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NUMBER
Primes, Factors and Multiples
Grade

G
C
B







Objective
Find the factors of a number
Recognise prime numbers
Find the reciprocal of a number
Find the Lowest Common Multiple (LCM) of two simple numbers
Find the Highest Common Factor (HCF) of two simple numbers
Write a number as a produce of its primes
Find the Lowest Common Multiple (LCM) of two or more numbers
Find the Highest Common Factor (HCF) of two or more numbers
Rounding
Grade
Objective

Round to the nearest integer
Write an integer correct to the nearest 10 or the nearest 100
Estimate answers to problems involving decimals
Round numbers to given powers of 10 and to given numbers of decimal
places
Estimate square roots
E

Round a number to one significant figure
D


Estimate answers to calculations involving division
Estimate answers to calculations such as
C



Estimate answers to calculations involving division by numbers less than one
Find minimum and maximum values
Estimate answers to calculations such as
B

Round to a given number of significant figures
G
F




Fractions
Grade

G
F
E
D
C
Objective
Find equivalent fractions

Simplify fractions such as

Arrange fractions in order of size

Work out fractions of quantities such as




Find one number as a fraction of another
Do calculations with simple fractions involving addition
Do calculations with simple fractions involving multiplication
Do calculations with simple fractions involving subtraction


Do calculations with simple fractions involving division
Do calculations with mixed numbers
24
36
5
8
of £20
Decimals
Grade
Objective

Write down the place value of a digit, for example, what is the value of the
4 in 0.24?
Order decimals, for example, which is bigger, 0.24 or 0.3?
E

Add and subtract decimals
D


Multiply two decimals such as 2.4 x 0.7
Convert decimals to fractions and fractions to decimals
C

Divide a number by a decimal such as 1 ÷ 0.2 and 2.8 ÷ 0.07
B


Identify recurring and terminating decimals
Convert recurring decimals to fractions and fractions to recurring decimals
F

Percentages
Grade
Objective
D







Understand that percentage means ‘out of 100’
Change a percentage to a fraction or a decimal and vice versa
Compare percentages, fractions and decimals
Work out a percentage of a given quantity
Calculate simple interest
Increase or decrease a quantity by a given percentage
Express one quantity as a percentage of another
C

Work out percentage increase or decrease
B



Understand how to use successive percentages
Work out compound interest
Work out reverse percentage problems
F
E
Ratio and Proportion
Grade
Objective
B


Solve simple ratio and proportion problems, such as finding the ratio of
teachers to students in a school
Solve more complex ratio and proportion problems, such as sharing out
money between two groups in the ratio of their numbers
Solve ratio and proportion problems using the unitary method
Calculate proportional changes using a multiplier
A


Solve direct and inverse proportion problems
Interpret graphs of direct and inverse proportion relationships
D
C


Negative Numbers
Grade

G

F

E
Objective
Understand positive and negative integers
Add and subtract negative integers
Multiply and divide negative integers
Indices and Standard Form
Grade
Objective
F

E



D



C
Calculate squares and square roots (with and without the use of a
calculator)
Calculate cubes and cube roots (with and without the use of a calculator)
Use function keys on a calculator for powers and roots
Use the 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 2, 3, 4, 5 and 10
Use index notation and index laws for positive and negative powers such as
w3 x w5

and
Use index notation and index laws for positive and negative powers such as
3w3y x 2w5y2 and
B
A
A*


Convert between numbers in ordinary and standard index form
Use standard index form with and without a calculator

Use index notation and index laws for fractional powers such as 16½

Use index notation and index laws for fractional powers such as 16¾
Surds
Grade
Objective
A

Rationalise the denominator of a surd, such as
A*

Simplify surds, such as write (3 - √5)² in the form a + b√5
Measures
Grade

G
Objective
Decide which metric unit to use for everyday measurements
F



Convert between imperial and metric units
Know rough metric equivalents of pounds, feet, miles, pints and gallons
Make sensible estimates of a range of measures in everyday settings
E

Solve simple speed problems




Solve more difficult speed problems
Understand and use compound measures such as speed and density
Recognise accuracy in measurements given to the nearest whole unit
Find the upper and lower bounds of simple calculations involving quantities
given to a particular degree of accuracy
Find the upper and lower bounds of more difficult calculations with
quantities given to a various degrees of accuracy
C
B
A-A*

ALGEBRA
Expanding and Factorising
Grade

F

Simplify expressions with more than one variable such as
2a + 5b + a – 2b
Multiply out expressions with brackets such as 3(x + 2) or 5(x – 2)
Factorise expressions such as 24x + 6
Expand (and simplify) harder expressions such as x(x² - 5) and
3(x + 2) – 5(2x – 1)
Expand (and simplify) quadratic expressions such as (x + 4)(x – 2),
(2x + y)(3x – 2y) and (x + 2)²
Factorise quadratic expressions such as 4x² + 6xy and x² - 8x – 16

Simplify rational expressions such as

Factorise harder quadratics such as a² - 16b² and 5x² + 13x - 6

Factorise harder quadratics expressions such as x² - 10x + a, writing them
in the form (x + b)² + c

Simplifying harder rational expressions such as
E

D



C

B
A
A*
Objective
Simplify expressions with one variable such as a + 2a + 3a
Sequences
Grade
G
F
E
D
C
Objective

Continue a sequence of numbers or diagrams
Write down terms of a simple sequence
Find a particular term in a sequence involving positive numbers
Write the term-to-term rule in a sequence involving positive numbers
Find a particular term in a sequence involving negative or fractional
numbers
Write the term-to-term rule in a sequence involving negative or fractional
numbers
Write the terms of a sequence or a series of diagrams given the nth term

Write the nth term of a sequence or a series of diagrams






Equations
Grade

F
E

D


C
B


Objective
Solve equations such as 3x  12 or x  5  9
x
 7 or 3x  1  9
2
Solve equations such as 3x – 4 = 5 + x or 2(5x + 1) = 28
Solve equations such as
Form and solve equations such as x 3  x  12 using trial and improvement
methods
2x x
73
 2 or
 5
Solve equations such as
3 4
x
Solve equations such as
Formulae
Grade
Objective
G

F





Use a formula written in words, such as
cost = 20  distance travelled
Use a simple formula such as P  2l  2 w
Substitute positive numbers into a simple formula
Write an expression from a problem
Substitute negative numbers into a simple formula
Use formulae from mathematics and other subjects
D

Substitute numbers into more complicated formulae such as C 
C


Find a solution to a problem by forming an equation and solving it
Rearrange linear formulae such as p  3q  5

Rearrange formulae that include brackets, fractions and square roots

Rearrange formulae where the variable appears twice
E
B
A
( A  1) D
9
Graphs of Linear Functions
Grade
E
D
C
B
A
Objective


Plot the graphs of straight lines such as x = 3 and y = 4
Complete a table of values for equations such as y  2 x  3 and draw the graph

Solve problems involving graphs, such as finding where the line y  x  2

crosses the line y = 1
Recognise the equations of straight-line graphs such as y  4 x  2


Find the gradients of straight-line graphs
Explore the gradients of parallel straight-line graphs

Explore the gradients of perpendicular straight-line graphs
Quadratic Graphs
Grade

D
C
Objective
Draw graphs of simple quadratic functions such as y  3x 2 and y  x 2  4

Draw graphs of harder quadratic functions such as y  x 2  2x  1


Find the points of intersection of quadratic graphs with lines
Use graphs to find the approximate solutions of quadratic equations

Use the points of intersection of a quadratic graph such as y  x 2  2 x  4
A
with lines such as y  2 x  1 to solve equations like x 2  2 x  4  2 x  1 and
simplify this to x 2  4 x  5  0
Quadratic Functions
Grade

B
A
A*
Objective
Solve quadratic equations such as x 2  8x  15  0 by factorisation

Solve equations such as x 2  2 x  1  0 by using the quadratic formula

Solve equations such as

Write quadratic expressions in forms like ( x  a) 2  b (that is, complete the

square)
Use completing the square to solve equations and find maximum and
minimum values
4
3

2
x  2 2x 1
Inequalities and Simultaneous Equations
Grade
C
B
Objective






and 3x  2 y  4

A
A*
Solve inequalities such as 3x < 9 and 12 ≤ 3n < 20
Solve linear inequalities such as 4x – 3 < 10 and 4x < 2x + 7
Represent sets of solutions on the number line
Solve linear inequalities such as x + 13 > 5x – 3
Solve a set of linear inequalities in two variables and represent the solution
as a region of a graph
Solve a pair of simultaneous equations in two unknowns such as 2 x  y  5


Know that each equation can be represented by a line on a graph and that
the point of intersection of the lines is the solution
Solve a pair of simultaneous equations where one is linear and one is nonlinear such as y  3x  2 and y  x 2
Solve a pair of simultaneous equations where one is linear and one is nonlinear such as x  5 y  13 and x 2  y 2  13
Non-linear Functions
Grade
B
A*
Objective





Complete tables for, and draw graphs of cubic and reciprocal functions
Use the graphs to solve equations
Solve cubic equations by drawing appropriate lines on graphs
Plot and sketch graphs of exponential functions
Recognise the shapes of graphs of functions
Transforming Functions
Grade
Objective

A*
Transform the graphs of y  f ( x) , such as linear, quadratic, cubic, sine and
cosine functions, using the transformations y  f ( x)  a , y  f ( x  a) ,
y  af ( x) and y  f (ax)
Algebraic Proofs
Grade

E
D
C
B
A
A*
Objective
Decide with a reason whether a simple statement is true or false





Decide with a reason whether a harder statement is true or false
Identify a counter example
Understand the difference between a demonstration and a proof
Show step-by-step deductions in providing a basic algebraic explanation
Show step-by-step deductions in providing a full mathematical explanation

Derive simple algebraic proofs using reasoning

Derive harder algebraic proofs using reasoning and logic
SHAPE & SPACE
Area & Volume
Grade
Objective



G
F






E
D













C
A
A*






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
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
Find the perimeter of a shape by counting sides of squares
Find the area of a square 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 solid by counting cubes and stating units
Recognise and name three-dimensional (3-D) solids
Sketch three-dimensional (3-D) solids
Work out the area and perimeter of a simple rectangle, such as 3 m by 8 m
Work out the area and perimeter of a harder rectangle, such as 3.6 m by
7.2 m
Find the area and perimeter of compound shapes
Find the volume of a cube or cuboid
Find the height of a cuboid, given volume, length and breadth
Draw a cuboid on an isometric grid and mark its dimensions
Find the area of a triangle, parallelogram, kite and trapezium
Find the area and perimeter of compound shapes
Convert between measures of area
Calculate the circumference of a circle to an appropriate degree of
accuracy
Calculate the area of a circle to an appropriate degree of accuracy
Change between area measures such as m2 to cm2
Draw plans and elevations of three-dimensional (3-D) solids
Calculate the surface area of prisms and cylinders
Calculate volumes of triangular prisms, parallelogram-based prisms and
cylinders
Calculate the perimeter and area of a semi-circle
Calculate volumes of prisms and cylinders
Change between volume measures such as m3 to cm3 or cm3 to litres
Calculate surface areas of prisms and cylinders
Find the volume and surface area of pyramids, cones and spheres
Find the volume of the top cone of a truncated cone
Find the length of a major arc of a circle
Find the area of a major sector of a circle
Find the area of a segment of a circle
Find the volume the frustum of a truncated cone
Angles
Grade
F
D
Objective





Express fractions of full turns in degrees and vice versa
Recognise acute, obtuse and reflex angles, estimate angles and measure
them accurately
Use properties of angles at a point and angles on a straight line, understand
the terms ‘perpendicular lines’ and ‘parallel lines’
Recognise corresponding angles and alternate angles
Understand and use three-figure bearings
Properties of Polygons
Grade
G
Objective




E
C






Identify isosceles, equilateral and right-angled triangles
Use the word ‘congruent’ when triangles are identical
Recognise and name shapes, such as isosceles triangle, parallelogram,
rhombus, trapezium and hexagon
Show that the angles of a triangle add up to 180° and use this to find
angles
Show that an exterior angle of a triangle is equal to the sum of the interior
opposite angles
Use angle properties of isosceles, equilateral and right-angled triangles
Calculate interior and exterior angles of a quadrilateral
Investigate tessellations
Classify a quadrilateral by geometric properties
Calculate exterior and interior angles of a regular polygon
Coordinates
Grade
Objective
G

F

E

Use coordinates in the first quadrant, such as plot the point
(3, 2)
Use coordinates in all four quadrants, such as plot the points (3, –2), (–2, 1)
and (–4, –3)
Draw lines such as x = 3 and y = x + 2
D




Solve problems involving straight lines
Draw lines such as y = 2x + 3
Find the midpoint of a line segment
Use and understand coordinates in three dimensions
C
Properties of Circles
Grade

B
A


Objective
Use the tangent / chord properties of a circle
Prove the tangent / chord properties of a circle
Use and prove the alternate segment theorem
Transformations
Grade
G
F
E
D
C
Objective

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
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



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

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
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




B
A





Draw the reflection of a shape in a mirror line
Draw a line of symmetry on a 2-D shape
Draw all the lines of symmetry on a 2-D shape
Give the order of rotations symmetry of a 2-D shape
Name, draw or complete 2-D shapes from information about their
symmetry
Draw the line of reflection for two shapes
Give a scale factor of an enlarged shape
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
Use map scales to find a distance
Reflect shapes in lines such as x = 2 and y = -1
Rotate shapes about the origin
Describe fully reflections and rotations about the origin
Identify reflection symmetry in 3-D solids
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 shape
Translate a shape using a description such as 4 units right and 3 units down
Reflect shapes in lines such as y = x and y = -x
Rotate shapes about any point
Describe fully reflections and rotations about any point
Find the centre of rotation and describe it fully
Combine reflections and rotations
Enlarge a shape by a fractional scale factor
 4 
Translate a shape by a vector such as 

 3
Transform shapes by a combination of translation, reflection and rotation
Compare the area of an enlarged shape with the original shape
Distinguish between formulae for perimeter, area and volume by
considering dimensions
Enlarge a shape by a negative scale factor
Compare areas and volumes of enlarged shapes
Construction & Loci
Grade
G
F
E
Objective

Measure a line accurately to the nearest millimetre
Recognise the net of a simple solid such as a cuboid
Measure or draw an angle accurately to the nearest degree
Draw the net of a simple solid such as a cuboid
Draw a triangle given three sides, or two angles and a side, or two sides and
the included angle
Draw a quadrilateral such as a kite or a parallelogram with given
measurements
Understand that giving the lengths of two sides and a non-included angle
may not produce a unique triangle
Construct and recognise the nets of 3-D solids such as pyramids and
triangular prisms
Draw plans and elevations of 3-D solids
Understand the idea of a locus
Construct the perpendicular bisector of a line
Construct the bisector of an angle
Construct the perpendicular from a point to a line
Construct the perpendicular from a point on a line
Construct angles of 60° and 90°
Construct accurately loci, such as those of points equidistant from two
fixed points
Solve loci problems, such as identifying points less than 3 cm from a point P

Construct the graphs of loci, including the circle x 2  y 2  r 2

Solve simultaneous equations graphically, such as y = x – 1 and x 2  y 2  16

Solve simultaneous equations graphically, such as y = 2x – 1 and x 2  y 2  27







D
C
A
A*









Vectors
Grade
Objective
A


Add, subtract and multiply vectors to solve vector geometry problems
Understand the relationship between parallel and perpendicular vectors
A*

Solve more difficult vector geometry problems
Similarity and Congruence
Grade

C
B
A
Objective
Match one side and one angle of congruent triangles, given some dimensions

Match sides and angles of similar triangles, given some dimensions



Prove that two triangles are congruent
Prove the construction theorems
Find the area of a 2-D shape, given the area of a similar shape and the
ratio
Find the volume of a 3-D solid, given the volume of a similar solid and the
ratio

Pythagoras’ Theorem
Grade
Objective
C




Use Pythagoras’ theorem to find the hypotenuse of a right-angled triangle
Use Pythagoras’ theorem to find any side of a right-angled triangle
Use Pythagoras’ theorem to find the height of an isosceles triangle
Use Pythagoras’ theorem in practical problems
B

Find the distance between two points from their coordinates
A

Use Pythagoras’ theorem in 3-D problems
Trigonometry
Grade
B
A
A*
Objective








Use sine, cosine and tangent to calculate a side in a right-angled triangle
Use sine, cosine and tangent to calculate an angle in a right-angled triangle
Sketch and draw trigonometric graphs
Use the sine rule and cosine rule to find the missing sides and missing
angles in any triangle
Use the formula for the area of a non right-angled triangle
Use trigonometry to find sides and angles in three dimensions
Find the angle between a line and a plane
Understand the graphs of trigonometric functions for angles of any size
HANDLING DATA
Averages
Grade
G
F
E
D
C
Objective












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
Write down the mode from a graph
Compare the mean and range of two distributions
Calculate the ‘fx’ column for a frequency distribution
Calculate the mean for a frequency distribution
Find the modal class for grouped data
Find the mean for grouped data
Find the median class for grouped data
Scatter Graphs
Grade
D
C
Objective





Draw a scatter graph by plotting points on a graph
Interpret the scatter graph
Draw a line of best fit ion the scatter graph
Interpret the line of best fit
Identify the type and strength of the correlation
Real-life Graphs
Grade

F
E
D
C
B
Objective
Plot points of a conversion graph and read off positive values



Read from a conversion graph for negative values
Interpret distance–time graphs
Calculate simple average speeds from distance–time graphs

Calculate complex average speeds from distance–time graphs


Interpret velocity–time graphs
Discuss and interpret graphs modelling real situations
Collecting Data
Grade

G

E
Objective
Design and use tally charts for discrete and grouped data
Design and use two-way tables for discrete and grouped data



Classify and know the difference between various types of data
Use a variety of different sampling methods
Design and use data collection sheets and questionnaires
C

Identify possible sources of bias in the design and use of data collection
sheets and questionnaires
A

Use stratified sampling methods
D
Representing Data
Grade
G
F
E
D
B
A
Objective
















Construct and interpret a pictogram
Construct and interpret a bar
Construct and interpret a dual bar chart
Interpret a pie chart
Construct a pie chart
Interpret a stem-and-leaf diagram
Construct a stem-and-leaf diagram (ordered)
Construct a frequency diagram
Interpret a time series graph
Construct and interpret a cumulative frequency diagram
Use a cumulative frequency diagram to estimate the median and
interquartile range
Construct and interpret a box plot
Compare two sets of data using box plots
Construct a time series and plot the moving averages
Use the trend line to estimate other values
Construct and interpret a histogram with unequal class intervals
Probability
Grade

G
F
E
D
C
B
A
A*














Objective
Understand and use the vocabulary of probability
Understand and use a probability scale
Express a probability as a fraction
Display outcomes systematically
Understand the difference between experimental and theoretical
probabilities
Understand and use relative frequency
Use a two-way table to find a probability
Understand mutually exclusive events
Use the fact that the probabilities of mutually exclusive events add up to 1
Use probability to estimate outcomes for a population
Use probability to estimate outcomes for a population
Complete a tree diagram
Understand dependent and independent outcomes
Use tree diagrams to find probabilities of successive independent events
Draw tree diagrams and use them to find probabilities of successive
dependent events