and lowest common multiple in simple cases, and primes (less than 100).372Use simple tests of divisibility.

5.10 (in part)

5.4

5.2, 5.4, 5.5

5.4

373Find the prime factor decomposition of a number.

5.5 (in part)


374Consolidate the rapid recall of number facts, including positive integer complements to 100 and multiplication facts to 10 x 10, and quickly derive associated division facts.

5.1, 5.2, 5.5, 5.6 (in part)

2.1–2.12, 5.1, 5.2 (part), 5.9

375Recall known facts, including fraction to decimal conversions; use known facts to derive unknown facts, including products involving numbers such as 0.7 and 6, and 0.03 and 8.

—

376Consolidate mental methods:§ find a difference by

counting up;§ add or adjust a multiple

of 10 then adjust.§ Add and subtract mentally

pairs of two digit numbers.

2.7, 2.8

2.7, 2.8

2.8, 2.9

377Consolidate and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings; solve simple word problems mentally.

— 6.4–6.7 378Extend mental calculations to squares, square roots, cubes and cube roots.

—

379Make and justify estimates and approximations of calculations.

— 2.19

§ Approximate first and use informal pencil and paper methods to EXTENSION addition and subtraction.

2.11, 2.12

380Use standard column procedures to add and subtract whole numbers and decimals with up to two places.

2.11, 2.12, 6.4

2.15, 2.16, 6.2

§ Extend written methods to:

§ HTU x U and U.t x U;§ TU x TU§ HTU ÷ U

§ Divide £.p by a two-digit number to give £.p.

§ Round up or down after division, depending on the context.

—5.95.76.9 (part)—

381Multiply and divide three-digit by two-digit whole numbers.382Extend to multiplying and dividing decimals with one or two places by single-digit whole numbers.

—

—

5.10–5.136.8–6.9

383Multiply and divide integers and decimals, including by decimals such as 0.6 or 0.06.384Understand where to position the decimal point by considering equivalent calculations.

—

—


See notes

See notes


386Carry out calculations with more than one step using brackets and the memory.387Use the square root and sign change keys.

17.1

—

20.1, 20.2, 20.75.3 (in part)

388Interpret the display in different 17.1– 20.5,


contexts (decimals, percentages). 17.5 20.6Fractions and percentages(66-77)

389Calculate simple fractions of quantities and measurements (whole-number answers).390Multiply a fraction by an integer.

8.3 (part)

—

8.3, 8.4

8.4

391Calculate fractions of quantities (fraction answers).392Multiply and divide an integer by a fraction.

—

—

393Recognise the equivalence of percentages, fractions and decimals.394Calculate simple percentages and use percentages to compare simple proportions.

15.3, 15.415.1, 15.4 (in part)

16.3, 16.416.5 (in part)



See notes

See notes

1G Notes396The first set of objectives in the ‘support’ column are covered in book 1G; see sections 8.2 and 8.5. The mental calculation skills listed in this column can be revised and practised in the mental and oral starter.

1R Notes§ Chapters 6, 8 and 16 provide a considerable amount of material for this unit. In

planning a series of lessons within this unit, it will be necessary to be selective about selection and presentation of the work involved; it may be possible to omit some of the exercises, or to present them orally. When solving problems, aim to reinforce the skills outlined at the bottom of the core column in the table.

§ Use of ± key not covered.§ Lowest common multiples not covered in 1R.

Algebra 5 (8 hours)



1R

Equations, formulas and identities(122-143)

397Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (e.g. inverse operations.)

— 11.7, 11.9

398Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (e.g. inverse operations, transforming both sides in same way.)

11.811.9


2.10, 5.1, 5.6, 5.7, 5.8, 5.9—

401Use simple formulae from mathematics and other subjects.

402Substitute positive integers into simple linear expressions and formulae and, in simple cases, derive a formula.

10.110.2

—

11.1, 11.3, 11.511.6, 11.7, 11.9

403Substitute integers into simple formulae, including examples that lead to an equation to solve, and positive integers into expressions involving small powers (e.g. 3x2 + 4 or 2x3 ).

—

Sequences, functions and graphs


3.1–3.4 3.1–3.4 405Begin to use linear expressions to describe the nth term of an arithmetic sequence.

3.6


(154-177)406Express simple functions in words, then using symbols407Represent them in mappings.

3.3 3.3

408Read and plot co-ordinates in all four quadrants.

— 409Generate coordinate pairs that satisfy a simple linear rule.410Plot the graphs of simple linear functions, where y is given explicitly in terms of x, on paper and using ICT.411Recognise straight-line graphs parallel to the x-axis or y-axis.

—

—

—

13.4

13.7

13.5

412Generate points in all four quadrants and plot the graphs of linear functions.413Recognise that equations of the form y = mx + c correspond to straight-line graphs.

13.2, 13.6, 13.7(See notes)13.6

414Begin to plot and interpret the graphs of simple linear functions arising from real-life situations.

13.813.9


415Suggest extensions to problems by asking ‘What if…?’; begin to generalise and to understand the significance of a counter-example.

—

1G Notes416The work on extending the coordinate grid to all four quadrants is covered in chapter 13 of book 1R.

1R Notes417The work on coordinates and graphs in chapter 13 goes beyond the requirements of the core programme, and includes the material needed in the extension list as well.




1R

Geometrical reasoning: lines, angles and shapes(184-212)

418Recognise reflection symmetry.419Recognise where a shape will be after reflection.420Recognise where a shape will be after translation.

1.31.41.5 (in part)—

421Begin to identify and use angle, side and symmetry properties of triangles and quadrilaterals.422Solve geometrical problems involving these properties, using step-by-step deduction and explaining reasoning with diagrams and text.

1.61.7

—

1.6, 1.7

14.8 (part)

423Solve geometrical problems using side and angle properties of equilateral, isosceles and right-angled triangles and special quadrilaterals.424Classify quadrilaterals by their geometric properties.

14.8 (in part), 14.9 (part)

1.7

425Calculate angles on a straight line, in a triangle, or around a point.

— 426Explore transformations and symmetries using ICT.

— —

Construction(220-223)

427Use a protractor to measure and draw acute and obtuse angles to the nearest degree.

13.6–13.9

428Use a ruler and protractor to construct a triangle given two sides and the included angle (SAS) or two angles and the included side (ASA).429Explore these constructions using ICT.

13.8 (inpart)

—

14.314.11

—

430Use straight edge and compasses to construct:

§ the mid-point and perpendicular bisector of a line segment;

§ the bisector of an angle;§ construct a triangle, given

three sides (SSS).

—

——


431Visualise 3-D shapes from 2-D drawings and identify different nets for a closed cube.

1.81.9[Part]

432Use ruler and protractor to construct simple nets of 3-D shapes, e.g. cuboid, regular tetrahedron, square-based pyramid, triangular prism.

— —

1G Notes433The required material on angles is covered in chapter 14 of book 1R. The work on translation and rotation is in chapter 18 of book 1R.

1R Notes434The angles work in this work is introductory; there is a lot more advanced work in book 2B, which covers the material in the extension section here.

Notes

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