GCSE Mathematics Unit 3 Foundation Tier
Grade Descriptors
Grade
G
F
E
D
C
Grade
G
F
E
D
Grade
F
E
D
C
Grade
F
E
D
C
Fractions and decimals
Understand positive and negative numbers
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 & subtract negative numbers
Simplify fractions
Calculate fractions of quantities
Arrange fractions and decimals in order
Multiply & divide by negative numbers
Express fractions as decimals & percentages
Add and subtract fractions
Find one quantity as a fraction or percentage of another
Solve problems involving fractions
Solve problems involving decimals
Add and subtract mixed numbers
Find the reciprocal of a number
Round numbers to a given power of 10, up to 3 decimals places
and one significant figure
Multiply and divide fractions
Angles
Recognise acute, obtuse and right angles
Understand the terms ‘perpendicular’ and ‘parallel’
Identify scalene, isosceles, equilateral and right-angled triangles
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
Recognise corresponding, alternate and interior angles in parallel
lines
Understand and use three figure bearings
Working with symbols
Simplify expressions
Substitute values into simple expressions
Simplify expressions with more than one letter
Understand the rules of arithmetic as applied to algebra, such as
x-y is not equal to y-x
Substitute negative values into expressions
Expand single brackets in context
Factorise expressions
Simplify expressions which involve brackets
Percentages and ratios
Understand that percentage means out of 100
Work out a percentage of a given quantity
Increase or decrease by a given percentage
Express one quantity as a percentage of another
Use ratio notation, reduce to its’ simplest form and link to fraction
notation
Solve simple ratio and proportion problems
Work out a percentage increase or decrease
Solve more complex ratio and proportion problems
Solve ratio and proportion problems using the unitary method
Grade
G
F
E
D
C
Grade
F
E
D
C
Grade
G
E
D
C
Grade
G
F
E
D
C
Perimeter and area
Find the perimeter of a shape by counting 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
Work out the area and perimeter of a simple rectangles such as
5m by 4m
Work out the area and perimeter of a harder rectangle such as
2.6cm by 8.3cm
Find the area of a triangle and parallelogram
Find the area and perimeter of shapes made from triangles and
rectangles
Calculate the circumference and area of a circle
Work out the perimeter and area of a semicircle
Equations
Set up and solve a simple equation such as 5x = 10 or x + 4 = 7
Set up and solve an equation involving fractions such as
x = 4 or 2x – 3 = 8
3
Set up and solve more complicated equations such as 3x+2 = 6–x
or 4(2x – 1) = 20
Set up and solve an equation such as 4x + 5 = 3(x + 4) or
2x – 7 = 1
4
Properties of polygons
Recognise and name shapes such as parallelograms, rhombus,
trapezium
Calculate interior and exterior angles of a quadrilateral
Classify a quadrilateral using geometric properties
Calculate exterior and interior angles of a regular polygon
Coordinates and graphs
Use coordinates in the first quadrant
Recognise the net of a simple solid
Use coordinates in all four quadrants
Use simple real-life graphs such as conversion graphs
Draw the net of a simple shape such as a matchbox tray
Draw lines such as x = 3 and y = x
Interpret horizontal lines on a distance-time graph
Use real-life graphs to find values such as distance on a distancetime graph
Draw a simple shape such as a cuboid on isometric paper
Make simple interpretations of real-life graphs
Draw the front, plan and side elevations of a solid on squared
paper
Carry out further interpretations of real-life graphs e.g. find the
average speed in km/h from a distance-time graph over time in
minutes
Grade
G
F
E
D
C
Grade
G
F
E
D
Grade
G
E
D
C
Grade
G
F
E
D
C
Grade
C
Reflections, rotations and translations
Draw a line of symmetry on a 2D shape
Draw the reflection of a shape in a mirror
Draw all the lines of symmetry on a 2D shape
Give the order of rotational symmetry of a 2D shape
Name, draw or complete 2D shapes from information about their
symmetry
Reflect shapes in the axes of a graph
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
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
Formulae
Use formula in words such as:
Total pay = rate per hour x number of hours + bonus
Substitute positive numbers into a simple formula such as
P=2L+2W
Use formula from mathematics and other subjects such as v=u+at
Use formulae such as P=2L+2W to find W given P and L
Substitute negative numbers into a simple formula such as
F=1.8C+32
Derive formulae such as C=35h+55
Substitute numbers into more complicated formulae such as
C=(A+1)D/9
Derive more complex formulae
Distinguish between an expression, an equation and a formula
Area and volume
Find the volume of a shape by counting cubes
Find the volume of a cuboid
Convert between square units such as changing 2.6m2 to cm2
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
Measures
Decide which is the most appropriate unit of measurement to use
in everyday situations
Convert between metric units
Measure the length of a line
Convert between metric and imperial units such as 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 80 km/h to mph
Calculate average speeds
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
Trial and improvement
Solve equations such as x3 + x = 12 using systematic trial and
improvement methods
Grade
F
E
D
C
Grade
G
F
E
D
C
Grade
G
F
E
D
C
Grade
D
C
Grade
C
Enlargements
State the scale factor of an enlargement
Enlarge a shape by a positive scale factor
Find the measurements of dimensions of an enlarged shape
Enlarge a shape by a positive scale factor from a given centre
Find the ratio of corresponding lengths in similar shapes and
identity this as the scale factor of enlargement
Use ratios in similar shapes to find missing lengths
Construction
Select congruent shapes
Measure a line accurately to the nearest millimetre
Use simple scale drawings
Measure and draw an angle to the nearest degree
Understand congruence and similarity
Use scales, such as a scale on a map
Draw scale drawings
Draw a triangle given three sides, or two sides and the included
angle, or two angles and a side
Draw a quadrilateral such as a kite, parallelogram or rhombus with
given measurements
Understand that giving the lengths of two sides and a non-included
angle may not produce a unique triangle
Construct perpendicular bisectors and angle bisectors
Loci
Measure and draw lines accurately
Measure and draw angles accurately
Use map scales to find a distance
Understand the idea of a locus
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 than 3cm
from a point P
Quadratics
Draw graphs of simple quadratics such as y=x2, y=x2 - 4 and
y=3x2
Draw graphs of harder quadratics such as y=x2 +2x + 1
Use a quadratic graph to estimate x- and y-values, giving answers
to an appropriate degree of accuracy
Pythagoras’ theorem
Use Pythagoras’ theorem to find the third side of a right-angled
triangle
Use Pythagoras’ theorem to prove that a triangle is right-angled