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MATHEMATICS GRADE PROGRESSION SUMMARY
Grade
9
Number
Algebra
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Apply and interpret limits
of accuracy
To manipulate surds
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
9
Grade
8
Find the equation of a tangent
to a curve at a given point
Recognise and use the
equation of a circle
Plot and interpret graphs
including reciprocals and
exponentials
Ratio, Proportion and
Rates of Change
 Interpret the gradient
of a straight line
graph as a rate of
change
 Interpret the gradient
at a point, on a curve,
as the instantaneous
rate of
change
 Understand, construct
and interpret
equations that
describe direct and
inverse proportion
Geometry and Measures
Probability and Statistics
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
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Know and apply the sine and
cosine rules to find unknown
sides and angles
Use vectors to construct
geometric arguments and
proofs

Construct and
interpret a histogram
including unequal
class intervals
Calculate the
probability for
successive
dependent events
using tree diagrams
and other
representations
All previous content is assumed and higher order thinking skills are required to solve problems interlinking topic areas
Number
Algebra
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Simplify surds such as
4(3 + √3) and
(2-√3)(4 + √3) in the
form a + b√3
Apply and interpret limits
of accuracy
Set up, solve and
interpret the answers in
growth and decay
problems, including
compound interest


Derive harder algebraic proofs
using reasoning and logic
Understand trigonometric
graphs for angles of any size
Solve a pair of simultaneous
graphs where one is linear
and one is non-linear such as
X+ 4y = 15 and x2 + y2 =9
Ratio, Proportion and
Rates of Change
 Compare lengths,
areas and volume
using ratio notation
 Interpret equations
that describe direct
and inverse
proportion
Geometry and Measures
Probability and Statistics
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


Use trigonometry to find sides
and angles in 3-D
Add, subtract and multiply
vectors to solve geometry
problems
Transform the graphs of y=f(x)
using transformations

Interpret, analyse
and compare the
distributions of data
sets through
appropriate
measures of
median, mean,
mode and range
Calculate the
probability for
independent events
using tree diagrams
and other
representations
8
Grade
7
Grade
6
Grade
Ofqual states that to achieve grade 8, candidates will be able to:
 perform procedures accurately
 interpret and communicate complex information accurately
 make deductions and inferences and draw conclusions
 construct substantial chains of reasoning, including convincing arguments and formal proofs
 generate efficient strategies to solve complex mathematical and non-mathematical problems by translating them into a series of mathematical processes
 make and use connections, which may not be immediately obvious, between different parts of mathematics
 interpret results in the context of the given problem
 critically evaluate methods, arguments, results and the assumptions made
Number
Algebra
Ratio, Proportion and
Geometry and Measures
Probability and Statistics
Rates of Change
 Use index notation and
 Derive simple algebraic proofs  Understand the
 Prove the circle theorems
 Use of mutually
index laws for simple
using reasoning
difference between
exclusive events
 Prove the construction
fractional powers such as  Recognise the shapes of
direct and inverse
and independent
theorems
16¼
proportion
events when solving
functions
 Find bearings using
probability problems
 Rationalise the
 Construct the graphs of loci,
trigonometry
denominator of a surd
 Interpret a
including the circle x2 + y2 =r2
 Calculate arc lengths, angles
such as 2/√5
cumulative
 Use completing the square
and areas of sectors of circles
frequency diagram
and the quadratic formula to
 Describe translations as 2-D
solve quadratic equations
vectors
Number
Algebra
Ratio, Proportion and
Geometry and Measures
Probability and Statistics
Rates of Change
 Convert recurring
 Simplify rational expressions
 Understand how to
 Use sine, cosine and tangent
 Use a cumulative
decimals to fractions and
involving quadratic
use successive
to calculate angles and sides
frequency diagram
vice versa
expressions
percentages written
in a right angled triangle
to estimate the
as multipliers and to
median and
 Work out reverse
 Complete tables for, and draw
 Bisect an angle and a straight
be able to interpret
interquartile range
percentages
graphs of reciprocal functions
line
the result
 Find the upper and lower  Use reciprocal graphs to solve
 Combinations of
bounds of simple
equations
transformations
calculations (addition and  Show step-by-step deductions
subtractions) involving
in providing a full
quantities given to a
mathematical explanation
particular degree of
 Solve inequalities with
accuracy
unknowns on both sides
 Use index notation for
multiplication and division
Number
Algebra
Ratio, Proportion and
Geometry and Measures
Probability and Statistics
5
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Find the reciprocal of a
number
Find minimum and
maximum values
Divide a number by a
decimal such as 1÷0.2
and 2.8 ÷0.07
Solving problems
involving standard form
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Find a solution to a problem
by forming an equation and
solving it
Draw graphs of harder
quadratics such as
y=x2 + 3x -5
Find the points of intersection
of quadratic graphs with lines
Use graphs to find the
approximate solutions of
quadratic equations
Understand the difference
between a demonstration
(‘show me’) and a proof
(‘prove…’)
Show step-by-step
deductions in providing a
basic algebraic explanation
Rates of Change
 Solve more difficult
speed problems
 Calculate proportional
changes using a
multiplier

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
Convert between measures of
area and volume
Construct angles and
perpendicular lines
Use Pythagoras’ theorem to
find the height of an isosceles
triangle
Understand how to match one
side and one angle of
congruent triangles

Use relative
frequency to
compare outcomes
of experiments
5
Ofqual states that to achieve grade 5, candidates will be able to:
perform routine single- and multi-step procedures effectively by recalling, applying and interpreting notation, terminology, facts, definitions and formulae
interpret and communicate information effectively
make deductions, inferences and draw conclusions
construct chains of reasoning, including arguments
generate strategies to solve mathematical and non-mathematical problems by translating them into mathematical processes, realising connections between
different parts of mathematics
 interpret results in the context of the given problem
 evaluate methods and results
Number
Algebra
Ratio, Proportion and
Geometry and Measures
Probability and Statistics
Rates of Change
 Estimate answers to
 Solve problems involving
 Solve more complex
 Draw a quadrilateral such as a  Calculate the mean
calculations involving
straight lines
ratio and proportion
kite of a parallelogram with
for a frequency
division
problems, such as
given measurements
distribution
 Draw graphs of simple
sharing
out
money
 Recall the cubes of 2, 3,
quadratic functions such as
 Understand that the lengths of  Find and compare
between two groups
4, 5, and 10
y=x2 and y=x2+ 2
two sides and a non-included
averages
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Grade
4
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
Grade
3
Grade
2
Perform calculations
involving BIDMIS
Do calculations with
mixed numbers


Number
Algebra


Round a number to one
significant figure
 Calculate cubes and
cube roots (with and
without a calculator)
 Multiply whole and
decimal numbers
 Divide numbers involving
remainders
 Work out a percentage of
an amount (with and
without a calculator)
 Understand percentage,
fraction and decimal
equivalences
 Introduction to standard
form
Number


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
Substitute negative numbers
into a simple formula
Complete a table of values for
equations such as y=3x + 3
and draw the graph
Read from a conversion graph
for negative values
Algebra
Change a percentage to 
a fraction or a decimal
and vice versa
Arrange fractions in order 
of size
Add and subtract

negative integers
in the ratio of their
numbers
Solve linear equations
involving fractions
Solve inequalities
Plot points of a conversion
graph and read off positive
values
Use a simple formula such as
P=2w + 2h
Solve simple equations such
as x/2 =9 or 4x – 2 = 22
Ratio, Proportion and
Rates of Change
 Understand and
interpret percentage
changes
 Use reverse
percentage to solve
problems
Ratio, Proportion and
Rates of Change

Use ratio to solve
simple problems
involving recipes and
‘best buys’
angle do not define a unique
triangle
 Find interior and exterior
angles of an irregular polygon
 Perform reflections of shapes
in diagonal lines
 Introduction to Pythagoras’
theorem
Geometry and Measures
Probability and Statistics
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Enlarge a shape by a positive
scale factor
Find the measurements of the
dimensions of an enlarged
shape
Recognise congruent shapes
Rotate and translate shapes
Understand the idea of a locus
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
Compare the mean
and range of two
distributions
Understand mutually
exclusive events
Work with discrete
and continuous data
Geometry and Measures
Probability and Statistics
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


Understand the terms
‘perpendicular lines’ and
‘parallel lines’
Give the order of rotational
symmetry of a 2-D shape
Give a scale factor of an
enlarged shape

Compare two
distributions using
the range and one of
the mode, median or
mean
Place probabilities
on a number line
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Multiply and divide
decimals to two places
Round numbers to a
given number of decimal
places
Recognise sequences
involving square and
cube numbers
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Plot the graphs of straight
lines such as x=3 and y=4
Find the area and perimeter of
compound shapes
2
Ofqual states that to achieve grade 2, candidates will be able to:
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



Grade
1
recall and use notation, terminology, facts and definitions; perform routine procedures, including some multi-step procedures
interpret and communicate basic information; make deductions and use reasoning to obtain results
solve problems by translating simple mathematical and non-mathematical problems into mathematical processes
provide basic evaluation of methods or results
interpret results in the context of the given problem
Number






Algebra
Find equivalent fractions 
Recognise cube numbers 
Add, subtract and
multiply simple decimals
Division of integers with
no remainders
Simplify fractions
Multiply two digit
numbers
Simplify expressions
Use a formula written in
words, such as cost = 20 x
distance travelled
Ratio, Proportion and
Rates of Change
 Use ratio notationincluding writing it in
its simplest form
Geometry and Measures
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

Probability and Statistics
Use the word ‘congruent’ when 
triangles are identical
Find the volume of a solid by
counting cubes and stating

units
Recognise, name and sketch
three- dimensional (3-D) solids 

Understand and use
the vocabulary of
probability
Design and use tally
tables for grouped
data
Find the median of
an odd set of
numbers
Interpreting real life
tables