Mathematics: Key Stage 3

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

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

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

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

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 different-looking expressions may be identical and prove simple algebraic identities

Unit 19 – Algebraic generalisation project (1)

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

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

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

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 cm² and m²
• 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

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

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 cm³ and m³

Y7 U6, U8

Y8 U6

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

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

Unit 5
Linear and non-linear 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 non-linear 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

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 right-angled triangles
• Solve associated problems in other shapes where right-angled triangles exist

Deduce whether a triangle is right-angled 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

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. real-life linear graphs)
  • Exponential
  • Reciprocal

Y9 U1
Y9 U2

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

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 right-angled triangles

Y9 U10
Y9 U17