Curriculum Area: Mathematics KS3: Years 7, 8 and...

Curriculum Area: Mathematics KS3: Years 7, 8 and 9

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Topics Year Curriculum How you can support your child’s learning at home E.g. Books, Websites, Family learning through visits

Theta 1 Scheme of Work (Year 7) All topics can be supported by using:

Unit Title Year 7 Programme of study www.pearsonactivelearn.com

1 Analysing and displaying

data

describe, interpret and compare observed distributions of a single variable through:

appropriate measures of central tendency (mean, mode, median) and

appropriate measures of spread (range, consideration of outliers)

construct and interpret vertical line (or bar) charts for ungrouped and grouped data

www.mathswatchvle.com

www.ttrockstars.com

All students will be given login details

2 Number skills use conventional notation for the priority of operations

round numbers and measures to an appropriate degree of accuracy

recognise and use relationships between operations including inverse operations

use the four operations, including formal written methods, with positive and negative

integers

order positive and negative integers

use the concepts and vocabulary of prime numbers, factors [or divisors] and prime

numbers

use integer powers and associated real roots (square, cube)

use approximation through rounding to estimate answers

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http://www.mathswatchvle.com/

http://www.ttrockstars.com/



Half-term test

3 Expressions, functions and

formulae

substitute numerical values into formulae and expressions, including scientific formulae

simplify and manipulate algebraic expressions to maintain equivalence: collecting like

terms, multiplying a term over a bracket

use and interpret algebraic notation: 3y in place of y + y + y and 3 × y

model situations or procedures by translating them into algebraic expressions or

formulae

4 Decimals and measures understand and use place value for decimals

order decimals and fractions

use the symbols =, ≠, <, >, ≤, ≥

understand and use place value for measures

work with coordinates in all four quadrants


decimals

derive formulae to calculate and solve problems involving perimeter and area of

parallelograms

End of term test

5 Fractions



order decimals and fractions

use the symbols =, ≠, <, >, ≤, ≥


fractions

define percentage as ‘number of parts per hundred’

interpret a percentage as a fraction or a decimal

interpret fractions and percentages as operators

6 Probability use appropriate language of probability

use the 0–1 probability scale

understand that probabilities of all possible outcomes sum to 1

record, describe and analyse the frequency of outcomes of simple probability

experiments involving randomness, fairness, equally and unequally likely outcomes

Half-term test

7 Ratio and proportion solve problems involving direct proportion

use ratio notation

reduce a ratio to simplest form

divide a given quantity into two parts in a given part:part ratio

use scale factors



understand that a multiplicative relationship between two quantities can be expressed

as a ratio or a fraction

express the division of a quantity into two parts as a ratio

End of term test

8 Lines and angles use the standard conventions for labelling the sides and angles of triangle ABC

draw and measure line segments and angles in geometric figures

apply the properties angles at a point and on a straight line

apply the properties vertically opposite angles

derive and use the sum of angles in a triangle

use the sum of angles in a triangle to deduce the angle sum in any polygon

use known results to obtain simple proofs

9 Sequences and graphs generate terms of a sequence from a term-to-term rule

generate terms of a sequence from a position-to-term

recognise arithmetic sequences

find the nth term

recognise geometric sequences and appreciate other sequences that arise

work with coordinates in all four quadrants

produce graphs of linear functions

interpret mathematical relationships both algebraically and graphically



Half-term test

10 Transformations derive properties of regular polygons

identify properties of, and describe the results of: translations

identify properties of, and describe the results of: rotations

identify properties of, and describe the results of: reflections

End of term test

End of year test



Theta 2 Scheme of Work (Year 8)

Unit Title Year 8 Programme of study

1 Number use the concepts and vocabulary of common factors

use the concepts and vocabulary of common multiples

use the concepts and vocabulary of highest common factor

use the concepts and vocabulary of lowest common multiple

use the concepts and vocabulary of prime factorisation


integers

use conventional notation for the priority of operations, including brackets, powers,

roots and reciprocals

use integer powers and associated real roots (square, cube and higher)

recognise powers of 2, 3, 4, 5



2 Area and volume derive and apply formulae to calculate and solve problems involving area of triangles,

parallelograms, trapezia

derive and apply formulae to calculate and solve problems involving volume of cuboids

(including cubes)

calculate and solve problems involving composite shapes

change freely between related standard units [for example time, length, area,

volume/capacity, mass]

Half-term test

3 Statistics, graphs and

charts


appropriate graphical representation involving discrete data


appropriate graphical representation involving continuous and grouped data




appropriate measures of central tendency (mean, mode, median)

construct and interpret frequency tables

construct and interpret bar charts



construct and interpret pie charts

Illustrate simple mathematical relationships between two variables (bivariate data)

using scatter graphs

4 Expressions and equations use and interpret algebraic notation: ab in place of a × b

use and interpret algebraic notation: a2 in place of a × a

use and interpret algebraic notation: a3 in place of a × a × a

use and interpret algebraic notation: coefficients written as fractions rather than as

decimals

use and interpret algebraic notation: brackets

understand and use the concepts and vocabulary of expressions, equations, inequalities,

terms and factors


terms

simplify and manipulate algebraic expressions to maintain equivalence: taking out

common factors

use algebraic methods to solve linear equations in one variable (including all forms that

require rearrangement)

End of term test

5 Real-life graphs model situations or procedures by using graphs

interpret mathematical relationships both algebraically and graphically



find approximate solutions to contextual problems from given graphs of a variety of

functions: including piece-wise linear graphs

6 Decimals and ratio use the four operations, including formal written methods, with positive and negative

decimals

round numbers and measures to an appropriate degree of accuracy [for example, to a

number of decimal places or significant figures]

use ratio notation

reduce a ratio to simplest form

divide a given quantity into two parts in a given part:part ratio

divide a given quantity into two parts in a given part:whole ratio

express the division of a quantity into two parts as a ratio

understand that a multiplicative relationship between two quantities can be expressed

as a ratio or a fraction

Half-term test

7 Lines and angles derive and illustrate properties of triangles, quadrilaterals, circles, and other plane

figures [for example, equal lengths and angles] using appropriate language and

technologies

understand and use the relationship between parallel lines and alternate and

corresponding angles



use the sum of angles in a triangle to deduce the angle sum in any polygon

apply angle facts, triangle congruence, similarity and properties of quadrilaterals to

derive results about angles and sides

End of term test

8 Calculating with fractions use the four operations, including formal written methods, with positive and negative

fractions


improper fractions and mixed numbers

work interchangeably with terminating decimals and their corresponding fractions (such

as 3.5 and 7/2 or 0.375 and 3/8)

use standard units of mass, length, time, money and other measures, including with

decimal quantities

9 Straight-line graphs recognise, sketch and produce graphs of linear 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




algebraically

solve problems involving direct proportion

solve proportion problems including graphical and algebraic representations

Half-term test

10 Percentages, decimals

and fractions

express one quantity as a percentage of another

compare two quantities using percentages

work with percentages greater than 100%

interpret percentages multiplicatively

End of term test

End of year test



Theta 3 (preparation for GCSE) Scheme of Work (Year 9)

Unit Title Year 9 Programme of study

1 Indices and standard form distinguish between exact representations of roots and their decimal approximations

interpret numbers in standard form A × 10n 1 ≤ A < 10, where n is a positive or negative

integer or zero

compare numbers in standard form A × 10n 1 ≤ A < 10, where n is a positive or negative

integer or zero

2 Expressions and formulae use and interpret algebraic notation: a2b in place of a × a × b

use and interpret algebraic notation: b/a in place of a ÷ b

simplify and manipulate algebraic expressions to maintain equivalence: expanding

products of two or more binomials



understand and use standard mathematical formulae

rearrange formulae to change the subject

Half-term test

3 Dealing with data describe, interpret and compare observed distributions of a single variable through:

appropriate graphical representation involving discrete data


appropriate graphical representation involving continuous and grouped data


appropriate measures of central tendency (mean, mode, median)



construct and interpret frequency tables

Illustrate simple mathematical relationships between two variables (bivariate data)

using scatter graphs

4 Multiplicative reasoning use compound units such as speed, unit pricing and density to solve problems

work with percentages greater than 100%

construct similar shapes by enlargement without coordinate grids



construct similar shapes by enlargement coordinate grids

interpret mathematical relationships both algebraically and geometrically

End of term test

5 Constructions use scale diagrams

use maps

derive and use the standard ruler and compass constructions: perpendicular bisector of

a line segment

derive and use the standard ruler and compass constructions: constructing a

perpendicular to a given line from/at a given point

derive and use the standard ruler and compass constructions: bisecting a given angle

recognise and use the perpendicular distance from a point to a line as the shortest

distance to the line

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

use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms,

cylinders and pyramids to solve problems in 3-D

use the properties of surfaces of cones and spheres to solve problems in 3-D

6 Equations, inequalities and

proportionality

use and interpret algebraic notation: coefficients written as fractions rather than as

decimals

use and interpret algebraic notation: brackets



substitute numerical values into formulae and expressions, including scientific formulae

understand and use the concepts and vocabulary of expressions, equations, inequalities,

terms and factors


terms

simplify and manipulate algebraic expressions to maintain equivalence: multiplying a

single term over a bracket

simplify and manipulate algebraic expressions to maintain equivalence: taking out

common factors

simplify and manipulate algebraic expressions to maintain equivalence: expanding

products of two or more binomials

Half-term test

7 Circles, Pythagoras and

prisms

calculate possible errors resulting from estimating, expressed using inequality notation a

< x ≤ b

calculate and solve problems involving perimeters of circles

calculate and solve problems involving areas of circles

use Pythagoras’ Theorem to solve problems involving right-angled triangles

End of term test

8 Sequences and graphs model situations or procedures by using graphs

recognise, sketch and produce graphs of 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


numerically


graphically


algebraically

use linear graphs to estimate values of y for given values of x and vice versa and to find

approximate solutions of simultaneous linear equations

use quadratic graphs to estimate values of y for given values of x and vice versa and to

find approximate solutions of simultaneous linear equations


functions: including piece-wise linear graphs


functions: exponential graphs


functions: reciprocal graphs

solve problems involving inverse proportion

9 Probability enumerate sets and unions / intersections of sets systematically, using tables and grids

enumerate sets and unions / intersections of sets systematically, using Venn diagrams

generate theoretical sample spaces for single and combined events with equally likely

and mutually exclusive outcomes

use sample spaces for single and combined events to calculate theoretical probabilities.



Describe simple mathematical relationships between two variables (bivariate data) in

observational and experimental contexts

Half-term test

10 Comparing shapes know and use the criteria for congruence of triangles

derive and illustrate properties of triangles, quadrilaterals, circles, and other plane

figures [for example, equal lengths and angles] using appropriate language and

technologies

identify and construct congruent triangles

use trigonometric ratios in similar triangles to solve problems involving right-angled

triangles

End of term test

End of year test

Curriculum Area: Mathematics KS3: Years 7, 8 and...

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