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New Number
Grade
Old KS2/3 Level
Old GCSE Grade
MATHS ASSESSMENT and PROGRESSION CRITERIA FRAMEWORK
10
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8a8b
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7b7c
6a6c
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Assessment and Progression Criteria:
Calculate or estimate gradients of graphs and
areas under graphs (including quadratic and
other non-linear graphs), and interpret results
in cases such as distance-time graphs, velocitytime graphs and graphs in financial contexts
GPs with
rational base
& integer
index
Simplify
surds,
rationalise
denominator
Calculate exactly
with surds.
Apply and
interpret limits of
accuracy,
including upper
and lower bounds
Calculate with
roots, & fractional
indices.
Convert between
recurring decimals
and fractions
Compound
measures Eg
density &
pressure.
Standard index
form including
conversions &
calculations
Understand
& use roots.
Set up, solve and
interpret the
answers in growth
& decay problems,
including
compound
interest
Interpret
direct and
inverse
proportion
equations
and graphs
Work with % greater
than 100%
Use fractions,
percentages
(including reverse
percentage and
simple) and ratio
as operators and
to describe
proportion.
Round numbers &
measures to an
appropriate degree
of accuracy & to
specified sig
figures.
Use rounding to
check answers and
determine, in the
context of a
problem, an
appropriate degree
of accuracy.
Estimate answers;
use estimates to
check calculations.
Round numbers and measures
to an appropriate degree of
accuracy or to a specified
number of decimal places.
Apply and interpret limits of
accuracy.
Order of operations.
F/G
U
4b3c
2c-1c
&P
levels
+
2
-
+
1
Foundation
E/F
5a4a
Add and subtract negative
numbers
Solve number & practical
problems including those
involving measure [Eg length,
mass, volume, money] using
decimal notation up to 3dp,
using formal written
methods for four operations:
Long multiplication up to 4
digit by 2 digit.
Divide by 1 and 2 digit
integers and interpret
remainders as whole number
remainders, fractions, or by
rounding, as appropriate for
the context.
Use the symbols
=, ≠, <, >, ≤, ≥.
Read Roman
numerals to 1000
(M) & recognise
years written in
Roman numerals
Solve quadratics
using the formula.
Solve simultaneous
equations with a
line & a quadratic.
Construct direct &
inverse proportion
equations
Change freely
between
compound units
(e.g. density,
pressure) in
numerical &
algebraic contexts
Use standard measures of
mass, time, length and
money as well as
compound measures
including decimal
quantities.
Convert between
compound measures.
Work with general
iterative processes; find
approximate solutions to
equations numerically
using iteration
Inequalities as
regions on graphs
and in set notation,
solve quadratic
inequalities
Recognise and use simple
geometric progressions (r^n where
n is an integer, and r is a rational
number > 0 or a surd) and other
sequences
Trig & exponential graphs.
Apply the concepts of average &
instantaneous rate of change (gradients
of chords and tangents) in numerical,
algebraic and graphical contexts
Transforming
graphs;
translation &
reflection of
given functions
Know the exact values of
sinθ and cosθ for θ = 0°, 30°,
45°, 60° and 90°; know the
exact value of tanθ for θ =
0°, 30°, 45° and 60°
3-D Trig
&
Pythag
Arc lengths, angles and
areas of sectors of
circles, surface area
and volume of
composite solids
Use vectors to
construct
geometric
arguments and
proofs (Vectors)
Real life graphs including
Construct and
Vectors:
Conditional
dist/time, speed/time
Volume and surface area
interpret
column vectors
probability,
and acceleration
of spheres, cones and
diagrams for
and related
expected
(including harder fuctions
pyramids. Congruence
grouped
diagramatic
frequencies
Eg reciprocal). Interpret
and similarity for length,
discrete data
representation;
with two-way
the gradient at a point
area and volume.
and continuous
add, subtract
tables, tree
on a curve as the
Sine and cosine rules &
data, including
and use scalar
diagrams and
instantaneous rate of
Area = ½ab sinC
unequal width
multiples
Venn diagrams.
change
histograms
Solve linear simultaneous equations
Set up algebraic
Apply & prove
Use gradient & intercept of y =
Compare
Calculate
Use the basic
algebraically.
expressions &
standard circle
mx + c lines.
distributions
probabilities
congruence
Solve quadratic equations through
eq’ns from
theorems
Find eq'n of straight line from 2
of using
using tree
criteria for
factorising where rearranging is needed
situations.
concerning
point or gradient and a point.
mean,
diagrams and
triangles
first. Factorise quadratics of the form ax² +
Change the
angles, radii,
Interpret straight line gradient as
median,
other
(SSS, SAS,
bx + c.
subject of
tangents and
a rate of change.
mode, range,
representations
ASA, RHS).
Simplify and manipulate algebraic
formulae.
chords, and use
Deduce roots of quadratic
quartiles and
of dependent &
Apply Basic
expressions (including those involving surds
Solve linear
them to prove
functions algebraically
inter-quartile
independent
2-D Trig
and algebraic fractions) by expanding
inequalities in
related results
Reciprocal graphs.
range
events.
products of two or more binomials
2 variables
Expand and factorise
Sketch and interpret
Use mathematical argument
Infer properties of populations or
Basic 2-D Trig.
quadratics (a = 1).
linear and quadratic
to show equivalency of
distributions from a sample, whilst
graphs.
Compare lengths,
algebraic expressions.
knowing the limitations of sampling.
The difference of 2 squares.
Enlargement
areas and
y
=
mx
+
c
with
parallel
Know the difference
including
Compare distributions using mean,
Solve quadratic equations
volumes using
lines.
between equation and
negative
median, mode and range and consider
graphically and by factorising
ratio notation.
identity.
scale factors
outliers.
(a=1)
Solve simultaneous
Area of circles &
equations graphically.
Understand and use
Cumulative frequency graphs,
Understand and use algebraic
compound shapes
composite functions
box plots, equal width histograms.
factors.
Cubic Graphs.
Fibbonacci &
quadratic
sequence,
nth term of
quadratic
sequence
Use y = mx + c to identify
perpendicular lines.
Identify and interpret roots,
intercepts, turning points of
quadratic functions
graphically.
Eq’ns & graphs: Circles
(centre origin), Exponential
(+ &- base)
Manipulate algebraic
expressions (including
laws of indices).
Use angle facts up to
parallel lines including
obtaining simple
proofs.
Find the nth term and
understand a reverse
process as an inverse
function.
Draw, interpret and
use bearings, scale
drawings and maps.
Solve addition &
subtraction multi-step
problems in contexts,
deciding which
operations & methods
to use & why.
Recognise and use
relationships between
operations, including
inverse operations (e.g.
cancellation to simplify
calculations and
expressions.
Formal written division
with answers up to 2dp
Round whole
numbers to a
required degree of
accuracy (nearest
10, 100 1000 etc).
Round decimals with
two decimal places
to the nearest whole
number & to one dp.
Interpret and use negative
numbers in context, count
forwards and backwards with
positive and negative whole
numbers, including through
zero
Understand and
use place value:
Read, write, order
and compare
numbers (up to
3dp and up to 10
000 000) and
determine the
value of each digit
Count forwards or
backwards in steps of
powers of 10 for any
given number up to
1 000 000
Add, subtract, multiply
and divide fractions
(mixed, proper or
improper) and simplify
answers.
Understand 3/8 means
3 divided by 8 and
evaluate it as a
decimal.
Read and write decimal
numbers as fractions
[for example, 0.71 =
71/100].
Recognise &use
thousandths and relate
them to tenths,
hundredths and
decimal equivalents
Add, subtract
multiply & divide
whole numbers
mentally & using
formal written
methods.
Multiply and divide
by 10, 100 and 1000
(including decimals)
Recall and use
equivalences between
simple fractions,
decimals and
percentages, including
in different contexts.
Compare two
quantities using
percentages.
Interpret % and %
changes as a fraction
or a decimal, &
interpret these
multiplicatively
Solve problems
involving % change,
including %
increase/decrease
Use and describe
congruence and similarity
(including finding lengths).
Translation (with vector
notation), rotation,
reflection and enlargement.
Solve loci
problems
including the
use of
standard ruler
and compass
constructions
Use the
mean,
mode,
median &
range to
compare
and analyse
sets of data.
Use charts, tables and diagrams (inc pie charts)
to interpret, analyse and compare data.
Use scatter diagrams and lines of best fit to find
correlation and make predictions.
Enumerate sets and combinations of sets
systematically using tables, grids and Venn
diagrams.
Perimeter of 2-D
Probabilities of mutually
shapes.
exclusive events sum to
Area of parallelograms,
Enumerate
one.
triangles and trapezia.
possibilities
Construct sample space
Volume and surface
of
diagrams to calculate
area of cubes and
combinations
theoretical probabilities.
cuboids (cm², cm³, m²
of two
Record describe and
& m³, extending to
variables.
analyse the frequency of
mm³ and km³)
Apply
outcomes of probability
Change freely between
systematic
experiments using tables
related standard units
listing
and frequency trees.
(e.g. time, length, area,
strategies
Understand that
volume/capacity,
including use
empirical unbiased
mass) in numerical
of the
samples tend towards
contexts.
product rule
theoretical probability
Construct and interpret
for counting
distributions, with
plans and elevations of
increasing sample size
3-D shapes.
Perimeter
of
composite
Solve problems involving similar
Use & interpret algebraic
Use standard conventions &
Complete, read &
Define percentage as
rectilinear shapes (measure
shapes or related quantities or
Describe
notation, for example: ab, 3y, a²,
notations for labelling & referring
interpret
‘number of parts per
& calculate in cm & m).
sizes using integer scale factors.
linear
a³, a²b , a/b, brackets &
to sides, angles, points, lines,
information in
hundred’.
Area of squares &
Solve problems involving unequal
number
coefficients written as fractions
vertices, edges, planes, parallel
tables, inc
Solve problems which
rectangles using standard
sharing & grouping using
sequences,
rather than as decimals.
lines, perpendicular lines, right
timetables.
require knowing
units (cm² & m²) & estimate
knowledge of fractions and
generate
Express missing number
angles, polygons, regular
Interpret &
percentage and decimal
areas of irregular shapes.
multiples.
terms from
problems algebraically.
polygons and polygons with
construct pie charts
equivalents of 1/2, 1/4, 1/5,
Recognise that shapes with
either a
Understand & use standard
reflection and/or rotation
& line graphs & use
2/ , 4/ and those fractions
Solve problems involving
same areas can have
5
5
term-to-term
mathematical formulae.
symmetries.
these to solve
multiplication & division,
with a denominator of a
different perimeters & viceor a positionSubstitute numerical values into
Use angle properties; round a
problems. Calculate
including scaling by simple
multiple of 10 or 25.
versa.
to-term rule
expressions and formulae (inc
point, straight line, vertically
& interpret the
fractions & problems involving
Estimate volume & capacity
Find % of an amount.
scientific).
opposite to find missing angles
mean as an average
simple rates.
using cm cubes & water.
Solve
problems
involving
Identify multiples,
Compare & order fractions,
Work with coordinates in
Use properties of rectangles to
Identify and apply circle
Apply ideas of
converting between units of
factors (divisors), all
including fractions > 1.
all four quadrants.
deduce related facts & find
definitions and
randomness, fairness
time.
factor pairs, common
Add and subtract fractions
Understand and use lines
missing lengths & angles.
properties, including:
and equally likely
Convert between miles & km.
factors,
common
with the same denominator
parallel to the axes, y=x
Derive & use the sum of angles in
tangent, arc, sector and
events to calculate
Understand and use
multiples
and
prime
and denominators that are
and y=-x.
a triangle (e.g. to deduce & use
segment.
expected outcomes of
approximate
equivalences
numbers (know primes
multiples of the same
Plot and interpret graphs
the angle sum in any polygon, &
Recognise, describe and
multiple future
between
metric
units
and
up to 19 and establish
number.
of non-standard (pieceto derive properties of regular
build simple 3-D shapes,
experiments.
common
imperial
units
such
as
whether others up to
Convert between mixed
wise linear) functions in
polygons) & find unknown angles
including making nets.
Relate relative
inches,
pounds
&
pints.
100 are prime). Prime
numbers and improper
real contexts, to find
in any triangles, quadrilaterals, &
Identify properties of
expected frequencies
Solve problems involving the
factors and
fractions.
approximate solutions to
regular polygons.
faces, surfaces, edges &
to theoretical
calculation and conversion of
decomposition.
Multiply proper fractions
problems such as simple
Distinguish between regular &
vertices of: cubes,
probability, using
units of measure, using
and mixed numbers by
kinematic problems
irregular polygons based on
cuboids, prisms,
appropriate language
Recognise square and
decimal notation up to three
whole numbers, supported
involving distance &
reasoning about equal sides &
cylinders, pyramids,
& the 0 - 1 probability
cube numbers and
decimal places where
by materials and diagrams
speed.
angles.
cones and spheres
scale.
associated notation.
appropriate.
Use conventional
notation for
priority of
operations,
including
brackets.
Use positive
integer powers
and associated
real roots (square,
cube and higher),
recognise powers
of 2, 3, 4, 5
Estimate powers
& roots of any
given positive
number
Order positive and negative
integers, decimals & fractions.
Complete the
square to solve
quadratics & find
vertex/turning point
Transformations:
Reflection, rotation,
translation & enlargement
(including fractional scale
factors). Understand which
properties of the shapes
are preserved or changed
after combined
transformations
Solve problems
involving direct and
inverse proportion,
understand links
between proportion,
ratio and fractions.
Convert between
terminating
decimals &
fractions
Use four
operations
on +ve & -ve
integers,
fractions and
decimals.
Construct and solve
simultaneous eq’ns
& interpret the
solutions.
Find the
equation of a
tangent to a
circle at a given
point
Equivalent fractions
including cancelling
and writing over same
denominator for
comparison (including
visual representations).
Write % as a fraction
with denominator 100,
& as a decimal
Understand and use place
value: Read, write, order and
compare whole numbers (up
1000) and determine the value
of each digit
Simplify & manipulate
algebraic expressions
by collecting like terms
& multiplying a single
term over a bracket.
Find pairs of numbers
that satisfy an eq’n
with 2 unknowns.
Solve linear equations
in one unknown
algebraically.
Understand and use
the concepts and
vocabulary of
expressions, eq’ns,
formulae, terms &
factors
Estimate, draw
and measure
angles.
Identify angles
round a point or
on a straight line
totalling 360°or
180° & other
multiples of 90°
Add, subtract multiply and
divide whole numbers
mentally.
Multiply and divide integers
by 10 and 100
Sequences of
triangular, square
& cube numbers,
simple APs.
Interpret simple
expressions as
functions with
inputs and
outputs.
Plot straight line
graphs from given
equation.
Simple Reflection
and Translation
on co-ordinate
axes
Compare and classify geometric
shapes based on their properties
and sizes. Find and use
properties of special triangles
and quadrilaterals and other
plane figures using appropriate
language.
Draw 2-D shapes using given
dimensions & angles
Understand visual
representations of
equivalent fractions
including tenths and
hundredths
Identify 3-D
shapes,
including cubes
and other
cuboids, from
2-D
representations
Draw and measure line segments.
Know angles are measured in
degrees: estimate and compare
acute, obtuse and reflex angles.
Grade 1 includes all the elements of Foundation as well. For students operating below grade 1, they can be graded at F3, F2 or F1 (F3 the highest)
Red text indicates fundamental concepts that should be thoroughly embedded. Repeated review until nailed!
Circle definitions
and properties:
centre, radius,
chord, diameter,
circumference,
know that the
diameter is twice
the radius
Convert
between
different units of
metric measure
(for example,
km & m; cm &
m; cm & mm; g
&kg; litre and
millilitre)
Solve comparison,
sum and difference
problems using
information
presented in a line
graph