KS3 Maths Now Scheme of Work – Year 8

YEAR 8 Practice Topic session Year 8 Autumn term Practice Topic 21 session Percentage changes 37

Subtopic

National Curriculum link

21.1 Percentage increases and decreases

Define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%

21.2 Using a multiplier 21.3 Calculating a percentage change Practice session 38

Topic 22 Graphs 22.1 Graphs from linear equations

Practice session 39

Topic 23 Correlation

Interpret fractions and percentages as operators

Work with coordinates in all four Substitute numerical values into formulae and expressions, including quadrants scientific formulae

22.2 Gradient of Work with coordinates in all four quadrants a straight line

22.3 Graphs from quadratic equations 23.1 Scatter graphs and correlation 23.2 Creating scatter graphs

Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics

Describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs

Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

Reduce a given linear equation in two variables to the standard form y = mx + c ; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

Reduce a given linear equation in two variables to the standard form y = mx + c ; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

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Practice session 40

Topic 24 24.1 Congruent Use the standard conventions for Congruence and shapes labelling the sides and angles of scaling triangle ABC, and know and use the criteria for congruence of triangles

24.2 Enlargements

Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids 24.3 Shape and Use scale factors, scale diagrams and maps ratio

Practice session 41

Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids

Use scale factors, scale diagrams and maps

Use ratio notation, including reduction to simplest form

Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction

24.4 Scales Year 8 Autumn half term Practice Topic 25 session Manipulating algebraic 42 expressions

25.1 Algebraic notation

25.2 Like terms Understand and use the concepts and vocabulary of expressions, 25.3 Expanding equations, inequalities, terms and brackets factors

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25.4 Using algebraic expressions 25.5 Using index notation

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Practice session 45

Use and interpret algebraic notation, including: • ab in place of a × b • 3y in place of y + y + y and 3 × y • a ² in place of a × a , a ³ in place of a × a × a ; a ²b in place of a × a × b • a /b in place of a ÷ b • coefficients written as fractions rather than as decimals • brackets

Topic 26 Working with fractions

Use and interpret algebraic notation, including: • ab in place of a × b • 3y in place of y + y + y and 3 × y • a ² in place of a × a , a ³ in place of a × a × a ; a ²b in place of a × a × b • a /b in place of a ÷ b • coefficients written as fractions rather than as decimals • brackets

Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors

Simplify and manipulate algebraic expressions to maintain equivalence by: • collecting like terms • multiplying a single term over a bracket • taking out common factors • expanding products of two or more

Use and interpret algebraic notation, including: • ab in place of a × b • 3y in place of y + y + y and 3 × y • a ² in place of a × a , a ³ in place of a × a × a ; a ²b in place of a × a × b • a /b in place of a ÷ b • coefficients written as fractions

Use the four operations, including 26.1 Adding and subtracting formal written methods, applied to integers, decimals, proper and fractions improper fractions, and mixed 26.2 Multiplying numbers, all both positive and fractions negative 26.3 Multiplying mixed numbers

Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 8/3)

26.4 Dividing fractions

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Practice session 46

Practice session 47

Topic 27 Circles 27.1 The circumference of a circle 27.2 Formula for circumference 27.3 Formula for area of a circle Topic 28 Finding 28.1 Using probabilities probability scales

28.2 Using a sample space

Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies

Calculate and solve problems involving: perimeters of 2D shapes (including circles), areas of circles and composite shapes

Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0–1 probability scale Understand that the probabilities of all possible outcomes sum to 1

Understand that the probabilities of all possible outcomes sum to 1

28.3 Estimating Record, describe and analyse the probabilities frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0–1 probability scale Progress assessment opportunity 4

End of term session Practice Topic session Year 8 Spring term Practice Topic 29 session Equations and formulae 48

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Practice session 50

Practice session

Topic 30 Proportion

Subtopic

Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities

Enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams

National Curriculum link

29.1 Equations Recognise and use relationships between operations including inverse with brackets 29.2 Equations operations with the variable on both sides 29.3 More complex equations

Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

29.4 Rearranging formulae

Recognise and use relationships between operations including inverse operations

30.1 Direct proportion 30.2 Graphs and direct proportion 30.3 Inverse proportion

Solve problems involving direct and inverse proportion, including graphical and algebraic representations

Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement) Understand and use standard mathematical formulae; rearrange formulae to change the subject

Recognise and use relationships between operations including inverse operations

Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

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30.4 Comparing direct and inverse proportion

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Topic 31 Applications of graphs

Practice session 53

Practice session 54

Topic 32 Comparing sets of data

Practice session 55

31.1 Step graphs

Interpret mathematical relationships Model situations or procedures by both algebraically and graphically translating them into algebraic expressions or formulae and by using graphs

31.2 Distancetime graphs

Work with coordinates in all four Model situations or procedures by Substitute numerical values into quadrants formulae and expressions, including translating them into algebraic expressions or formulae and by using scientific formulae graphs

31.3 More time graphs 31.4 Graphs showing growth

Interpret mathematical relationships Model situations or procedures by both algebraically and graphically translating them into algebraic expressions or formulae and by using graphs

32.1 Grouped frequency tables 32.2 Drawing frequency diagrams 32.3 Comparing data

Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

32.4 Which average to use Year 8 Spring half term Practice Topic 33 session Percentage changes 56

Practice session 57

Practice session 58

Topic 34 Polygons

33.1 Simple interest 33.2 Percentage increases and decreases 33.3 Calculating the original value 33.4 Using percentages 34.1 Angles in polygons

34.2 Constructions

Practice session 59

34.3 Angles in regular polygons

Find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs

Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

Find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs

Find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs

Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and

Define percentage as ‘number of parts per hundred’, interpret Interpret fractions and percentages percentages and percentage changes as a fraction or a decimal, as operators interpret these multiplicatively, express one quantity as a Recognise and use relationships between operations including inverse operations

Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

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34.4 Regular polygons and tessellations

Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures Use and interpret algebraic notation, including: • ab in place of a × b • 3y in place of y + y + y and 3 × y • a ² in place of a × a , a ³ in place of a × a × a ; a ²b in place of a × a × b • a /b in place of a ÷ b • coefficients written as fractions rather than as decimals • brackets

Practice session 60

Topic 35 35.1 Multiplying Expressions and out brackets equations 35.2 Factorising algebraic expressions

Practice session 61

35.3 Equations with brackets 35.4 Equations with fractions Progress assessment opportunity 5

End of term session Practice Topic session Year 8 Summer term Practice Topic 36 Prisms session and cylinders 62

Practice session 63

Practice session 64

Practice session 65

Practice session 66

Subtopic

36.1 Metric units for area and volume 36.2 Volume of a prism 36.3 Surface area of a prism 36.4 Volume of a cylinder 36.5 Surface area of a cylinder Topic 37 37.1 Speed Compound units 37.2 More about proportion 37.3 Unit costs Topic 38 Solving 38.1 Graphs equations from equations graphically of the form 38.2 Graphs from quadratic equations 38.3 Solving quadratic equations by drawing graphs Topic 39 39.1 Calculating Pythagoras’ the length of the theorem hypotenuse

Simplify and manipulate algebraic expressions to maintain equivalence by: • collecting like terms • multiplying a single term over a bracket • taking out common factors Use algebraic methods to solve Substitute numerical values into formulae and expressions, including linear equations in one variable (including all forms that require scientific formulae rearrangement)

National Curriculum link

Change freely between related standard units [for example time, length, area, volume/capacity, mass] Derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)

Use standard units of mass, length, time, money and other measures, including with decimal quantities

Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D

Use compound units such as speed, Change freely between related unit pricing and density to solve standard units [for example time, length, area, volume/capacity, mass] problems

Use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations

Use Pythagoras’ theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles

39.2 Calculating the length of a shorter side 39.3 Using Pythagoras’ theorem to solve problems Year 8 Summer half term Practice Topic 40 40.1 Negative session Working with powers of ten decimals 67

Understand and use place value for decimals, measures and integers of any size

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40.2 Standard form for small numbers 40.3 Rounding appropriately

Practice session 68 Practice session 69

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Practice session 72

End of term session

Topic 41 Manipulating brackets

Interpret and compare numbers in standard form A × 10ⁿ 1≤A<10, where n is a positive or negative integer or zero Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]

Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b

40.4 Mental calculations 40.5 Solving problems 41.1 More about brackets 41.2 Factorising expressions containing powers

Simplify and manipulate algebraic expressions to maintain equivalence by: • collecting like terms • multiplying a single term over a bracket • taking out common factors 41.3 Expanding • expanding products of two or more the product of binomials two brackets

41.4 More than two brackets Topic 42 42.1 Introducing Use Pythagoras’ theorem and trigonometric ratios in similar Trigonometric trigonometric triangles to solve problems involving ratios ratios right-angled triangles 42.2 Finding trigonometric ratios of angles 42.3 Using trigonometric ratios to find angles 42.4 Using trigonometric ratios to find lengths Progress assessment opportunity 6

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