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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 360o, that angles on a straight line total 180o, 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 180o
  • know and use the fact that the interior angles of a quadrilateral sum to 360o
  • 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 different-looking 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 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


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 cm3 and m3

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 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


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 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

 

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. real-life 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 right-angled triangles

Y9 U10
Y9 U17