Linear scheme of work
Foundation Topic list
Topic/Content/References
Shape 1: Lines, Angles & Shapes
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Recognise acute, obtuse and right angles
Understand the terms ‘perpendicular’ and ‘parallel’
Identify scalene, isosceles, equilateral and right-angled triangles
Recognise and name shapes such as parallelogram, rhombus, trapezium
Recognise reflex angles
Estimate angles and measure them accurately
Use properties of angles at a point and on a straight line
Use angle properties of triangles including the sum to 180°
Show that the exterior angle of a triangle is equal to the sum of the interior opposite angles
Calculate interior and exterior angles of a quadrilateral
Recognise corresponding, alternate and interior angles on parallel lines
Understand and use three-figure bearings
Classify a quadrilateral using geometric properties
Calculate exterior and interior angles of a regular polygon
Number 1: Types of number, estimating and approximating including surds
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Understand place value in large numbers
Add and subtract large numbers (up to 3 digits)
Understand positive and negative numbers
Find the factors of a number
Round to the nearest integer
Multiply and divide whole numbers by 10, 100, 1000
Multiply large numbers (2 digits by 2 digits)
Add and subtract positive and negative numbers
Use inverse operations to check answers
Use hierarchy of operations to carry out calculations (BIDMAS)
Round numbers to given powers of 10 and to a given number of decimal places
Multiply and divide positive and negative numbers
Recognise prime numbers
Round a number to one significant figure
Estimate answers to solve problems
Round numbers to significant figures
Round numbers to different degrees of accuracy, decimal places and significant figures
Write a number as a product of prime factors
Find the highest common factor (HCF) of two numbers
Find the least common multiple (LCM) of two simple numbers
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Topic/Content/References
Algebra 1: Making sense of algebra and sequences
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Continue a sequence of diagrams or numbers
Write the terms of a simple sequence
Simplify an expression such as 5a + 2a – 3a
Work out the value of an expression such as 3x + 2y when x = 4 and y = 3
Simplify expressions like: 5a + 5b – a + 2b
Understand the rules of arithmetic as applied to algebra, such as x – y is not equal to y – x
Work out the value of an expression such as 2x - 3y for negative3 values of x and/or y
Find a term in a sequence with negative or fractional numbers
Expand brackets such as 4(x – 3)
Factorise an expression such as 6x – 8
Write the terms of a sequence or a series of diagrams given the nth term
 Expand and simplify an expression such as 3(3x – 7) – 2(3x + 1)
 Write the nth term of a sequence or a series of diagrams
Number 2: Fractions, decimals and ratio
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Understand positive and negative integers
Find the fraction of a shape shaded
Put integers and simple fractions in order
Find equivalent fractions
Express simple decimals and percentages as fractions
Add and subtract negative numbers
Simplify fractions
Calculate fractions of quantities
Arrange fractions and decimals in order
Write place value of decimal digit such as 3 in 0.63
Order decimals such as 0.46 and 0.5
Multiply and divide negative numbers
Express fractions as decimals and percentages
Add and subtract fractions
Add, subtract and multiply decimals
Convert simple fractions to decimals and decimals to fractions
Find one quantity as a fraction or percentage of another
Solve problems involving fractions
Solve problems involving decimals
Find one quantity as a fraction of another
Use ratio notation including reduction to its simplest form and its various links to fraction
notation
Divide a quantity in a given ratio
Solve simple ratio and proportion problems, such as finding the ratio of teachers to
students in a school
Add and subtract fractions and decimals
Multiply and divide decimals
Add and subtract mixed numbers
Find the reciprocal of a number
Round numbers to a given power of 10, up to three decimal places and one significant
figure
Multiply and divide fractions
Multiply and divide mixed numbers
Convert fractions to decimals
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Topic/Content/References
 Solve more complex ratio and proportion problems such as sharing money in the ratio of
peoples ages
 Solve more ratio and proportion problems using the unitary method
 Recognise that recurring decimals are exact fractions and that some exact fractions are
recurring decimals
 Understand the effect of multiplying and dividing by numbers between 0 and 1
Handling Data 1: Statistical measures
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Find the mode for a set of numbers
Find the median for an odd set of numbers
Work out the range for a set of numbers
Calculate the mean for a set of numbers
Find the median for an even set of numbers
Calculate the ‘fx’ column for a frequency distribution
Compare the mean and range of two distributions
Calculate mean and range for a frequency distribution
Find the modal class of grouped data
Find the mean for grouped data
Find the median class for grouped data
Algebra 2: Index Notation
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Work out or know simple squares and square roots
Work out or know simple cubes and cube roots
Use terms square, positive square root, negative square root, cube and cube root
Recall integer squares from 2 x 2 to 15 x 15 and the corresponding square roots
Recall the cubes of 1, 2, 3, 4, 5 and 10 and the corresponding cube roots
Use index notation and index laws for positive and negative powers including 10³ x 10⁵and
10³
10⁷
Algebra 3: Solving Equations
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 Solve equations such as 3x – 12 = 2(2x - 5)
Set up and solve a simple equation such as: 5x = 10 or x + 4 = 7
Set up and solve more complicated equations such as: 3x + 2 = 6 – x or 4(2x – 1) = 20
Distinguish between an expression, an equation, an identity and a formula
Derive complex expressions and formulae
Substitute numbers into formulae such as:
Shape 2: Nets, elevations and Pythagoras’ Theorem
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Recognise the net of a simple solid
Draw the net of a simple shape such as a matchbox tray
Draw a simple shape such as a cuboid on isometric paper
Draw the elevations of a solid on squared paper
Use Pythagoras’ Theorem to find the third side of a right-angled triangle
Use Pythagoras’ Theorem to prove that a triangle is right angled
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Topic/Content/References
Number 3: Working with Percentages
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 Understand that percentage means ‘number of parts per 100’ and use this to compare
proportions
 Change a percentage to a fraction or a decimal and vice versa
 Work out a percentage of a given quantity
 Compare pe rcentages, decimals and fractions
 Increase or decrease by a given percentage. For example, find the new price of a £490 TV
after a 15% reduction.
 Express one quantity as a percentage of another
 Use ratio notation, including reduction to its simplest form and its links to fraction notation
 Solve simple ratio and proportion problems, such as finding and simplifying a ratio
 Compare harder percentages, fractions and decimals
 Work out a percentage increase or decrease
 Solve more complex ratio and proportion problems using the unitary method
 Solve ratio and proportion problems using the unitary method
Shape 3: Measures
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Decide which is the most appropriate unit of measurement to use in everyday situations
Covert between metric units
Measure the length of a line
Convert between metric and imperial units such kilograms and pounds
Measure and scale a line
Make sensible estimates of lengths
Convert between metric and imperial units such as speed, for example, convert 80km/h to
mph
 Calculate average speed
 Use compound measures such as speed
 Recognise that measurements to the nearest unit may be inaccurate by up to one half unit
in either direction
Algebra 4: Using expressions and formulae
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 Derive more complex expressions and formulae
 Distinguish between an expression, an equation and a formula
 Rearrange linear formulae such as p = 3q + 5
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Use a formula in words such as: Total pay = rate per hour × no. of hours + bonus
Substitute positive numbers into a simple formula such as: P = 2L + 2W
Use formulae from other subjects such as : v = u + at
Derive simple expressions
Use formulae such as: P = 2L + 2W to find W given P and L
Substitute negative numbers into simple formulae such as: F = 1.8C + 32
Use formulae from mathematics and other subjects
Derive expressions and formulae such as: C = 35h + 55
Substitute numbers into more complicated formulae such as: C =
Shape 4: Area, perimeter and volume
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Find the perimeter of a shape by counting the sides of squares
Find the area of a shape by counting squares
Estimate the area of an irregular shape by counting squares and part squares
Name the parts of a circle
Find the volume of a shape by counting cubes
Work out the area and perimeter of a simple rectangle such as 5m by 4m
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Topic/Content/References
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Find the volume of a cuboid
Work out the area and perimeter of a simple rectangle such as 2.6cm by 8.3cm
Find the area of a triangle, trapezium and parallelogram
Find the area and perimeter of shapes made from triangles and rectangles
Calculate the circumference and area of a circle
Convert between square units such as changing 2.6m2 to cm2
Work out the perimeter and area of a semicircle and compound shapes made from parts of
a circle
 Convert between cube units such as changing 3.7m3 to cm3
 Find the volume of prisms including cylinders
 Find the surface area of simple prisms
Handling Data 2: Collecting data
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Design and use tally charts for discrete and grouped data
Understand and name different types of data
Design and use data collection sheets, surveys and questionnaires
Design and use two-way tables for discrete and grouped data
Understand and name other types of data collection methods
Identify possible sources of bias in the design and use of data collections sheets and
questionnaires
 Understand the data-handling cycle
 Understand that increasing sample size generally leads to better estimates
Algebra 5: Coordinates, plotting and sketching graphs
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Use coordinates in the first quadrant
Use coordinates in all four quadrants
Draw lines such as: x = 3 and y = x
Produce a table of values for equations such as: y = 3x – 5 or x + y = 7 and draw their graphs
Solve problems such finding where the line y = 3x – 5 crosses the line y = 4
Find the coordinates of the midpoint of a line segment
Draw graphs of quadratics such as: y = x2 + 2x + 1
Use a graph to estimate x and y values, giving answers to an appropriate degree of accuracy
Draw graphs of harder quadratics such as: y = x2 + 2x + 1
Find the gradients of straight – line graphs
Number 4: Ratio and proportion
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 Use ratio notation including reduction to its simplest form and its links to fraction notation
 Solve simple ratio and proportion problems, such as finding and simplifying a ratio e.g. the
ratio of teachers to students in a school
 Divide a quantity in a given ratio
 Solve more complex ratio and proportion problems, such as sharing money in the ratio of
people’s ages
 Solve ratio and proportion problems using the unitary method
Algebra 6: Equations with fractions and simultaneous equations
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 Set up and solve an equation involving fractions such as
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 Solve equations such as:
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= 4 or 2x – 3 = 8
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Topic/Content/References
Shape 6: Transformations and vectors
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Draw a line of symmetry on a 2-D shape
Draw the reflection of a shape in an mirror line
Draw all the lines of symmetry on a 2-D shape
Give the order of rotational symmetry on a 2-D shape
Name, draw or complete 2-D shapes from information about their symmetry
State the scale factor of an enlargement
Reflect shapes in the axes of a graph
Enlarge a shape by a positive scale factor
Find the measurements of the dimensions of an enlarged shape
Reflect shapes in lines parallel to the axes, such as x=2 and y=-1
Rotate shapes about the origin
Describe fully, reflections in a line and rotations about the origin
Translate a shape using a description such as 4 units right and 3 units down
Enlarge a shape by a positive scale factor from a given centre
Compare the area of an enlarged shape with the original area
Reflect shapes in lines such as y=x and y=-x
Rotate shapes about any point
Describe fully, reflections in any line parallel to the axes, y=x or y=-x and rotations about any
point
Find the centre of a rotation and describe it fully
Translate a shape by a vector such as
Find the ratio of corresponding lengths in similar shapes and identify this as the scale factor
of enlargement
Use ratios in similar shapes to find missing lengths
Handling data 3: Drawing graphs and charts
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Construct and interpret a pictogram
Construct and interpret a bar chart
Construct and interpret a dual bar chart
Interpret a pie chart
Construct a pie chart
Interpret a stem-and-leaf diagram
Construct a histogram (frequency diagram) with equal class intervals
Construct and interpret an ordered stem-and–leaf diagram
Construct and interpret line graphs
Interpret a line graph
Draw a scatter graph by plotting points on a graph
Interpret the scatter graph
Construct a frequency polygon
Draw a line of best fit on the scatter graph
Interpret the line of best fit
Identify the type and strength of the correlation
Handling data 4: Probability
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Understand and use the language of probability
Construct and interpret a bar chart
Understand and use a probability scale
Express a probability as a fraction
Display outcomes systematically
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Topic/Content/References
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Understand the differences between experimental and theoretical probability
Construct a histogram (frequency diagram) with equal class intervals
Construct and interpret an ordered stem-and–leaf diagram
Construct and interpret line graphs
Interpret a line graph
Draw a scatter graph by plotting points on a graph
Interpret the scatter graph
Construct a frequency polygon
Draw a line of best fit on the scatter graph
Interpret the line of best fit
Identify the type and strength of the correlation
Algebra 7: Real life graphs
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Plot points on conversion graphs
Read values from conversion graphs
Read a value from a conversion graph for a negative value
Interpret horizontal lines on a distance-time graph
Carry out simple interpretation of graphs such as finding a distance from distance-time
graphs
 Carry out more advanced interpretation of graphs such as finding a simple average speed
from distance
 Construct linear functions from real
 Further interpret real-life graphs, for example the average speed in km/h from a distancetime graph over time in minutes
Shape 8: Constructions and loci
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Select congruent shapes
Measure a line accurately to the nearest millimetre
Measure and draw lines accurately
Use simple scale drawings
Measure and draw an angle to the nearest degree
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Measure and draw angles accurately
Understand congruence and similarity
Use scales, such as scale on a map
Use map scales to find a distance
 Draw scale drawings
 Draw a triangle given three sides (SSS), two sides and the included angles (SAS) or two
angles and the included side (ASA)
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 Draw a quadrilateral such as kite, parallelogram or rhombus with given measurements
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 Understand that giving the lengths of two sides and a non-included angle may not produce
a unique triangle
 Understand the idea of locus
 Construct perpendicular bisectors and angle bisectors
 Recognise that measurements to the nearest unit may be inaccurate by up to one half unit
in either direction
 Construct the locus of points equidistant from two fixed points
 Construct the locus of points equidistant from two fixed lines
 Solve loci problems, for example the locus of points less that 3cm from a point P
 Match one side and one angle of congruent triangles given some dimensions
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Topic/Content/References
Algebra 8: Quadratic, cubic, circular and exponential functions
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 Draw graphs of quadratics such as: y = x2, y = x2 – 4 and y = 3x2
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 Draw graphs of quadratics such as: y = x2 + 2x + 1
 Use a graph to estimate x and y values, giving answers to an appropriate degree of accuracy
 Draw graphs of harder quadratics such as: y = 2x2 - 7x + 5
Algebra 9: Inequalities
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 Represent and interpret inequalities on a number line
 Substitute numbers into formulae such as:
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 Solve an equality such as 2x – 7 <9
 Find the integer solutions of an inequality such as: -8 < 2n ≤ 5
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