Mathematics: Key Stage 3
Year 7
Autumn 1: Place Value, Addition and Subtraction
Unit 1  Place Value (1)

 Read and write whole numbers in figures and words
 Multiply, and divide, any whole number by 10, 100, 1000, or 10 000
 Round whole numbers to the nearest 1000, 100 or 10

Unit 2 & 3 – Addition and subtraction (2)

 Use mental strategies
 Add and subtract using formal algorithms
 Calculate and work with perimeters
 Model solve word problems

Unit 4 – Addition and subtraction of decimals (2)

 Understand decimal notation and place value
 Read and write decimals in figures and words
 Convert between decimals and fractions where the denominator is a factor of 10 or 100
 Use the number line to display decimals and round decimals to the nearest whole number, to 1 or 2 decimal places
 Use correctly the symbols <, >, etc. and the associated language to order a set of decimals
 Multiply and divide decimals by 10, 100, 1000, or 10 000
 Solve word problems involving the addition and subtraction of money in decimal notation
 Use written methods in column format for addition and subtraction of decimals
 Extend existing mental calculation to include decimals
 Calculate the perimeter of rectangles, squares and rectilinear figures

Autumn 2: Multiplication and Division
Unit 5, 6, 7 & 8 multiplication and division (5)

 Use multiplication facts to solve mental calculations
 Use the terms ‘product’, ‘multiple’ and ‘LCM’
 Understand and use the column method to multiply integers and decimals
 Divide whole numbers and decimals by whole numbers
 Use the terms ‘quotient’, ‘remainder’, ‘factor’, ‘HCF’
 Represent multiplication word problems using bar models
 Find the area of a rectangle and triangle
 Solve problems involving length, perimeter and area
 Estimate answers in calculations and check that results are reasonable
 Measure time, calculate with time and solve time word problems
 Find the mean average, interpreting average as “total amount ÷ number of items" and solve word problems involving average

Spring 1: 2D Shapes
Unit 9 – Working with units (1)

 Record and order measurements using decimal notation
 Estimate and/or measure:
 length in kilometres (km) /metres (m)/ centimetres (cm)/ millimetres (mm)
 mass in kilograms (kg) /grams (g)
 volume of liquid in litres (l) / millilitres (ml)

Unit 10 – Angles (1)

 Draw and measure acute and obtuse angles reliably to the nearest degree
 Estimate the size of any given angle
 Recognise acute, right, obtuse and reflex angles
 Know and use the fact that the angles round a point total 360^{o}, that angles on a straight line total 180^{o}, and that vertically opposite angles are equal

Unit 11 & 12 – Triangles and quadrilaterals (2)

 Classify triangles and quadrilaterals according to their properties
 Use a ruler and protractor to construct triangles and quadrilaterals from given data
 Know and use the fact that the sum of interior angles of a triangle is 180^{o}
 know and use the fact that the interior angles of a quadrilateral sum to 360^{o}
 Solve problems involving coordinates in the first quadrant

Unit 13
Symmetry and tessellation (1)

 Identify lines of symmetry in any shape
 Identify the order of rotational symmetry in any shape
 Create shapes given details of their symmetries
 Investigate and create tessellations

Spring 2: Fractions
Unit 14 – Understand and use fraction (2)

 Represent fractions using area diagrams, bar models and number lines
 Recognise and name equivalent fractions
 Convert fractions to decimals
 Convert terminating decimals to fractions in their simplest form
 Convert between mixed numbers and improper fractions
 Compare and order numbers
 Convert simple fractions and decimals to percentages
 Express one quantity as a fraction of another

Unit 15 – Fractions of amounts (1)

 Find a fraction of a set of objects or quantity
 Find the whole given a fraction

Unit 16 – Multiplying and dividing decimals (2)

 Multiply a whole number or fraction by a whole number or fraction
 Multiply a mixed number and a whole number
 Divide a whole number or proper fraction by a whole number or proper fraction

Summer 1: Algebra
Unit 17 – Order of operations (2)

 Carry out calculations involving all four operations
 Understand and use brackets
 Use simple index notation

Unit 18 – Introduction to algebra (2)

 Recognise and continue sequences
 Represent an unknown number using a letter
 Write and understand simple algebraic expressions
 Substitute numerical values into formulae and expressions
 Collect like terms and simplify expressions
 Multiply out brackets, identify and take out common factors to factorise
 Recognise that differentlooking expressions may be identical and prove simple algebraic identities

Unit 19 – Algebraic generalisation project (1)

Summer 2: Percentages and Handling Data
Unit 20 – Percentages (2)

 Understand percentage as a fractional operator with denominator of 100
 Express a part of a whole as a percentage
 Convert between fractions, decimals and percentages
 Find fractions and percentages of given quantities
 Find the whole given a part and the percentage
 Increasing and decreasing by a percentage

Unit 21 – Handling data (2)

 Understand the difference between types of data
 Construct and interpret
 Tables (including tally and two way)
 Bar charts (including comparative and composite)
 Pictograms
 Line graphs
 Read and interpret pie charts
 Draw pie charts from raw data
 Explore misleading graphical representations

Year 8
Autumn 1: Working with Numbers
Unit 1 – Primes and factorising (2 weeks)

 Find the factors and multiples of a number
 Find the prime factors of a number
 Determine HCF and LCM by prime factorisation
 Find squares, square roots, cubes and cube roots using prime factorisation
 Use indices to record repeated multiplication

Y7 U5, U16

Unit 2– Add and subtract fraction (3)

 Use equivalent fractions
 Add and subtract fractions with like and unlike denominators
 Add and subtract fractions mixed numbers and improper fractions
 Convert between improper fractions and mixed numbers
 Add and subtract fractions mixed numbers and improper fractions

Y7 U13, U14, U15

Autumn 2: Number and Algebra
Unit 3– Positive and negative numbers (2)

 Represent and order positive and negative integers on a number line (using the symbols >, ³, <, and £)
 Show addition and subtraction on a number line
 Apply the four basic operations on positive and negative integers
 Calculate with rational and decimal numbers (including negative numbers)

Y7 U16

Unit 4 – Sequences, expressions and equations (3)

 Recognise and represent number patterns (including finding an algebraic expression for the ^{th} term)
 Distinguish between terms and coefficients in algebraic expressions
 Distinguish between like and unlike terms in algebraic expressions
 Simplify expressions, collect like terms and expand and factorise linear expressions
 Substitute numerical values into formulae and expressions
 Solve linear equations in one unknown
 Solve simple fractional equations that can be reduced to linear equations
 Formulate a linear equation in one unknown to solve problems

Y7 U16, U17
Y8 U3

Spring 1: 2D Geometry
Unit 5 – Triangles, quadrilaterals and angles in parallel lines (3)

 Construct a triangle from given information (sides/angles)
 Classify special quadrilaterals on the basis of their properties: define a parallelogram, rhombus and trapezium
 Construct a quadrilaterals from given information (sides/angles)
 Identify the different types of angles formed by parallel lines and a transversal such as corresponding angles, alternate angles and interior angles
 Use the various properties of angles to find unknown angles
 Find unknown angles in geometrical figures involving square, rectangle, parallelogram, rhombus, trapezium and triangle

Y7 U9, U10, U11

Unit 6 – Length and area: parallelograms and trapezia (2)

 Convert between cm^{2} and m^{2}
 Find the area and perimeter of a figure made up of some of the following shapes: square, rectangle, triangle
 Find the areas of parallelograms and trapezia
 Find the areas and perimeters of composite plane figures
 Solve word problems involving area and perimeter

Y7 U4, U7, U8, U10, U11

Spring 2: Proportional Reasoning
Unit 7 – Percentage change (2)

 Use percentages greater than 100%
 Express one quantity as a percentage of another
 Compare two quantities by percentage
 Increase or decrease a quantity by a given percentage
 Understand how to compare quantities using percentages
 Reverse percentages: find the original quantity given a part of it and its percentage
 Reverse percentages: find the original quantity when we know its final value after the percentage increase or decrease
 Solve problems involving percentages and reverse percentages

Y7 U19

Unit 8 – Ratio and rate (3)

 Interpret and , where , and are whole numbers
 Compare two or more quantities by ratio
 Understand the relationship between ratios and fractions
 Write equivalent ratios, and find the missing term in a pair of equivalent ratios
 Express ratios involving rational numbers in their simplest form
 Divide a quantity in a given ratio
 Find the whole/ one part when a whole is divided into parts in a given ratio
 Solve word problems involving ratio
 Use the relationship between distance, time and speed
 Write speed in different units such as km/h, m/min, m/s and cm/s
 Convert from one unit of speed to another (e.g. km/h to m/s)
 Solve word problems involving speed, uniform speed and average speed

Y7 U13, U14, U15

Summer 1: 2D and 3D Geometry
Unit 9 – Rounding (1)

 Round off a number to a required number of decimal places
 Round off a number to a required number of significant figures
 Estimate the answer to a given problem
 Identify rounding and truncation errors

Y7 U1, U4

Unit 10 – Circumference and area of a circle (2)

 Use formulae to calculate the area and circumference of a circle
 Find the area and perimeter of
 semicircle (half circle)
 quarter circle
 Solve word problems involving area and perimeter


Unit 11 – 3D shapes and nets (1)

 Recognise nets of 3D shapes
 Build and name 3D shapes
 Draw plans and elevations of a given solid
 Identify a solid from its plans and elevations


Unit 12 – Surface area and volume (2)

 Find the volumes of cubes and cuboids
 Find the volumes of prisms and cylinders
 Find the volumes of composite solids
 Explore the surface area of cubes, cuboids, cylinders other prisms and composite solids
 Convert between cm^{3 }and m^{3}

Y7 U6, U8
Y8 U6

Summer 2: Handling data
Unit 13 –statistics (2)

 Find the mean, median more and range from raw datasets
 Use the mean/median/mode to compare data sets
 Use an average plus the range to compare datasets
 Find the mode, median and mean from tables and graphical representations (not grouped)
 Explore methods of data collection including surveys, questionnaires and the use of secondary data
 Appreciate the difference between discrete and continuous data
 Classify and tabulate data
 Conduct statistical investigations using collected data
 Draw, analyse and interpret graphs including those met in year 7

Y7 U20

Year 9
Autumn 1: Graphs and Proportion
Unit 1 Coordinates (1 week)

 Plot coordinates in all four quadrants
 Find the midpoint of a line segment joining two points
 Find an endpoint of a line segment, given the midpoint and one endpoint
 Solve problems using coordinate grids

Y8 U3

Unit 2 Linear graphs (2 weeks)

 Identify the equations of horizontal and vertical lines
 Plot coordinates from a rule to generate a straight line
 Identify key features of a linear graph
 Make links between the graphical and the algebraic representation
 Identify parallel lines from algebraic equations

Y7 U18
Y8 U4

Unit 3 Proportion (2 weeks)

 Recognise when two quantities are directly or inversely proportional to each other
 Recognise the graphical representation of a proportional relationship
 Solve proportion problems
 Interpret and use conversion graphs and other graphs of proportional relationships

Y8 U8

Unit 4 Scales and standard form (1)

 Use standard form to express very large and small numbers
 Convert between standard form and ordinary numbers
 Order large and small numbers
 KS4 content: Use standard form to solve simple problems
 Use scales to solve distance and area problems in context

Y7 U4

Autumn 2: Algebra
Unit 5 Linear and nonlinear sequences (1 week)

 Recognise that linear and quadratic expressions can be used to represent sequences of different types
 Recognise arithmetic and geometric sequences and appreciate other sequences that may arise
 Solve problems involving linear and nonlinear sequences in a variety of contexts

Y7 U18
Y8 U4

Unit 6 Expanding and factorising (2 weeks)

 Multiply a term over a single bracket
 Expand products of two or more binomials
 Factorise expressions into a single bracket
 KS4 Content: Factorise quadratic expressions where the coefficient of is equal to one

Y7 U18
Y8 U4

Unit 7 Changing the subject of a formula (2 weeks)

 Write expressions, equations and formulae to represent relationships
 Use substitution to find the value of one variable given other values
 Make links between solving linear equations and rearranging formulae
 Apply “changing the subject” to equations of straight lines
 Manipulate familiar formulae such as formulae for area and perimeter

Y7 U18
Y8 U4

Spring 1: 2D Geometry
Unit 8 Constructions (1 week)

 Use the standard ruler and compass constructions for:
 perpendicular bisector of a line segment
 constructing a perpendicular to a given line from/at a given point
 bisecting a given angle
 Understand and use the perpendicular distance from a point to a line as the shortest distance to the line

Y7 U10 Y7 U11 Y7 U12
Y8 U5

Unit 9 Congruence (1 week)

 Know the criteria for congruence of triangles
 Apply properties of plane figures, and the criteria for congruence, using appropriate language

Y7 U11 Y7 U12
Y8 U5

Unit 10 Pythagoras’ theorem (2 weeks)

 Derive Pythagoras’ theorem
 Use Pythagoras’ theorem to find missing sides in rightangled triangles
 Solve associated problems in other shapes where rightangled triangles exist
Deduce whether a triangle is rightangled by considering its sides

Y8U1

Unit 11 Angles in polygons (1 week)

 Derive the proof of the sum of the angles in a triangle
 Find the formula for sum of the angles of any polygon
 Understand and use the sum of the exterior angles of a polygon
 Solve problems involving the angles/number of sides in a regular polygon

Y7 U10 Y7 U11 Y7 U12
Y8 U5

Spring 2: Equations and Inequalities
Unit 12 Linear equations and inequalities (3 weeks)

 Form and solve linear equations and inequalities in one unknown, including those where the unknown appears on both sides
 Rearrange and solve linear equations and inequalities given in any form, including those involving fractions and brackets

Y7 U18 Y8 U4
Y9 U2

Unit 13 Graphical solutions (2 weeks)

 Use linear and quadratic graphs to estimate values of for given values of
 Use linear graphs to find approximate solutions of simultaneous linear equations
 KS4 content: Solve simultaneous equations algebraically
 Find approximate solutions to contextual problems from given graphs of a variety of functions including:
 Piecewise linear (e.g. reallife linear graphs)
 Exponential
 Reciprocal

Y9 U1 Y9 U2

Summer 1: Handling Data and Probability
Unit 14 Probability (3 weeks)

 Understand and use the probability scale from 0 to 1
 Understand and use the language associated with probability
 Understand the relationship between relative frequency and theoretical probability
 Understand that different trials of an experiment may produce different outcomes
 Systematically list outcomes using a variety of representations
 Use Venn diagrams and understand the meaning of union and intersection
 KS4 content: Frequency tree diagrams

Y7 U4 Y7 U14 Y7 U15 Y7 U16 Y7 U20

Unit 15 Working with data (1 week)

 Appreciate the difference between discrete and continuous data
 Understand why the exact mean cannot be found from grouped data
 Find an estimate of the mean from grouped data and continuous data
 Describe, interpret and compare distributions, involving appropriate measures of central tendency and spread

Y8 U13

Unit 16 Scatter graphs (1 week)

 Plot scatter graphs
 Describe the type of correlation observed
 Interpret correlation in context

Y9 U1 Y9 U2

Summer 2: Geometry
Unit 17 Similarity and enlargement (1 week)

 Enlarge shapes from a given centre, with and without coordinate grids
 Understand that the corresponding angles of similar shapes are equal
 Solve problems involving similar triangles

Y8 U8 Y9 U9

Unit 18 Transformations (2 weeks)

 Translate a shape by a given vector
 Reflect a shape in a line, including on coordinate axes
 Rotate a shape about a centre, including on coordinate axes
 Identify the type of transformation carried out by comparing an object and image

Y8 U3
Y9 U1 Y9 U2

Unit 19 Trigonometry (2 weeks)

 Develop an understanding of the trigonometric ratios
 Solve problems using trigonometric ratios in rightangled triangles

Y9 U10 Y9 U17
