Sample Medium Term Plans for Maths Using Impact Maths

Key Stage 3 Sample medium term plans for maths using Impact Maths Year 8  We have given references to the sections in 2G, 2B and 2R. Contents  For ease of reference, the layout is very similar to the DfES sample medium-term plans, with the Impact sections in the column(s) alongside. Planning with the Framework 1  We have repeated the DfES’s columns of ‘support’, ‘core’ and ‘extension’ to help with differentiation across sets. Year 7 planning chart 2  We have also retained the dependencies between topics as the DfES sample plans. Autumn term 3 Number/algebra 1 3 How to use this document Shape, space and measures 1 4 This is a reproduction of the sample medium-term plans produced by the National Handling data 1 5 Numeracy Strategy, reproduced with permission and acknowledgement to the DfES. Number 2 6 Algebra 2 7 Details of how these charts can be used for planning are given on p1. In addition to Shape, space and measures 2 8 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 Spring term 10 packs. The cross-references in the teaching objectives for the oral and mental Algebra 3 10 activities refer to the lesson starters in the 1R pupil performance pack. There is also a Number 3 11 short narrative for each topic of work, giving advice on using Impact and other Shape, space and measures 3 12 resources. Algebra 4 13 Handling data 2 14 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 Summer term 16 provide extension material. Number 4 16 Algebra 5 17 Solving problems 19 A matching guide for Year 7 is now available, and Year 9 will be available in the Shape, space and measures 4 20 spring term. Handling data 3 21 Notes on tables (in pt) section covers point in part. (pt) part of section covers point.

About the author Working with the Impact guide Derek Huby is an experienced primary and secondary numeracy consultant, as well as being an experienced maths teacher and head of department. The 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 Acknowledgement Mathematics. This document provides a detailed guide of how to deliver the We would like to thank Derek Huby and Jim Newall for their work in the preparation of framework using Impact materials. this document. 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 8 using Impact.

For example:  Core objectives are in bold as in the medium-term plans. Impact maths sample medium-term plans for mathematics some of the work they have been taught earlier. To begin with, these schools should Planning with the Framework 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 [The text of this page is reproduced with permission from the Department for adjustments for Years 8 and 9. A decision like this would need to be reviewed before Education and Skills.] the start of the next school year to allow for improving standards over time.

The Framework for teaching mathematics: Years 7, 8 & 9 provides teachers with How the plans are set out guidance on meeting the National Curriculum requirements for mathematics. It sets Teaching objectives for oral and mental activities are placed at the beginning of the out yearly teaching programmes showing how objectives for teaching mathematics plan for each term. Objectives for the main activities are set out in four main columns: can be planned from Year 7 to Year 9. A key task in developing medium-term plans  The first identifies the areas of mathematics studied in the unit and identifies links for Key Stage 3 mathematics is to identify the objectives for the units of work that are to the supplement of examples in the Framework. going to be taught. In doing this, schools may choose to start from their existing  The second identifies support objectives from previous yearly teaching schemes of work, or alternatively, may find that these sample plans provide a useful programmes. These are linked to the core objectives for each unit. starting point.  The third column sets out the core objectives for the year group, the ones you would expect to focus on for the majority of pupils. 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  The fourth provides extension objectives, to stretch able pupils, drawn from the examples of planning charts in the Framework. There are many other ways to next year’s teaching programme. These are linked to the core objectives for the unit. 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:  Progression in the teaching objectives for each strand of the curriculum;  Links between the teaching objectives, bringing together related ideas across the strands;  Opportunities 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);  How 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

Impact maths sample medium-term plans for mathematics Page 1 Key Stage 3 National Strategy

YEAR 8 PLANNING CHART

Autumn 36 hours Number/algebra 1 Integers, powers and roots SSM1 Sequences functions and graphs Geometrical reasoning: lines, 6 hours angles and shapes Handling data 1 Construction Probability Algebra 2 6 hours 6 hours Number 2 Equations and FDPRP formulae SSM 2 6 hours 6 hours Measures and mensuration 6 hours

Spring 33 hours Algebra 3 Number 3 Integers, powers and Place value roots SSM 3 Calculations Sequences, functions Transformations Calculator methods and graphs Geometrical reasoning: FDPRP 6 hours lines, angles and shapes Solving problems 6 hours 9 hours Algebra 4 Handling data 2 Equations and formulae Handling data Graphs 6 hours 6 hours

Summer 36 hours Number 4 Calculations Algebra 5 Measures Sequences, functions and 6 hours graphs Equations and formulae Solving problems 8 hours Solving problems, SSM 4 Handling data 3 including FDPRP Geometrical reasoning: lines, angles and shapes Handling data, including 6 hours Transformations probability Mensuration 7 hours 9 hours

35 weeks 105 hours

Using and applying mathematics to solve problems should be integrated into each unit.

Impact maths sample medium-term plans for mathematics Page 2 Key Stage 3 National Strategy Year 8: Autumn term Numbers in the LH column refer to the supplement of examples for the core teaching programme YEAR 8 – AUTUMN TERM Teaching objectives for the oral and mental activities 2R 2R  Order, add, subtract, multiply and divide integers. 5.3 (pt),  Multiply and divide a two-digit number by a one-digit number. 8.1–8.4  Use partitioning to multiply, e.g. 13  1.4.  Multiply and divide decimals by 10, 100, 1000. 5.3  Use approximations to estimate the answers to calculations, e.g. 39  3  Count on and back in steps of 0.4, 0.75, /4… 2.8.  Round numbers, including to one or two decimal places.  Know and use squares, positive and negative square roots, cubes of  Solve equations, e.g. 3a – 2 = 31. 14.3, 14.5 numbers 1 to 5 and corresponding roots.  Convert between fractions, decimals and percentages. 3.5  Visualise, describe and sketch 2-D shapes. 7.3 3.1B, 6.2  Find fractions and percentages of quantities.  Estimate and order acute, obtuse and reflex angles.

 Know or derive complements of 0.1, 1, 10, 50, 100, 1000.  Use metric units (length, mass, capacity) and units of time for  Add and subtract several small numbers or several multiples of 10, calculations. e.g. 250 + 120 – 190.  Use metric units for estimation (length, mass, capacity).  Use jottings to support addition and subtraction of whole numbers and  Convert between m, cm and mm, km and m, kg and g, litres and ml, decimals. cm² and mm².  Calculate using knowledge of multiplication and division facts and 5.3, 5.5  Discuss and interpret graphs. place value, e.g. 432  0.01, 37  0.01. 12.1, 12.3, 12.6A&B,  Recall multiplication and division facts to 10  10. 12.7, 13.5  Use factors to multiply and divide mentally, e.g. 22  0.02, 420  15. 5.3, 5.5  Apply mental skills to solve simple problems.

Teaching objectives for the main activities

Number/ SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R Algebra 1 (6 programme programme programme hours) Integers,  Understand negative 10.1, 10.2 8.2  Add, subtract, multiply and 1.6, 1.3, 8.3, powers and numbers as positions on a 10.3, divide integers. 1.8, 1.8, 8.4, roots (48–59) number line. 10.4, 1.11– 1.9, 8.5 10.7 1.14, 3.1,  Order, add and subtract 10.2, 10.1, 8.1, 3.1– 3.2, positive and negative integers in 10.5 10.3 8.3 3.4, 3.7– context. 10.6 10.4 3.8– 3.11, 10.8 3.11, 10.4 10.9 10.4– 10.9  Use tests of divisibility. See See See  Recognise and use multiples, 3.5, 3.3– 1.2  Use the prime factor – notes notes notes factors (divisors), common factor, 3.6 3.5 decomposition of a number highest common factor, lowest See common multiple and primes. notes

 Find the prime factor – – – Impact maths sample medium-term plans for mathematics Page 3 Key Stage 3 National Strategy Year 8: Autumn term Numbers in the LH column refer to the supplement of examples for the core teaching programme decomposition of a number (e.g. 8000 = 2³ x5³).  Recognise the first few 3.7 3.6 1.3  Use squares, positive and negative 3.6, 3.6, 1.3  Use ICT to estimate square 18.1 triangular numbers, squares of square roots, cubes and cube roots, 3.7 3.11 roots and cube roots. (in pt) numbers to at least 12 x12 and and index notation for small positive (in pt)  Use index notation for integer 10.2 the corresponding roots. integer powers. see powers and simple instances of the notes index laws.  Know and use the index laws in 10.3 generalised form for multiplication and division of integer powers. Sequences and  Generate and describe integer 5.1– 5.1– 9.1, functions (144– sequences. 5.4 5.4 9.2, 157) 9.4  Generate terms of a simple 5.4 5.4 9.4  Generate terms of a linear 5.4, 5.4, 9.1– sequence, given a rule. sequence using term-to-term and 17.2, 17.3, 9.4, position-to-term definitions of the 17.4 17.5 18.3, sequence, on paper and using a 18.5 spreadsheet or graphical calculator.  Generate sequences from 16.1 16.1 9.1,  Begin to use linear expressions to – 5.4 9.5 practical contexts and describe 9.4 describe the nth term of an arithmetic the general term in simple sequence, justifying its form by cases. referring to the activity or practical context from which it was generated. Notes (2G) Notes (2B) Notes (2R)  Tests of divisibility are covered in 1G.  Tests of divisibility are covered in 1G and 1R.  Tests of divisibility are covered in 1R.  HCF, LCM and prime factors are covered in 3G.  Cubes and index notation are covered in 3G.

Shape, space SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R and measures programme programme programme 1 (6 hours) Geometrical  Use correctly the vocabulary, 2.9, 2.9 2.5, reasoning: notation and labelling 9.1– 9.1– 7.1 lines, angles conventions for lines, angles and 9.4 9.3 and shapes shapes. (178–189)  Identify parallel and 9.1 9.1 2.10  Identify alternate angles and – – 2.10  Explain how to find, calculate perpendicular lines. corresponding angles. and use:  Know the sum of angles at 2.7, 2.7 2.4  the sums of the interior and 2.9 a point, on a straight line and 2.8 2.8 2.10 2.6 exterior angles of in a triangle, and recognise quadrilaterals, pentagons and vertically opposite angles.  Understand a proof that: 2.10 hexagons. 2.8  Use angle measure.  the sum of the angles of a (in pt)  the interior and exterior angles of  Distinguish between and 2.2 2.2 2.1 triangle is 180º and of a regular polygons. estimate the size of acute, 2.3– 2.3– 2.2, quadrilateral is 360º Impact maths sample medium-term plans for mathematics Page 4 Key Stage 3 National Strategy Year 8: Autumn term Numbers in the LH column refer to the supplement of examples for the core teaching programme obtuse and reflex angles. 2.6 2.6 2.3  the exterior angle of a triangle is – – 2.7 equal to the sum of the two interior opposite angles.  Solve geometrical problems using 9.2 9.1, 7.3  Solve problems using 2.10 side and angle properties of (in pt) 9.2 properties of angles, of parallel equilateral, isosceles and right-angled see and intersecting lines, and of triangles and special quadrilaterals, notes triangles and other polygons. explaining reasoning with diagrams  Know the definition of a circle 7.1 and text. and the names of its parts.  Classify quadrilaterals by their 9.2 9.2 7.4 geometric properties. Construction  Use a ruler and protractor to:  Use straight edge and  Use straight edge and – (220–223)  measure and draw lines to the 2.4, 2.4, 2.2, compasses to construct: compasses to construct a triangle, nearest millimetre and 2.5 2.5 2.3  the mid-point and – – – given right angle, hypotenuse and angles, including reflex perpendicular bisector of a line side (RHS). angles, to the nearest segment. degree. – – –  the bisector of an angle. – – 7.5  construct a triangle given two  the perpendicular from a point – – – sides and the included angle to a line. (SAS) or two angles and the  the perpendicular from a point – – – included side (ASA). on a line. Solving  Investigate in a range of contexts: 9.4 7.3 problems shape and space. 17J (14–17) Notes (2G) Notes (2B) Notes (2R)  Side and angle properties of triangles are not covered.

Handling data SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R 1 (6 hours) programme programme programme Probability  Use the vocabulary of probability 7.1– 7.1, 4.1, (276–283) when interpreting the results of an 7.5 7.6 4.5 experiment.  Appreciate that random processes – – – are unpredictable.  Understand and use the 7.3 7.1, 4.1  Know that if the probability of an 7.4 7.5, 4.3–  Identify all the mutually exclusive 4.5 probability scale from 0 to 1. 7.2 event occurring is p, then the (in pt) 7.6 4.5 outcomes of an experiment. probability of it not occurring is 1 – p. see notes

 Find and justify 7.4 7.3, 4.2  Find and record all possible – – 4.6  Know that the sum of 4.6 probabilities based on equally 7.4 mutually exclusive outcomes for probabilities of all mutually likely outcomes in simple single events and two successive exclusive outcomes is 1 and use contexts. events in a systematic way, using this when solving problems.  Identify all the possible 7.5, 7.4 4.2 diagrams and tables. mutually exclusive outcomes of a 7.6 Impact maths sample medium-term plans for mathematics Page 5 Key Stage 3 National Strategy Year 8: Autumn term Numbers in the LH column refer to the supplement of examples for the core teaching programme singe event.  Collect data from a simple – 7.6 7.5  Estimate probabilities from see 7.6 4.5  Compare experimental and – experiment and record in a experimental data. notes theoretical probabilities in a range frequency table.  Understand that: of contexts.  Estimate probabilities based – 7.6 7.5  if an experiment is repeated there 7.6 4.5  Appreciate the difference 4.5 on this data. may be, and usually will be, between mathematical explanation different outcomes. and experimental evidence.  increasing the number of times an – 4.5 experiment is repeated generally leads to better estimates of probability. Notes (2G) Notes (2B) Notes (2R)  (1 – p) is covered in 3G.

Number 2 (6 SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R hours) programme programme programme Fractions,  Use fraction notation to 6.1 6.1 3.1  Know that a recurring decimal is a – – 3.4 decimals, express a smaller whole number fraction. percentages as a fraction of a larger one.  Use division to convert a fraction to 8.8 – 3.5, (60 – 77)  Simplify fractions by 6.5 6.2 3.2 a decimal. (pt), 5.6 cancelling all common factors 3.3 17.7 and identify equivalent  Order fractions by writing them with – 6.3 5.6, fractions. a common denominator or by 5.8  Convert terminating decimals – – – converting them to decimals. to fractions.  Add and subtract simple 6.3, 6.5 3.6  Add and subtract fractions by 6.6 6.5 3.6,  Use efficient methods to add, 3.8 fractions and those with common 6.6 writing them with a common (in pt) 3.7 subtract, multiply and divide 3.10 denominators denominator – fractions, interpreting division as a  Calculate fractions of 6.4 6.5 3.1  Calculate fractions of quantities – 3.8 multiplicative inverse. quantities (whole-number (fraction answers) –  Cancel common factors before 3.12 answers).  Multiply and divide an integer by a – 3.9 multiplying or dividing.  Multiply a fraction by an – 6.4 3.9 fraction. integer.  Understand percentage as 8.8 8.9, –  Interpret percentage as the 8.7– 8.9– 6.1,  Solve problems involving 6.7, the 'number of parts per 100' 8.9 8.11 operator 'so many hundredths of' and 8.9 8.12 6.2 percentage changes. 6.8 express one given number as a percentage of another.  Calculate simple percentages. 17.3 8.8 6.2  Use the equivalence of fractions, 8.8, 8.14 6.4, (pt), decimals and percentages to 8.9 6.5 8.9, compare proportions. 8.14  Calculate percentages and find – 8.13, 6.3 the outcome of a given percentage 17.4 increase or decrease. Calculations  Understand addition and 6.6 6.5 3.6, (82–85, 88– subtraction of fractions. (in pt) 3.7 Impact maths sample medium-term plans for mathematics Page 6 Key Stage 3 National Strategy Year 8: Autumn term Numbers in the LH column refer to the supplement of examples for the core teaching programme 101)  Use the laws of arithmetic and 1.11– 1.3, 3.8– inverse operations. 1.14, 1.7– 3.10 5.2– 1.9, 5.4 3.1, 3.2, 3.7– 3.11  Consolidate the rapid recall of 3.1, 3.1, –  Recall known facts, including 1.5 1.7 5.5  Use known facts to derive 5.5 number facts, including positive 3.2, 3.2 fraction to decimal conversions. unknown facts. integer complements to 100 and 3.4  Use known facts to derive unknown 1.12 1.7 5.5 multiplication facts to 10 x10, (in pt) facts, including products involving and quickly derive associated numbers such as 0.7 and 6, and 0.03 division facts. and 8.  Consolidate and extend mental see see 5.1,  Extend mental methods of – methods of calculation, working with notes notes 5.5 calculation, working with factors, decimals, fractions and percentages. see powers and roots.  Solve word problems mentally. notes Notes (2G) Notes (2B) Notes (2R)  Mental methods of calculation are covered by starters 1.3, 1.5, 1.7,  Mental methods of calculation are covered by starters 8.2  Mental methods of calculation are 1.11, 1.12, 6.1, 6.2, 6.5, 8.1–8.3. and 8.3. covered by starters 5.1, 5.3–5.5.

Algebra 2 (6 SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R hours) programme programme programme Equations and  Use letter symbols to 4.1, 13.2 10.1  Begin to distinguish the different 4.1, Ch 4 10.1 formulae represent unknown numbers 13.3 roles played by letter symbols in 4.2 start (112-119, 138- or variables. equations, formulae and functions. 143)  Know the meanings of the 4.3, 4.1, 10.1  Know the meanings of the words 13.1 13.1 14.1 words term, expression and 13.6 13.4 formula and function. (pt) (pt) equation.  Know that algebraic operations 4.1, 4.2, 10.4,  Use index notation for integer 10.3 follow the same conventions and order 4.2, 4.5 14.1 powers and simple instances of the as arithmetic operations. 4.5, index laws. 4.6, 13.4

 Use index notation for small 3.11 see 10.1, positive integer powers. (in pt) notes 10.2 see notes  Simplify linear algebraic 4.2 4.1– 10.1  Simplify or transform linear 4.3 4.1 10.4,  Simplify or transform algebraic 10.6 expressions by collecting like 4.3 expressions by collecting like 4.4 4.3 14.6 expressions by taking out single- 10.7 terms. terms. term common factors.  Multiply a single term over a – 4.4 10.5, bracket. 14.7  Use formulae from mathematics 13.1 13.1 14.1 Impact maths sample medium-term plans for mathematics Page 7 Key Stage 3 National Strategy Year 8: Autumn term Numbers in the LH column refer to the supplement of examples for the core teaching programme and other subjects.  Substitute integers into simple 13.3– 13.3– 14.3 formulae, and positive integers into 13.6, 13.6 expressions involving small powers see (e.g. 3x² + 4 or 2x³). notes  Derive simple formulae. 13.3 13.3 14.2 (pt) (pt) Notes (2G) Notes (2B) Notes (2R)  Index notation is covered in 3G.  Index notation is covered in 3B.  Powers are covered in 3G.

Shape, space SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R and measures programme programme programme 2 (6 hours) Measures and  Convert one metric unit to 9.7 9.8 –  Use units of measurement to 9.7, 9.8, see  Convert between area 15.3 mensuration another (e.g. grams to 9.8 9.9 estimate, calculate and solve 9.8, 9.9, notes measures (mm² to cm², cm² to m², (in pt) (228-231, 234- kilograms). 9.10 problems in everyday contexts 9.10 9.11 and vice versa) and between 241)  Read and interpret scales – involving length, area, volume, volume measures (mm³ to cm³, cm³ on a range of measuring capacity, mass, time and angle. to m³, and vice versa). instruments.  Know rough metric equivalents of 9.9 9.10 7.10 imperial measures in daily use (feet, miles, pounds, pints, gallons).  Know and use the formula for 14.2 14.2 –  Deduce and use formulae for the see 14.3– 15.1–  Know and use the formulae 15.4 the area of a rectangle. area of a triangle, parallelogram notes 14.5 15.3 for the circumference and area  Calculate the perimeter and 14.4 14.4 and trapezium. of a circle. area of shapes made from  Calculate areas of compound 14.1– 15.2 rectangles. shapes made from rectangles and 14.5 triangles.  Calculate the surface area of see see see  Know and use the formula for 14.6, 14.10, 15.5  Calculate the surface area and – cubes and cuboids. notes notes notes the volume of a cuboid. 14.7 14.11 volume of right prisms. Calculate volumes and surface – – see areas of cuboids and shapes made notes from cuboids. Solving  Investigate in a range of contexts: – – – Problems measures. (18–21) Notes (2G) Notes (2B) Notes (2R)  For area of a triangle etc., see starters 14.1 and 14.3.  Surface area of a cuboid is covered in 1G and 1R.  Using units of measurement in everday  Surface area of a cuboid is covered in 1G. contexts is covered in 1R.  Surface area of a cuboid is covered in 1R.

Impact maths sample medium-term plans for mathematics Page 8 Key Stage 3 National Strategy Year 8: Spring term Numbers in the LH column refer to the supplement of examples for the core teaching programme YEAR 8 – SPRING TERM Teaching objectives for the oral and mental activities 2R 2R  Order, add, subtract, multiply and divide integers. 5.3, 8.1–8.4  Solve equations, e.g. n(n – 1) = 56. 14.3, 14.5  Round numbers, including to one or two decimal places.  Know and use squares, positive and negative square roots, cubes of  Visualise, describe and sketch 2-D shapes, 3-D shapes and simple 7.3 (in pt) numbers 1 to 5 and corresponding roots. loci.  Know or derive quickly prime numbers less than 30.  Estimate and order acute, obtuse and reflex angles.  Convert between improper fractions and mixed numbers. 3.1A  Find the outcome of a given percentage increase or decrease. 6.5  Use metric units (length, area and volume) and units of time for calculations.  Know complements of 0.1, 1, 10, 50, 100, 1000.  Use metric units for estimation (length, area and volume).  Add and subtract several small numbers or several multiples of 10,  Recall and use the formula for perimeter of rectangles and calculate e.g. 250 + 120 – 190. areas of rectangles and triangles. 5.3, 5.5  Calculate using knowledge of multiplication and division facts and  Calculate volumes of cuboids. place value, e.g. 432  0.01, 37  0.01, 0.04  8, 0.03  5.  Discuss and interpret graphs. 12.1, 12.3,  Recall multiplication and division facts to 10  10. 5.3, 5.5 12.6A&B,  Use factors to multiply and divide mentally, e.g. 22  0.02, 420  15. 12.7, 13.5  Multiply and divide a two-digit number by a one-digit number.  Multiply by near 10s, e.g. 75  29, 8  –19.  Apply mental skills to solve simple problems.  Use partitioning to multiply, e.g. 13  1.4.  Use approximations to estimate the answers to calculations, e.g. 39  2.8.

Teaching objectives for the main activities

Algebra 3 (6 SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R hours) programme programme programme Sequences,  Express simple functions in 5.2 5.2 9.2  Express simple functions in see 5.4 see  Find the inverse of a linear – functions, words. 5.3 5.3 9.3 symbols. notes notes function. graphs  Represent mappings expressed 5.4 (160-177) algebraically.  Generate coordinate pairs 11.2, 11.2, 12.5  Generate points in all four 11.1– 11.1– 12.1–  Plot graphs of linear functions (y 12.8 that satisfy a simple linear rule. 11.3 11.3, quadrants and plot the graphs of 11.5 11.5 12.4, given implicitly in terms of x), e.g. 18.9 17.8 linear functions, where y is given 12.10 ay + bx = 0, y + bx + c = 0, on  Recognise straight-line 11.3 11.2, 12.3, explicitly in terms of x, on paper and 18.9 paper and using ICT. graphs parallel to the x-axis or y- 11.3 12.4 using ICT.  Given values for m and c, find 12.7 axis.  Recognise that equations of the – 11.4 12.6, the gradient of lines given by form y = mx + c correspond to 12.7 equations of the form y = mx + c. straight-line graphs.

 Construct linear functions arising 11.4– 11.7 12.9  Discuss and interpret distance– – from real-life problems and plot their 11.6 time graphs. Impact maths sample medium-term plans for mathematics Page 9 Key Stage 3 National Strategy Year 8: Spring term Numbers in the LH column refer to the supplement of examples for the core teaching programme corresponding graphs.  Discuss and interpret graphs 11.6 11.7 12.9 arising from real situations. Notes (2G) Notes (2B) Notes (2R)  Expressing simple functions in symbols is covered in 3G.  See starter 12.6B for expressing simple functions in symbols. This topic is also covered in 1R.

Number 3 (9 SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R hours) programme programme programme Place value  Understand and use decimal 1.1 1.1 see  Read and write positive integer see – see  Extend knowledge of integer 5.8 (36–47) notation and place value. notes powers of 10. notes notes powers of 10.  Multiply and divide integers 3.4, 3.8,  Multiply and divide integers and  Multiply and divide by any and decimals by 10, 100, 1000, 8.3 8.3 decimals by 0.1, 0.01. integer power of 10. and explain the effect.  Order decimals. 8.6 8.8 5.2  Round positive whole 1.7, 1.4, 1.4  Round positive numbers to any 1.7, 1.4 1.4– numbers to the nearest 10, 100 1.9 1.5, given power of 10. 1.9 1.6 or 1000 and decimals to the see 8.6  Round decimals to the nearest – 8.6 5.7– nearest whole number or one notes whole number or to one or two decimal 5.9 decimal place. places.  Consolidate and extend 1.5, 1,7, 5.1,  Consolidate and extend mental see see 5.1,  Extend mental methods of – mental methods of calculation 1.12 8.1 5.5 methods of calculation, working with notes notes 5.5 calculation, working with decimals, to include decimals, fractions (in pt) decimals, fractions and percentages, see fractions, percentages, factors, and percentages, accompanied squares and square roots, cubes and notes powers and roots. where appropriate by suitable cube roots. jottings.  Solve word problems mentally.  Make and justify estimates and 1.7– 1.6 1.6 approximations of calculations. 1.10  Consolidate standard column 1.13, 1.8, 5.1  Use standard column 5.1 procedures for addition and 1.14, 1.9, procedures to add and subtract (in pt) subtraction of integers and decimals 8.2 8.2 integers and decimals of any size, with up to two places. including a mixture of large and small numbers with differing numbers of decimal places.  Multiply and divide three- 3.8, 3.7,  Use standard column procedures 3.8– 3.9, 5.3,  Multiply and divide by decimals, – digit by two-digit whole 3.9, 3.9, for multiplication and division of 3.11 3.10 5.4 dividing by transforming to division numbers. 3.11 3.10 integers and decimals, including by by an integer. decimals such as 0.6 or 0.06.

 Extend to multiplying and  Understand where to position the dividing decimals with one or 8.4, 8.4, decimal point by considering 8.4, 8.4, 5.3, two places by single-digit 8.5 8.5 equivalent calculations. 8.5 8.5 5.4 whole numbers.  Check a result by considering 1.10 8.7 5.9 Impact maths sample medium-term plans for mathematics Page 10 Key Stage 3 National Strategy Year 8: Spring term Numbers in the LH column refer to the supplement of examples for the core teaching programme whether it is of the right order of (in pt) (in pt) (in pt) magnitude and by working the problem backwards.  Carry out calculations with 17.1 17.1 18.1  Carry out more difficult calculations 17.1, 17.1, 18.1,  Use a calculator efficiently and – more than one step using effectively and efficiently using the 17.3, 17.2, 18.2, appropriately to perform complex brackets and the memory. function keys for sign change, powers, 17.7 17.9 18.10 calculations with numbers of any  Use the square root and sign 17.1 17.1 18.1 roots and fractions; use brackets and size, knowing not to round during change keys. the memory. intermediate steps of a calculation.  Enter numbers and interpret the – 17.2 18.2 display in different contexts (negative 17.4 18.4 numbers, fractions, decimals, 17.9 18.10 percentages, money, metric measures, time). Notes (2G) Notes (2B) Notes (2R)  Rounding of decimals is not covered.  Mental methods of calculation are covered by starters 8.2  Place value is covered in 1R.  For reading and writing positive integer powers of 10, see starter 1.2. and 8.3.  Reading and writing of positive integer  Mental methods of calculation are covered by starters 1.3, 1.5, 1.7, power of 10 is covered in 1R. 1.11, 1.12, 6.1, 6.2, 6.5, 8.1–8.3.  Mental methods of calculation are covered by starters 5.1, 5.3–5.5.

Shape, space SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R and measures programme programme programme 3 (6 hours) Geometrical  Know that if two 2D shapes are see see see reasoning: lines congruent, corresponding sides and notes notes notes angles and angles are equal. shapes (190–191) Transformations  Recognise and visualise the  Transform 2D shapes by simple 2.1 2.1 11.1,  Know that translations, 11.2 (202–215) transformation and symmetry of combinations of rotations, reflections 11.2, rotations and reflections 11.3 a 2-D shape: and translations, on paper and using 18.11 preserve length and angle and  reflection in given mirror lines, 2.1 2.1 11.1 ICT. map objects on to congruent and line symmetry.  Identify all the symmetries of 2D 2.1 2.1 11.1, images.  rotation about a given point, 2.1 2.1 11.1 shapes. 11.2,  Identify reflection symmetry in – and rotation symmetry. 18.11 3D shapes.  translation. – – 11.1  Explore these transformations and symmetries using ICT. 17.6 17.7 18.8  Understand and use the language – – 11.4,  Enlarge 2D shapes, given a 11.5, and notation associated with 11.5 centre of enlargement and a whole- 11.6 enlargement. number scale factor, on paper.  Enlarge 2D shapes, given a – – 11.6  Identify the scale factor of an 11.4 centre of enlargement and a enlargement as the ratio of the positive whole-number scale factor. lengths of any two corresponding  Explore enlargement using ICT. – – 18.11 line segments. Impact maths sample medium-term plans for mathematics Page 11 Key Stage 3 National Strategy Year 8: Spring term Numbers in the LH column refer to the supplement of examples for the core teaching programme  Recognise that enlargements 11.4 preserve angle but not length, and understand the implications of enlargement for perimeter.  Understand the relationship – – 3.11  Consolidate understanding of the – – 3.11,  Use proportional reasoning to between ratio and proportion. relationship between ratio and 3.13 solve a problem.  Solve simple problems about proportion.  Interpret and use ratio in a range ratio and proportion using  Reduce a ratio to its simplest form, – – 3.12 of contexts. informal strategies. including a ratio expressed in different units, recognising links with fraction notation. Notes (2G) Notes (2B) Notes (2R)  Congruence of 2D shapes is covered in 3G.  Congruence of 2D shapes is covered in 3B.  Congruence of 2D shapes could be covered using starter 2.8.

Algebra 4 (6 SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R hours) programme programme programme Equations and  Use letter symbols to 4.1 13.2 10.1  Begin to distinguish the different 4.1, Ch4 10.1  Construct and solve linear 14.5 formulae represent unknown numbers 13.3 roles played by letter symbols in 4.2 start equations with integer (in pt) (112–113, 122– or variables. equations, formulae and functions. coefficients (with and without 125, 138–143)  Know the meanings of the 4.3 4.1 10.1  Know the meanings of the words 13.1 13.1 14.1 brackets, negative signs anywhere words term, expression and 13.6 13.4 formula and function. (pt) (pt) in the equation, positive or negative equation. solution), using an appropriate method.  Construct and solve simple 13.6– 13.4– 14.3  Construct and solve linear 13.6– 13.4– 10.8,  Use formulae from mathematics 14.1 linear equations with integer 13.8 13.6 equations with integer coefficients 13.8 13.6 14.3– and other subjects. coefficients (unknown on one (unknown on either or both sides, (in pt) (in pt) 14.7  Substitute numbers into 10.8 side only) using an appropriate without and with brackets) using expressions and formulae. method (e.g. inverse operations). appropriate methods (e.g. inverse  Derive a formula and, in simple 14.2 operations, transforming both sides in cases, change its subject. (in pt) same way.)  Use formulae from mathematics 13.1 13.1 14.1 and other subjects.  Substitute integers into simple 13.3– 13.3– 14.3 formulae, including examples that 13.6 13.6 lead to an equation to solve.  Derive simple formulae. 13.3 13.3 14.2 (pt) (pt) Notes (2G) Notes (2R) Notes (2R)  Constructing and solving linear equations references the same  Constructing and solving linear equations references the  Constructing and solving linear materials as ‘Algebra 5’. You will need to decide which sections will be same materials as ‘Algebra 5’. You will need to decide which equations references the same materials as covered in each unit. sections will be covered in each unit. ‘Algebra 5’. You will need to decide which sections will be covered in each unit.

Handling data SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R Impact maths sample medium-term plans for mathematics Page 12 Key Stage 3 National Strategy Year 8: Spring term Numbers in the LH column refer to the supplement of examples for the core teaching programme 2 (6 hours) programme programme programme Handling Data  Given a problem that can be – – –  Discuss a problem that can be see see 13.1 (248-273) addressed by statistical addressed by statistical methods and notes notes see methods, suggest possible identify related questions to explore. notes answers.  Decide which data to collect to – – 13.1  Discuss how data relate to a – answer a question, and the degree of problem; identify possible sources, accuracy needed. including primary and secondary  Identify possible sources. – – 13.1 sources.  Design a data collection sheet – – 13.1  Plan how to collect the data, – – 13.1 or questionnaire to use in a including sample size. simple survey.  Design and use two-way tables for – 12.6 13.8  Construct frequency tables for 12.1 12.2 13.4 discrete data. discrete data.  Collect data using a suitable – – 13.1  Gather data from specified – method, such as observation, secondary sources, including controlled experiment, including data printed tables and lists from ICT- logging using ICT, or questionnaire. based sources.  Calculate statistics for small 12.1, 15.1– 16.1–  Calculate statistics, including with a 15.1– 12.3, 16.1– sets of discrete data: 15.1– 15.5 16.6 calculator. 15.5 15.1– 16.7 15.5 15.5  find the mode, median and 15.1, 15.1, 16.1,  Recognise when it is appropriate to 15.1– 15.1– 16.1– range. 15.3, 15.3, 16.2, use the range, mean, median and 15.5 15.6, 16.7, 15.5 15.5 16.4 mode. 17.6 18.6  calculate the mean, including 15.4 15.4, 16.3,  Construct and use stem-and-leaf – – 13.3 from a simple frequency (in pt) 15.6 16.5 diagrams. table, using a calculator for a larger number of items.  Construct, on paper and using 12.3, 12.2 13.2  Construct, on paper and using 18.6 ICT, graphs and diagrams to 12.4, 12.3 ICT: represent data, including: 12.5,  pie charts for categorical data. – 12.4, 13.6,  bar-line graphs. 12.6 – 13.2 12.5 13.7  bar charts and frequency  Use ICT to generate pie – – 18.6 diagrams for discrete data. 12.2 12.2 13.2, charts.  simple scatter graphs. 13.4  Identify which are most useful in the – 12.6 13.8 context of the problem. – – –  Interpret tables, graphs and 12.1– 12.7– 13.2–  Interpret graphs and diagrams – diagrams for discrete data, and draw 12.6 12.8 13.8 and draw inferences to support or inferences that relate to the problem cast doubt on initial conjectures. being discussed.  Relate summarised data to the 15.2– 15.2 16.5,  Have a basic understanding of 13.8 questions being explored. 15.3 16.6 correlation.  Write a short report of a – – –  Communicate orally and on paper – – – Impact maths sample medium-term plans for mathematics Page 13 Key Stage 3 National Strategy Year 8: Spring term Numbers in the LH column refer to the supplement of examples for the core teaching programme statistical enquiry and illustrate the results of a statistical enquiry and with appropriate diagrams, the methods used, using ICT as graphs and charts, using ICT as appropriate. appropriate.  Justify the choice of what is – – –  Justify the choice of what is – – – presented. presented. Solving  Solve more complex problems by Ch Ch Ch problems breaking them into smaller steps or 16 16 17 (28–29) tasks, choosing and using resources, including ICT. Notes (2G) Notes (2R) Notes (2R)  Discussing a problem that can be addressed by statistical methods is  Discussing a problem that can be addressed by statistical  Starter 13.1A can be used to discuss a covered in 3G. methods is covered in 3R. problem that an be addresses by statistical methods.

Impact maths sample medium-term plans for mathematics Page 14 Key Stage 3 National Strategy Year 8: Summer term Numbers in the LH column refer to the supplement of examples for the core teaching programme YEAR 8 – SUMMER TERM Teaching objectives for the oral and mental activities 2R 2R  Order, add, subtract, multiply and divide integers. 5.3, 8.1–8.4  Use approximations to estimate the answers to calculations, e.g. 39   Multiply and divide decimals by 10, 100, 1000, 0.1, 0.01. 2.8.  Round numbers, including to one or two decimal places.  Know and use squares, cubes, roots and index notation.  Solve equations, e.g. n(n – 1) = 56,  +  = –46. 14.3, 14.5  Know or derive prime factorisation of numbers to 30.  Convert between fractions, decimals and percentages. 3.5  Visualise, describe and sketch 2-D shapes, 3-D shapes and simple 7.3 (in pt) 6.5 loci.  Find the outcome of a given percentage increase or decrease.  Estimate and order acute, obtuse and reflex angles.  Know complements of 0.1, 1, 10, 50, 100.  Use metric units (length, mass, capacity, area and volume) and units  Add and subtract several small numbers or several multiples of 10, of time for calculations. e.g. 250 + 120 – 190.  Use metric units for estimation (length, mass, capacity, area and  Use jottings to support addition and subtraction of whole numbers and volume). decimals. 5.3, 5.5  Convert between m, cm and mm, km and m, kg and g, litres and ml,  Calculate using knowledge of multiplication and division facts and cm² and mm². place value, e.g. 432  0.01, 37  0.01, 0.04  8, 0.03  5.  Recall multiplication and division facts to 10  10. 5.3, 5.5  Discuss and interpret graphs. 12.1, 12.3,  Use factors to multiply and divide mentally, e.g. 22  0.02, 420  15. 12.6A&B,  Multiply by near 10s, e.g. 75  29, 8  –19 12.7, 13.5  Use partitioning to multiply, e.g. 13  1.4.  Calculate a mean using an assumed mean. 16.3 (in pt), 16.5 (in pt)  Apply mental skills to solve simple problems.

Teaching objectives for the main activities

Number 4 (6 SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R hours) programme programme programme Calculations  Understand addition and 3.1– 3.1– 3.6  Understand the effects of – (82–87, 92– subtraction of fractions and integers, 3.11, 3.11, 3.7 multiplying and dividing by 107, 110–111) and multiplication and division of 6.6 6.5 numbers between 0 and 1. integers.  Use the laws of arithmetic and 1.11– 1.3, 3.8– inverse operations. 1.14, 1.7– 3.10 5.2– 1.9, 5.4 3.1, 3.2, 3.7– 3.11

 Use the order of operations, 13.4 13.3 14.4  Understand the order of – including brackets, with more complex precedence and effect of powers. Impact maths sample medium-term plans for mathematics Page 15 Key Stage 3 National Strategy Year 8: Summer term Numbers in the LH column refer to the supplement of examples for the core teaching programme calculations.  Consolidate and extend 1.5, 1.7, 5.1,  Consolidate and extend mental see see 5.1,  Extend mental methods of – mental methods of calculation 1.12 8.1 5.5 methods of calculation, working with notes notes 5.5 calculation, working with decimals, to include decimals, fractions (in pt) decimals, fractions and percentages, fractions, percentages, factors, and percentages, accompanied squares and square roots, cubes and powers and roots. where appropriate by suitable cube roots. jottings.  Solve word problems mentally.  Make and justify estimates and 1.7– 1.6 1.6 approximations of calculations. 1.10  Consolidate standard column 1.13, 1.8, 5.1  Use standard column 5.1 procedures for addition and 1.14, 1.9, procedures to add and subtract (in pt) subtraction of integers and decimals 8.2 8.2 integers and decimals of any size. with up to two places.  Multiply and divide three- 3.9, 3.9, –  Use standard column procedures 3.8– 3.9, 5.3,  Multiply and divide by decimals, – digit by two-digit whole 3.11 3.10 for multiplication and division of 3.11 3.10 5.4 dividing by transforming to division numbers. integers and decimals, including by by an integer.  Extend to multiplying and 8.4, 8.4, 5.3, decimals such as 0.6 or 0.06. dividing decimals with one or 8.5 8.5 5.4  Understand where to position the 8.4, 8.4, 5.3, two place by single digit decimal point by considering 8.5 8.5 5.4 numbers. equivalent calculations.  Check a result by considering 1.10 8.7 5.9 whether it is of the right order of (in pt) (in pt) (in pt) magnitude and by working the problem backwards. Measures  Convert one metric unit to 9.7, 9.8, –  Use units of measurement to 9.7, 9.8, see (228–231) another (e.g. grams to 9.8, 9.9 estimate, calculate and solve problems 9.8, 9.10, notes kilograms). 9.10, in everyday contexts. 9.10 9.11 14.5 Notes (2G) Notes (2B) Notes (2R)  Mental methods of calculation are covered by starters 1.3, 1.5, 1.7,  Mental methods of calculation are covered by starters 8.2  Mental methods of calculation are 1.11, 1.12, 6.1, 6.2, 6.5, 8.1–8.3. and 8.3. covered by starters 5.1, 5.3–5.5.  Using units of measurement is covered in 1R.

Algebra 5 (8 SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R hours) programme programme programme Equations and  Simplify linear algebraic 4.2 4.1– 10.1  Simplify or transform linear 4.3, 4.1, 10.4,  Simplify or transform algebraic 10.6, formulae expressions by collecting like 4.3 expressions by collecting like 4.4 4.3 14.6 expressions by taking out single- 10.7 (116–137) terms. terms. term common factors.  Multiply a single term over a – 4.4 10.5 bracket. 14.7  Construct and solve simple 13.6– 13.4– 14.3  Construct and solve linear 13.6– 13.4– 10.8,  Construct and solve linear 14.5 linear equations with integer 13.8 13.6 equations with integer coefficients 13.8 13.6 14.3– equations with integer (in pt) coefficients (unknown on one (unknown on either or both sides, (in pt) (in pt) 14.7 coefficients (with and without side only) using an appropriate without and with brackets) using brackets, negative signs anywhere Impact maths sample medium-term plans for mathematics Page 16 Key Stage 3 National Strategy Year 8: Summer term Numbers in the LH column refer to the supplement of examples for the core teaching programme method (e.g. inverse operations). appropriate methods (e.g. inverse in the equation, positive or negative operations, transforming both sides in solution), using an appropriate same way.) method.  Use systematic trial and 14.10 improvement methods and ICT tools to find approximate solutions to equations such as x³ + x = 20.  Begin to use graphs and set up 13.8 13.3 14.2  Solve problems involving direct – equations to solve simple problems proportion using algebraic methods, involving direct proportion. relating algebraic solutions to graphical representations of the equations.  Use ICT as appropriate. –  Generate coordinate pairs 11.3 11.2, 12.5  Plot the graphs of linear 11.5 11.4 12.4,  Plot graphs of linear functions (y 12.7, that satisfy a simple linear rule. 11.3, functions, where y is given (in pt) 11.5 12.6, given implicitly in terms of x), e.g. 18.9 17.8 explicitly in terms of x, on paper and 12.7 ay + bx = 0, y + bx + c, on paper  Recognise straight-line 11.2, 11.2, 12.3, using ICT. and using ICT. graphs parallel to the x-axis or y- 11.3 11.3 12.4 axis.  Construct linear functions arising 11.4– 11.7 12.9 from real-life problems and plot their 11.6 corresponding graphs.  Discuss and interpret graphs 11.4– 11.7 12.9 arising from real situations. 11.6  Solve more demanding problems Ch Ch Ch and investigate in a range of contexts: 16 16 17 algebra.  Break a complex calculation Ch Ch Ch  Solve more complex problems by Ch Ch Ch  Use trial and improvement where – into simpler steps, choosing and 16 16 17 breaking them into smaller steps or 16 16 17 a more efficient method is not using appropriate and efficient tasks, choosing and using efficient obvious. operations, methods and techniques for calculation, algebraic resources, including ICT. manipulation. Notes (2G) Notes (2B) Notes (2R)  Constructing and solving linear equations references the same  Constructing and solving linear equations references the  Constructing and solving linear materials as ‘Algebra 4’. You will need to decide which sections will be same materials as ‘Algebra 4’. You will need to decide which equations references the same materials as covered in each unit. sections will be covered in each unit. ‘Algebra 4’. You will need to decide which sections will be covered in each unit.

Solving SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R problems (6 programme programme programme hours) Solving  Solve more demanding problems – 9.4 6.6– problems and investigate in a range of contexts: 6.8, (2–35) number and measures. 7.3, Impact maths sample medium-term plans for mathematics Page 17 Key Stage 3 National Strategy Year 8: Summer term Numbers in the LH column refer to the supplement of examples for the core teaching programme 17.1  Represent problems Ch Ch Ch  Identify the necessary Ch Ch Ch mathematically, making correct 16 16 17 information to solve a problem. 16 16 17 use of symbols, words,  Represent problems and diagrams, tables and graphs. interpret solutions in algebraic or graphical form, using correct notation.  Break a complex calculation Ch Ch Ch  Solve more complex problems by Ch Ch Ch  Solve increasingly demanding – into simpler steps, choosing 16 16 17 breaking them into smaller steps or 16 16 17 problems and evaluate solutions. and using appropriate and tasks, choosing and using efficient  Explore connections in – efficient methods and techniques for calculation. mathematics across a range of resources, including ICT. contexts.  Use logical argument to establish Ch Ch Ch  Present a concise, reasoned – the truth of a statement. 16 16 17 argument, using symbols,  Give solutions to an appropriate diagrams, graphs and related degree of accuracy in the context of explanatory text. the problem.  Understand the significance of – – –  Suggest extensions to problems, Ch Ch Ch a counter-example. conjecture and generalise. 16 16 17  Identify exceptional cases or counter-examples. Ratio and  Understand the relationship – – 3.11  Consolidate understanding of the see see 3.11,  Use proportional reasoning to – proportion between ratio and proportion. relationship between ratio and notes notes 3.13 solve a problem, choosing the (78–81)  Solve simple problems about – – 3.11 proportion. correct numbers to take as 100%, ratio and proportion using  Reduce a ratio to its simplest form, 3.12 or as a whole. informal strategies. including a ratio expressed in different  Compare two ratios. – units, recognising links with fraction  Interpret and use ratio in a range – notation. of contexts, including solving word  Divide a quantity into two or 3.13 problems. more parts in a given ratio.  Use the unitary method to solve 3.13 simple word problems involving ratio and direct proportion. Notes (2G) Notes (2B) Notes (2R)  Ratio and proportion are covered in much more detail in 3G.  Ratio and proportion are covered in much more detail in 3B.

Shape, space SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R and measures programme programme programme 4 (9 hours) Geometrical  Use 2D representations to 9.5 9.5, 7.7, reasoning: lines, visualise 3D shapes and deduce 9.7 7.9 angles and some of their properties. shapes (198– 201) Impact maths sample medium-term plans for mathematics Page 18 Key Stage 3 National Strategy Year 8: Summer term Numbers in the LH column refer to the supplement of examples for the core teaching programme  Use ruler and protractor to 9.6 9.6 7.8  Know and use geometric properties – 9.7 7.9  Visualise and use 2D 7.9 construct simple nets of 3D of cuboids and shapes made from representations of 3D objects. (in pt) shapes, e.g. cuboid, regular cuboids. 7.9 tetrahedron, square-based  Begin to use plans and elevations. – 9.7 7.9  Analyse 3D shapes through 2D (in pt) pyramid, triangular prism. projections, including plans and elevations. Transformations  Make simple scale drawings. – – 11.4  Use and interpret maps and – (216–217) scale drawings. Coordinates  Use conventions and notation 11.4 11.1 12.1,  Given the coordinates of points A – – – (218–219) for 2-D coordinates in all four 12.2, and B, find the mid-point of the line quadrants. 12.5 segment AB.  Find coordinates of points – – 12.9 determined by geometric information. Construction  Use a ruler and protractor to:  Use straight edge and  Use straight edge and – and loci  measure and draw lines to the 2.4, 2.4, 2.2, compasses to construct: compasses to construct a triangle, (220–227) nearest millimetre and 2.5 2.5 2.3  a triangle, given three sides (SSS). – – 7.4 given right angle, hypotenuse and angles, including reflex  Use ICT to explore this side (RHS). angles, to the nearest construction. – – 18.7, degree. – – – 18.8  Construct a triangle given two sides and the included angle (SAS) or two angles and the included side (ASA).  Explore these constructions using ICT. 17.6 17.7 18.7  Find simple loci, both by reasoning see see 18.8 and by using ICT, to produce shapes notes notes and paths, e.g. an equilateral triangle.

Mensuration  Use bearings to specify direction. see see see (232-233, 238- notes notes notes 241)

 Calculate the surface area of see see see  Know and use the formula for 14.6 14.10 15.5  Calculate the surface area and – cubes and cuboids. notes notes notes the volume of a cuboid. 14.7 volume of right prisms.  Calculate volumes and surface see see see areas of cuboids and shapes made notes notes notes from cuboids. Notes (2G) Notes (2B) Notes (2R)  Simple loci are covered in 3G.  Simple loci are covered in 3B.  Bearings are covered in 3R.  Bearings are covered in 3G.  Bearings are covered in 3B  Surface area of a cuboid is covered in  Surface area of a cuboid is covered in 1G.  Surface area of a cuboid is covered in 1G and 1R. 1R.

Handling data SUPPORT from the Y7 teaching 2G 2B 2R CORE from the Y8 teaching 2G 2B 2R EXTENSION from the Y9 teaching 2R Impact maths sample medium-term plans for mathematics Page 19 Key Stage 3 National Strategy Year 8: Summer term Numbers in the LH column refer to the supplement of examples for the core teaching programme 3 (7 hours) programme programme programme Handling Data  Given a problem that can be – – –  Discuss a problem that can be see see 13.1 (248–275) addressed by statistical addressed by statistical methods and notes notes see methods, suggest possible identify related questions to explore. notes answers.  Decide which data to collect to see see 13.1  Discuss how data relate to a – answer a question, and the degree of notes notes problem. accuracy needed.  Identify possible sources, –  Identify possible sources. 13.1 including primary and secondary sources.  Design a data collection sheet – – 13.1  Plan how to collect the data, – 13.1  Design a survey or experiment 13.1 or questionnaire to use in a including sample size. to capture the necessary data (in pt) simple survey.  Construct frequency tables with 12.1 12.2 13.4 from one or more sources.  Construct frequency tables for 12.1 12.2 13.4 given equal class intervals for sets of  Determine the sample size and 13.1 discrete data, grouped where continuous data. degree of accuracy needed. (in pt) appropriate in equal class Design, trial and if necessary 13.1 intervals. refine data collection sheets. (in pt)  Construct tables for large 16.5, discrete and continuous sets of raw 16.6 data, choosing suitable class (in pt) intervals.  Collect data using a suitable – – 13.1 method, such as observation, controlled experiment, including data logging using ICT, or questionnaire.  Calculate statistics for small 12.1, 15.1– 16.1–  Calculate statistics, including with a 15.1– 15.1– 16.1– sets of discrete data: 15.1– 15.5 16.6 calculator. 15.5 15.5 16.7, 15.5 18.6  find the mode, median and 15.1, 15.1, 16.1,  Calculate a mean using an – 15.6 16.3, range, and the modal class 15.3, 15.3, 16.2, assumed mean. 16.5 for grouped data. 15.5 15.5 16.4  Know when it is appropriate to use  calculate the mean, including 15.4 15.4, 16.3, the modal class for grouped data. 15.2 15.2 16.1 from a simple frequency (in pt) 15.6 16.5 table, using a calculator for a larger number of items.  Construct, on paper and using 12.3– 12.2, 13.2  Construct, on paper and using 18.6 ICT, graphs and diagrams to 12.6 12.3 ICT: represent data, including:  bar charts and frequency – – 13.2,  frequency diagrams for 12.6 12.2 13.2 diagrams for continuous data. 13.4, grouped discrete data. 13.5  Use ICT to generate pie 17.5 – 18.6  simple line graphs for time 12.5 12.7 13.2 charts. series.  Identify which are most useful in – – – the context of the problem. Impact maths sample medium-term plans for mathematics Page 20 Key Stage 3 National Strategy Year 8: Summer term Numbers in the LH column refer to the supplement of examples for the core teaching programme  Interpret tables, graphs and – 12.7, 13.2, diagrams for continuous data, and 12.8 13.4 draw inferences that relate to the problem being discussed.  Relate summarised data to the – 12.7, 13.1, questions being explored. 12.8 13.2  Compare two distributions using the – – 16.7  Compare two or more 16.7 range and one or more of the mode, distributions and make inferences, median and mean. using the shape of the distributions, the range of data and appropriate statistics.  Write a short report of a – – –  Communicate orally and on paper – – – statistical enquiry and illustrate the results of a statistical enquiry and with appropriate diagrams, the methods used, using ICT as graphs and charts, using ICT as appropriate. appropriate.  Justify the choice of what is – – –  Justify the choice of what is – – – presented. presented.  Compare experimental and see 7.6 4.5  Appreciate the difference – theoretical probabilities in different notes between mathematical explanation contexts. and experimental evidence.  Solve more complex problems by Ch Ch Ch breaking them into smaller steps or 16 16 17 tasks, choosing and using graphical representation, and also resources, including ICT. Notes (2G) Notes (2B) Notes (2R)  Data collection is covered in more detail in 3G.  Data collection is covered in more detail in 3G.  Comparison of experimental and theoretical probabilities is covered in 3G.

Impact maths sample medium-term plans for mathematics Page 21 Notes

Impact maths sample medium-term plans for mathematics Page 22 Key Stage 3 Sample medium term plans for maths using Impact Maths Year 8

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