Cambridge Primary
Cambridge Primary Mathematics 0096 Progression Grid
Number
Counting and sequences
Stage 1
Stage 2
1Nc.01 Count objects
from 0 to 20, recognising
conservation of number
and one-to-one
correspondence.
2Nc.01 Count objects
from 0 to 100.
Ensure learners use one-toone matching, and know that
numbers are in a fixed order.
Develop numbers 20 to 99
first before revisiting teen
numbers (11-19) as learners
find them difficult to learn
because in English they do
not follow the same wording
convention as other
numbers.
e.g.
= 2 = two
Learners visualise, then
count numbers orally before
being introduced to the
number symbols.
Ensure learners recognise
conservation of number.
e.g. there are fewer objects
in the first row than the
second row.
Stage 3
Stage 4
Stage 5
Stage 6
When counting, learners
group objects in twos, fives
or tens.
e.g. 34 = three groups of ten
and two groups of two.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
1
1Nc.02 Recognise the
number of objects
presented in familiar
patterns up to 10, without
counting.
2Nc.02 Recognise the
number of objects
presented in unfamiliar
patterns up to 10, without
counting.
Ensure learners have instant
recognition of number
patterns recognition without
counting (subitising).
Use resources to represent a
variety of groupings for the
same number.
Use resources such as ten
frames, dice, spinners, cards
and dominoes to help
learners visualise without
counting.
using ten frames to
represent the number 5
e.g.
e.g.
1Nc.03 Estimate the
number of objects or
people (up to 20), and
check by counting.
2Nc.03 Estimate the
number of objects or
people (up to 100).
3Nc.01 Estimate the
number of objects or
people (up to 1000).
Ensure learners understand
that estimating is more
appropriate in some contexts
and accurate counting in
others.
e.g. choose from 10, 20, 50
or 100 when the number of
objects is 47
Learners provide a range
when estimating large
numbers, e.g. that there are
between 300 and 500 when
there are 420 objects.
e.g. learners should be able
to recognise if the amount of
sweets is enough for the
number of people.
Learners interpret and
discuss estimations made by
self and others.
Use examples with objects
that are not easily countable
(raisins in a box).
Cambridge Primary Mathematics 0096 Progression Grid v1.2
As learners become more
confident encourage them to
refine (narrow) their range.
Encourage learners to
mentally group objects into
tens or hundreds when
estimating.
2
Ensure learners understand
that estimating means
getting a number that is as
close as possible to the
actual number.
Learners interpret and
discuss estimations made by
self and others.
Learners interpret and
discuss estimations made by
self and others.
1Nc.04 Count on in ones,
twos or tens, and count
back in ones and tens,
starting from any number
(from 0 to 20).
2Nc.04 Count on and
count back in ones, twos,
fives or tens, starting from
any number (from 0 to
100).
3Nc.02 Count on and
count back in steps of
constant size: 1-digit
numbers, tens or
hundreds, starting from
any number (from 0 to
1000).
4Nc.01 Count on and
count back in steps of
constant size: 1-digit
numbers, tens, hundreds
or thousands, starting
from any number, and
extending beyond zero to
include negative numbers.
5Nc.01 Count on and
count back in steps of
constant size, and extend
beyond zero to include
negative numbers.
6Nc.01 Count on and
count back in steps of
constant size, including
fractions and decimals,
and extend beyond zero
to include negative
numbers.
Ensure learners make the
connections between
counting on and addition,
and counting back and
subtraction.
Ensure learners relate
counting on from zero (and
back) to the 2, 5, and 10
times tables.
Ensure learners relate
counting on from zero, (and
back) to 2, 3, 4, 5, 6, 8, 9
and 10 times tables.
e.g. count on or count back
in hundreds from 344: 344,
244, 144, …
Use examples that start at a
positive number and go
beyond zero.
Use examples that require
knowledge of all times
tables, focusing on 7, 8 and
9 and on those that start at a
positive number and go
beyond zero.
Use fraction and decimal
examples that include tenths,
hundredths and thousandths
and fraction examples that
use small denominators.
e.g. count back from 5 in
threes: 5, 2, -1, …
e.g. count back from 15 in
sevens: 15, 8, 1, -6, …
from 0.7; starting from ,
e.g. find 1 less than 19,
count back 1, find 10 less
than 19 count back 10.
Ensure learners can also
count on (and back) not only
starting from zero.
e.g. count on in tens from
seven: 7, 17, 27, 37, …
or count on in 100s from
159: 259, 359, 459, …
Cambridge Primary Mathematics 0096 Progression Grid v1.2
e.g. count back in tenths
1
3
1
count on in steps of ;
3
starting from 0.4, count back
in steps of 0.2.
Ordering and comparing
decimals are covered in the
sub-strand Fractions,
decimals and percentages
when equivalence is
introduced.
3
1Nc.05 Understand even
and odd numbers as
‘every other number’
when counting (from 0 to
20).
2Nc.05 Recognise the
characteristics of even
and odd numbers (from 0
to 100).
3Nc.03 Use knowledge of
even and odd numbers up
to 10 to recognise and
sort numbers.
4Nc.02 Recognise and
explain generalisations
when adding and
subtracting combinations
of even and odd numbers.
Use the ten frame to show
the pattern of odd and even
numbers. Even numbers
show pairs, odd numbers
show pairs with one extra.
e.g. Even numbers have the
digit 0, 2, 4, 6 or 8 in the
ones place. Odd numbers
have the digit 1, 3, 5, 7 or 9
in the ones place.
e.g. 589 is odd because it
has the digit 9 in the ones
place.
even + even = even and
Ensure learners know that if
the total number of objects
belongs to the 2 times table
(can be counted in twos)
then it is an even number.
Learners recognise that an
even number of objects can
be shared into 2 equal
groups and odd numbers
cannot.
Ensure learners understand
that if numbers can be
divided by 2 then the number
is even, if they cannot then
the number is odd.
Ensure learners understand
that when counting on from
an even number (including
zero), every alternate
number is even, when
counting on from an odd
number every alternate
number is odd.
even – even = even,
odd + odd = even and odd –
odd = even,
odd + even = odd and odd –
even = odd,
Start by using examples with
numbers between 0 and 10
so learners can recognise
the generalisations
e.g. 3 + 3 = 6 so odd + odd =
even
3 + 2 = 5 so odd + even =
odd
Use examples that learners
will understand the
underlying structure
5 + 5 = 10
4 + 1 + 4 + 1 = 10
4 +1 + 4 +1 = 10
4 + 4 + 2 = 10
The two left over (1 and 1)
make an even number.
3Nc.04 Recognise the
use of an object to
represent an unknown
quantity in addition and
subtraction calculations.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
4Nc.03 Recognise the
use of objects, shapes or
symbols to represent
unknown quantities in
addition and subtraction
calculations.
5Nc.02 Recognise the
use of objects, shapes or
symbols to represent two
unknown quantities in
addition and subtraction
calculations.
6Nc.02 Recognise the
use of letters to represent
quantities that vary in
addition and subtraction
calculations.
4
Any object can represent an
unknown. An unknown has a
fixed value. Use objects
familiar to learners.
An object, shape or symbol
can represent an unknown.
Start with easy recognisable
shapes.
e.g.
e.g. a farmer has two pieces
of wood that are different
lengths (metres) and the
sum of the lengths is 45
metres. What lengths are the
pieces of wood? Give all
possible lengths.
Learners are shown a picture
of two identical bars of
chocolate with a price tag of
$2 for both
price of chocolate + price of
chocolate = $2
+
+
= $2
1m
44m
=
$3
1m
+
+
= 12 kg
What is the value of one
?
Total
e.g. A more difficult example
might be:
45m
++++=1.3kg
45m
Learners are shown a picture
of a bar of chocolate and a
football with a price tag of
$10 for both.
+
=
$10
Learners recognise that the
unknowns are the price of
Cambridge Primary Mathematics 0096 Progression Grid v1.2
+
What are the possible values
of  and ?
44m
-
represents a mass in
kg
= 45
Allow learners to use their
own strategies then suggest
strategies for checking that
they have found all possible
answers.
Variables can be different
values.
e.g.
e.g. Four identical cans have
a mass of 12 kg, what is the
mass of 1 can?
metres
Learners are shown a $10
note and how much they
have left after buying a
football. The unknown
represents the price of a
football.
$10
Use examples with numbers
that are easy to calculate as
this objective is about
understanding pre-algebra
and not complex
calculations.
e.g.
+
=
$25
A
B
Learners are presented with
two cups, one labelled A and
the other labelled B. They
are given 10 counters.
Learners are asked to find all
of the different ways that
they can place the counters
into the cups. This problem
can be represented
algebraically by writing A + B
= 10. A and B vary because
they can have lots of
different values. For
example, if A = 0, then B
=10; if A = 1, then B = 9; if A
= 2, then B = 8 and so A + B
= 10.
Link to other strands such as
Geometry and Measure.
e.g.
s
Learners are shown two
pictures, one picture of two
identical bars of chocolate
with a price tag of $25 for
both and another picture of a
football and piece of
chocolate with a price tag of
$21 for both.
The perimeter (p) of a
square with side length (s)
could be represented as p =
s + s + s+ s.
The value of s would be
different for different size
squares.
5
the chocolate and the price
of the football and can
represent the objects as
shapes.
e.g.
Learners recognise that the
unknowns are the price of
the chocolate and the price
of the football.
+  = 10
where the square represents
the price of the chocolate bar
and the circle represents the
price of the football.
Learners are shown a $10
note and how much they
have left after buying a
football. The unknown
represents the price of a
football.
$10
-
=
$3
Learners recognise that the
unknown is the price of the
football and can represent
the object as a shape.
e.g. 10 -
=
+
$21
price of chocolate + price of
chocolate = $25
price of football + price of
chocolate = $21
or  +  = 25
+  = 21
Learners should be able to
find the solution that each
chocolate bar costs $12.50
and the football costs $8.50.
$10
-
=
-
$1
=3
The circle represents the
price of the football.
$10
-
=
$8
Learners should be able to
find the solution that the
chocolate costs $2 and
therefore the ball costs $7
or 10 -  = 8
10 -
Cambridge Primary Mathematics 0096 Progression Grid v1.2
-=1
6
1Nc.06 Use familiar
language to describe
sequences of objects.
2Nc.06 Recognise,
describe and extend
numerical sequences
(from 0 to 100).
3Nc.05 Recognise and
extend linear sequences,
and describe the term-toterm rule.
4Nc.04 Recognise and
extend linear and nonlinear sequences, and
describe the term-to-term
rule.
5Nc.03 Use the
relationship between
repeated addition of a
constant and
multiplication to find any
term of a linear sequence.
6Nc.03 Use the
relationship between
repeated addition of a
constant and
multiplication to find and
use a position-to-term
rule.
Look at these shapes and
describe what you see.
Ensure the focus is on
identifying patterns of
numbers.
Term-to-term rules describe
how a term is produced from
the term or terms before it
and is also known as
recursion rule.
Term-to-term rules describe
how a term is produced from
the term or terms before it
and is also known as
recursion rule.
Use examples where
sequences are formed by
adding and subtracting a
constant.
e.g. the sequence of odd
numbers 1, 3, 5, 7, 9, 11, …
has the recursion rule: 'the
next term is 2 more than the
previous term'. Therefore, 13
(11 + 2), 15 (13 + 2), and 17
(15 + 2) are the next three
terms.
Use examples of addition,
subtraction, multiplication
and division, with or without
using a number line,
extending beyond zero to
include negative numbers.
Ensure learners recognise
that the pattern: 4, 8, 12, 16
are the answers to the four
times table, and so the 10th
term in the sequence can be
found with 4 x 10 = 40.
e.g. they are all squares, and
the colour is blue, green, red,
blue, green, red so the next
one is blue.
Patterns may be based on
colour, shape or size of
objects including
symmetrical patterns in the
environment (link to
geometry and measure).
e.g. when counting in ones
or twos from 21 to 29,
learners recognise the
pattern: the tens digit stays
the same and the ones digit
changes.
Examples should use
numbers that are easily
accessible to learners (2, 5
or 10 times tables) as this
learning objective focusses
on recognition of patterns
rather than complex
calculations.
e.g.
 the sequence 5, 10, 20, 40
… has the recursion rule:
'the next term is two times
the previous term’.
 1, 2, 4, 8, 16 ….
(doubling);
 1000, 200, 40, 8, 1.6 ….
(÷5)
Use examples where the rule
is given.
e.g. if the rule is ‘add 2 and
multiply by 3’, the next
number in the sequence 1, 9
would be 33.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
e.g. the following sequence
has steps of constant sizes
11, __, __, 23. Therefore, to
find the missing numbers,
learners need to identify that
from 11 to 23 is 12 (three
jumps of four).
Ensure learners understand
the difference between a
term and position as this will
assist them when they are
formally introduced to
algebra in the Lower
Secondary curriculum.
Use tables or mapping
diagrams to assist learners
in seeing connections
between the terms, pattern
and position.
Position
1
2
3
4
5
6
10
?
20
100
Term
3
6
9
12
15
?
?
45
?
?
7
3Nc.06 Extend spatial
patterns formed from
adding and subtracting a
constant.
4Nc.05 Recognise and
extend the spatial pattern
of square numbers.
e.g. continue the pattern by
adding 3 triangles
3 + 3 + 3 is nine triangles
Cambridge Primary Mathematics 0096 Progression Grid v1.2
6Nc.04 Use knowledge of
square numbers to
generate terms in a
sequence, given its
position.
Use visual examples to
assist learners to see the
pattern.
e.g. diagrams are provided.
Learners extend the pattern
to the 10th term.
is 3 triangles
3 + 3 is six triangles
5Nc.04 Recognise and
extend the spatial pattern
of square and triangular
numbers.
The diagram shows that the
first term is 1 (1x1), the
second term is 4 (2x2), so
the next term will be 9 (3x3).
1
1
dot
2
3
dots
3
6
dots
4
10
dots
e.g. a diagram with the first
term 1 (12) and second term
4 (22) is given. Learners
recognise that the fifth term
will be 52 = 25, and the tenth
term will be 102 = 100.
8
Number
Money
Stage 1
Stage 2
Stage 3
1Nm.01 Recognise
money used in local
currency.
2Nm.01 Recognise value
and money notation used
in local currency.
3Nm.01 Interpret money
notation for currencies
that use a decimal point.
This includes:
This includes recognising
the currency symbol for your
country (e.g. $, £, €, ₹)
e.g. the notation $1.50
means 1 dollar and 50 cents
or 3 dollars and 25 cents is
the same as $3.25
 Differentiating the size and
colour of notes and coins
(if appropriate).
 Playing with fake money
(without focusing on value
and notation).
Stage 4
Stage 5
Stage 6
Ensure learners understand
to the left of the decimal
point is dollars and to the
right of the decimal point is
cents. So the decimal point
is a separator for dollars and
cents.
Although some countries do
not use decimal notation or
coins, Cambridge
International adopts dollar
notation as an internationally
recognised currency.
2Nm.02 Compare values
of different combinations
of coins or notes.
3Nm.02 Add and subtract
amounts of money to give
change.
e.g. 1 dollar is the same as
two 50 cents coins:
In local currency and also in
the dollar currency:
The concept of money is completed in Stage 3. From Stage 4 onwards, learners continue to
use money in context, e.g. creating and solving problems, using decimal notation, discounted
prices, converting between currencies, recognising when two quantities are directly
proportional. Learners are not introduced to decimal places until Stage 5.
1, 5, 10, 25, 50 cents
1, 2, 5, 10, 20, 50 and 100
dollars
e.g. to pay $3.55 you could
use three 1 dollar notes, 50
cents and 5 cents or three 1
Cambridge Primary Mathematics 0096 Progression Grid v1.2
9
From Stage 2, Cambridge
International adopts dollar
notation as the standard
notation for money as it is an
internationally recognised
currency.
dollar notes, five 10 cents
and 5 cents. Or if you used
four 1 dollar notes, you
would receive 45 cents
change.
Even though decimal places
are not introduced until
Stage 5, you can still ask
learners questions related to
money
e.g. Sara has $10. She buys
a pen for 4 dollars and 60
cents and a pencil for 3
dollars and 30 cents. How
much change will she be
given?
2 dollars and 30 cents.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
10
Number
Integers and powers
Stage 1
Stage 2
Stage 3
Stage 4
1Ni.01 Recite, read and
write number names and
whole numbers (from 0 to
20).
2Ni.01 Recite, read and
write number names and
whole numbers (from 0 to
100).
3Ni.01 Recite, read and
write number names and
whole numbers (from 0 to
1000).
4Ni.01 Read and write
number names and whole
numbers greater than
1000 and less than 0.
e.g. Number name is ‘one’
and is represented by the
symbol ‘1’
Ensure learners understand
the relationship between
number names and
numbers, and only include
place value if this has
already been covered (see
sub-strand Place value,
ordering and rounding).
Ensure learners understand
the relationship between
number names and
numbers, and only include
place value if this has
already been covered (see
sub-strand Place value,
ordering and rounding).
Ensure learners understand
that 6542 is read as 6
thousands, 5 hundreds and
forty-two but 86 542 is read
as 86 thousands and not 8
ten thousands. This links to
place value.
e.g. number name is
‘twenty’, and is represented
by the symbols ‘20’ using
two numerals (digits) ‘2’ and
‘0’ and is the same as 2 tens
and 0 ones (place value).
e.g. number name is ‘three
hundred and forty-one’, and
is represented by the
symbols ‘341’ and is the
same as 3 hundreds, 4 tens
and 1 one (place value).
Ensure learners understand
that number words and
numbers are in a fixed order.
One-to-one correspondence
is covered in the sub-strand
Counting and sequences
Stage 5
Stage 6
For negative numbers,
initially only use examples
that use number lines, scales
(e.g. thermometer). or other
resources to assist
calculations. Show position
of positive and negative
numbers around zero
recognising that negative
numbers are to the left of
zero on a number line.
Ensure learners understand
that in English the number
-34 is read as “negative thirty
four” and not “minus thirty
four”.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
11
1Ni.02 Understand
addition as:
- counting on
- combining two sets.
Introduce these concepts of
addition using concrete
apparatus, then pictorial
representations before using
the abstract notation of the +
symbol.
Start with numbers to 10,
ensuring that examples do
not use numbers greater
than 20.
2Ni.02 Understand and
explain the relationship
between addition and
subtraction.
3Ni.02 Understand the
commutative and
associative properties of
addition, and use these to
simplify calculations.
Initially use materials
(counters, dominos or dice)
and symbols that show small
numbers.
Ensure learners understand
that these properties do not
apply to subtraction because
e.g. 1 + 2 = 3 and 2 + 1 = 3,
so 3 - 1 = 2 and 3 – 2 = 1
5 – 3 = 2 whereas 3 – 5  2
(negative numbers are
covered in Stage 4).
Then use examples that total
10 to reinforce complements
of ten (number pairs) and the
relationship between addition
and subtraction.
Ensure learners understand
that when numbers are
added their order can be
changed without affecting
the total.
e.g. if 6 + 4 = 10, and 4 + 6 =
10, then 10 – 6 = 4, 10 – 4 =
6.
e.g.
Ensure learners understand
that addition and subtraction
are inverses.
Do not use any examples
where the total is greater
than 100.
 2 + 3 = 5 is the same as
3+2=5
 3 + 4 + 6 = 13 is the same
as 6 + 4 + 3 = 13 or 4 + 6 +
3
At this stage, learners have
not been introduced to
brackets so introduce
associative property of
addition informally
e.g. If 2 + 3 + 5 = 10 then
2+3+5=
2 + 3 + 5 = 5 + 5 = 10 or
⏟
5
2+⏟
3 + 5 = 2 + 8 = 10
8
Cambridge Primary Mathematics 0096 Progression Grid v1.2
12
1Ni.03 Understand
subtraction as:
- counting back
- take away
- difference.
Introduce these concepts of
subtraction using concrete
apparatus, then pictorial
representations before using
abstract notation of the symbol.
Ensure learners know
“difference” in the form of
‘How many more or how
many less?’
1Ni.04 Recognise
complements of 10.
2Ni.03 Recognise
complements of 20 and
complements of multiples
of 10 (up to 100).
3Ni.03 Recognise
complements of 100 and
complements of multiples
of 10 or 100 (up to 1000).
Complements to 10 is the
same as number bonds, or
number pairs that total 10. It
is important to include 0 and
10.
Ensure learners are secure
with numbers to 20 before
introducing numbers to 100.
Ensure learners are using
their knowledge of the
addition number facts to 10
and 20 and the related
subtraction facts.
10 + 0 = 10,
0 + 10 = 10,
9 + 1 = 10,
1 + 9 = 10 etc.
Numbers that total less than
10 are covered later in this
sub-strand
e.g. 6 + 1 = 7, 8 – 2 = 6
e.g.
Use addition and subtraction
examples
15 + 5 = 20, 20 – 5 = 15, 12
+ 8 = 20, 20 – 8 = 12, 20 –
12 = 8).
For complements of 100,
initially use numbers that end
in 0 or 5.
Complements of multiples of
10 (up to 100)
e.g. 70 + 30 = 100 or
85 + 15 = 100
e.g. 20 + 60 = 80, 70 - 30 =
40
and then 76 + 24 = 100 or
13 + 87 = 100
Numbers that total less than
100 (that do not require
Cambridge Primary Mathematics 0096 Progression Grid v1.2
13
regrouping) are covered later
in this sub-strand
e.g. 0 + 15 = 15 , 15 – 0 =
15, 41 + 36 = 77, 82 – 31 =
51
Complements of multiples of
10 (up to 1000) refer to
multiples of 10 within 1000
e.g. 430 + 280 = 710,
640 - 270 = 370.
Complements of multiples of
100 (up to 1000) refer to
multiples of 100 within 1000,
e.g. 400 + 300 = 700,
800 - 200 = 600.
Start with multiples of 100
first, e.g. 400 + 300 = 700,
800 - 200 = 600, and then
multiples of 10, e.g.
430 + 280 = 710,
640 - 270 = 370.
1Ni.05 Estimate, add and
subtract whole numbers
(where the answer is from
0 to 20).
2Ni.04 Estimate, add and
subtract whole numbers
with up to two digits (no
regrouping of ones or
tens).
3Ni.04 Estimate, add and
subtract whole numbers
with up to three digits
(regrouping of ones or
tens).
4Ni.02 Estimate, add and
subtract whole numbers
with up to three digits.
5Ni.01 Estimate, add and
subtract integers,
including where one
integer is negative.
6Ni.01 Estimate, add and
subtract integers.
Ensure learners can
estimate simple calculations
so that they recognise when
an answer is incorrect
without a formal calculation.
For addition calculations, the
total should not exceed 100.
For addition calculations, the
total cannot exceed 1000.
Use examples that require
regrouping of ones and tens.
Also use examples such as:
Do not use examples that
require regrouping of ones or
bridging through ten.
For subtraction calculations,
initially do not use numbers
with zeros. e.g. 207 – 29 =
e.g. 358 + 45, 328 – 49,
Use examples that find the
difference between positive
and negative integers, and
between two negative
integers.
e.g. 1 + 5 = 6 cannot equal
17
e.g. 35 + 8 and 45 – 6
Use addition and
subtractions examples such
as:
Add a pair of numbers by
putting the larger number
first and counting on.
Use the + sign and know that
= sign represents
equivalence.
Use examples such as:
 Add four or five small
numbers 1 + 2 + 2 + 3
 Add and subtract numbers
that do not require
regrouping
e.g. 12 + 7 = 19
Cambridge Primary Mathematics 0096 Progression Grid v1.2
 Pairs of 2-digit numbers 14
+ 27 or 27 – 19
 3-digit with 1-digit numbers
243 + 8 or 243 – 8
 3-digit numbers with 2-digit
numbers
or 134 + 345 + 412
Ensure learners can
estimate simple calculations
so that they recognise when
an answer is incorrect
without a formal calculation.
For large numbers learners
can check using a calculator.
 Pairs of 3-digit numbers
243 + 171 + 359
 Integers with more than 3digits
 243 + 23 + 3478
For addition use examples
that add a positive integer to
a negative integer. For
negative integers only, start
with small numbers and
include examples that use
number lines or scales to
support calculations.
e.g. 30 – 5 = 25, - 30 – 5 = 35, - 30 + 5 = -25, 30 + 5 =
35
Learners start to understand
addition and subtraction of
integers using number line
and familiar contexts such as
rise and fall of temperature.
e.g. -5 + 405 = 400.
14
17 – 5 = 12.
Ensure learners know that
number facts on either side
of the = sign have the same
value.
35 + 4, 30 + 9 45 – 3, 29 – 9,
12 + 12, 25 – 20, 17-15, 55 41. Present the calculations
in different formats.
e.g. 36 + 23 and 36
23 +
e.g.
6 + 5 = 10 + 1
For subtraction, the minuend
(number from which you are
subtracting) must be 20 or
less.
243 + 28 or 243 – 28, 243
+ 71 or 243 – 71
3-digit numbers with
multiples of 10 or 100
243 + 90 or 243 – 90
243 + 200 or 243 – 200
 Pairs of 3-digit numbers
243 + 128 or 243 – 128
243 + 171 or 243 – 171
For both addition and
subtraction calculations, do
NOT use examples that
require regrouping before
introducing examples that do
require regrouping.
e.g. 235 + 23 = 258 and 174
– 139 = 35 then examples
that require regrouping of
ones and tens 325 + 449 =
774
For subtraction, use
examples that subtract a
positive number from any
integer where the result is
negative and use a number
line to support learners if
required e.g. 30 – 35 = -5
Ensure learners can
estimate simple calculations
so that they recognise when
an answer is incorrect
without a formal calculation.
For large numbers learners
can check using a calculator.
e.g. if the temperature falls
from 2 degrees to
-4 degrees, learners count
six steps (from right to left)
on a number line to conclude
that it is a fall of 6 degrees.
Ensure learners can
estimate simple calculations
so that they recognise when
an answer is incorrect
without a formal calculation.
For large numbers learners
can check using a calculator.
Ensure learners can
estimate simple calculations
so that they recognise when
an answer is incorrect
without a formal calculation.
For large numbers learners
can check using a calculator.
2Ni.05 Understand
multiplication as:
- repeated addition
- an array.
Multiplication as repeated
addition:
2+2+2+2+2=10 and 2 x 5 =
10 (2 multiplied by 5 = 10
Cambridge Primary Mathematics 0096 Progression Grid v1.2
3Ni.05 Understand and
explain the relationship
between multiplication
and division.
Ensure learners understand
the inverse relationship
between multiplication and
division, e.g. 3 x 5 = 15, and
15 ÷ 5 = 3.
15
Ensure that for the
commutative law all
examples only use the timestables facts that are familiar
to the learners,
3+3+3+3=12 and 3 x 4 =12
(3 multiplied by 4 = 12)
Ensure that for the distribute
law all examples only involve
whole numbers less than 20
multiplied by 2, 3, 4 or 5.
Multiplication as an array:
Use the × sign and know that
= sign represents
equivalence.
Ensure learners know that
number facts on either side
of the = sign have the same
value.
e.g. 6 x 5 = 10 x 3
2Ni.06 Understand
division as:
- sharing (number of
items per group)
- grouping (number of
groups)
- repeated subtraction.
Use the ÷ sign and know that
= sign represents
equivalence.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
3Ni.06 Understand and
explain the commutative
and distributive properties
of multiplication, and use
these to simplify
calculations.
4Ni.03 Understand the
associative property of
multiplication, and use
this to simplify
calculations.
5Ni.02 Understand which
law of arithmetic to apply
to simplify calculations.
6Ni.02 Use knowledge of
laws of arithmetic and
order of operations to
simplify calculations.
Ensure that for the
commutative law all
examples only use the timestables facts that are familiar
to the learners, i.e. 1x, 2x,
For multiplication
calculations, the total should
not exceed 1000.
Learners should continue to
apply the laws of arithmetic
for addition and multiplication
to calculate efficiently,
understanding for which
Use examples where there is
more than one multiplication
e.g.
25 x 3 x 4 + 5
16
3x, 4x, 5x, 6x, 8x, 9x and
10x.
Ensure that for the
distributive law all examples
only involve whole numbers
less than 20 multiplied by 2,
3, 4 or 5.
At this stage, learners have
not been introduced to
brackets so introduce the
commutative and distributive
properties of multiplication
informally, e.g.
At this stage, learners have
not been introduced to
brackets so introduce the
associative property of
multiplication informally
calculations they work and
which they do not.
Learners could use the laws
of arithmetic to swap the 3
and 4 to simplify to:
25 x 4 x 3 + 5
=100 x 3 + 5
e.g.
= 300 + 5
=305
or applying and associative
and commutative laws:
Commutative law:
Distributive law:
5Ni.03 Understand that
the four operations follow
a particular order.
6Ni.03 Understand that
brackets can be used to
alter the order of
operations.
Use examples that only use
one multiplication/division
and one
addition/subtraction..
e.g.
e.g. 3 + 5 x 2 = 13 , 8 + 8 ÷
2 = 12, 15 – 10 ÷ 5 = 13.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
4 + 1 x 7 = 11
(4 + 1) x 7 = 35
Ensure learners understand
that when calculations
17
Ensure learners understand
that when calculations
include a mixture of
operations (addition,
subtraction, multiplication
and division) the operations
must be calculated in a
particular order (division/
multiplication, then addition/
subtraction) to obtain the
correct solution.
include a mixture of
operations (addition,
subtraction, multiplication
and division) the operations
must be calculated in a
particular order (division/
multiplication, then addition/
subtraction) to obtain the
correct solution. If brackets
are included, then the order
changes to brackets first,
then division/ multiplication
then addition/ subtraction.
Examples using brackets
should only include one pair
of brackets: one of
multiplication/division OR
one of addition/subtraction.
1Ni.06 Know doubles up
to double 10.
2Ni.07 Know 1, 2, 5 and
10 times tables.
3Ni.07 Know 1, 2, 3, 4, 5,
6, 8, 9 and 10 times
tables.
4Ni.04 Know all times
tables from 1 to 10.
At Stage 1 language of
multiplication or times tables
should be avoided, as this is
introduced at Stage 2.
Ensure learners understand
the relationship between 2, 5
and 10 times tables.
Recognise the relationship
between multiples of 2, 5
and 10, and between
multiples of 2 and 4.
Ensure learners understand
the relationship between 2,
4, and 8 times tables: 4x
(double 2x) and 8x (triple 2x
or double 4x). Similarly,
relationships between 3, 6,
and 9 times tables: 6x
(double 3x) and 9x (triple
3x).
Use the language of doubles
as multiplication by 2.
e.g. double 2 is 4 and 2 x 2 =
4, double 5 is 10 or 5 x 2 =
10
Ensure learners also know
the division facts relating to
the 1, 2, 5 and 10 times
tables.
The two times table:
2 x 1 and not 1 x 2
2x2
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Use the language of doubles
to make connections
between times tables, e.g.
learn 4 times table by
doubling 2 times table. 2 x 4
= 8, double 8 is 16 so 4 x 4 =
16
Similarly introduce the 6
times table using the
relationship with the 3 times
table (double 3x), and the 8
times table using the
relationship with the 4 times
table (double 4x), and also
Ensure learners also know
the division facts relating to
all times tables from 1 to 10.
18
2x3
2x4
2x5
2x6
2x7
2x8
2x9
2 x 10
the relationship with the 2
times table (triple 2x).
Ensure learners understand
how the 9 times table can be
derived using the 3 times
table (triple 3x).
Ensure learners also know
the division facts relating to
the 1, 2, 3, 4, 5, 6, 8, 9 and
10 times tables.
3Ni.08 Estimate and
multiply whole numbers
up to 100 by 2, 3, 4 and 5.
4Ni.05 Estimate and
multiply whole numbers
up to 1000 by 1-digit
whole numbers.
5Ni.04 Estimate and
multiply whole numbers
up to 1000 by 1-digit or 2digit whole numbers.
6Ni.04 Estimate and
multiply whole numbers
up to 10 000 by 1-digit or
2-digit whole numbers.
Use examples such as:
Use examples such as:
Use examples use as:
-
Multiples of 10 or 100
with 1-digit numbers
23 x 60
1237 x 4
23 x 62
5147 x 20
60 x 8, 300 x 7
237 x 40
-
Two-digit with one-digit
numbers
237 x 48
-
23 x 6
-
Three-digit with one-digit
numbers
Ensure learners can
estimate simple calculations
so that they recognise when
an answer is incorrect
without a formal calculation.
For large numbers learners
can check using a calculator.
237 x 4
Ensure learners can
estimate simple calculations
so that they recognise when
an answer is incorrect
without a formal calculation.
For large numbers learners
can check using a calculator.
Ensure learners can
estimate simple calculations
so that they recognise when
an answer is incorrect
without a formal calculation.
For large numbers learners
can check using a calculator
Multiplication examples to
include:
2458 x 25
3472 x 39
Following example could be
checked with a calculator:
7566 x 78
Ensure learners are secure
with all times tables facts up
to 10 x 10 and recognise that
Cambridge Primary Mathematics 0096 Progression Grid v1.2
19
multiplication and division
are inverse operations.
3Ni.09 Estimate and
divide whole numbers up
to 100 by 2, 3, 4 and 5.
4Ni.06 Estimate and
divide whole numbers up
to 100 by 1-digit whole
numbers.
5Ni.05 Estimate and
divide whole numbers up
to 1000 by 1-digit whole
numbers.
6Ni.05 Estimate and
divide whole numbers up
to 1000 by 1-digit or 2digit whole numbers.
Ensure learners can
estimate simple calculations
so that they recognise when
an answer is incorrect
without a formal calculation.
For large numbers learners
can check using a calculator.
Use examples where
answers have remainders
expressed as a whole
number.
Use examples such as:
Use examples such as:
-
2-digit with 1-digit
numbers
35 ÷ 5 or 35 ÷ 8
35 ÷ 5 or 35 ÷ 8
72 ÷ 24 or 72 ÷ 12
3-digit with 1-digit
numbers
125 ÷ 25 or 120 ÷ 24
Ensure learners are secure
in the 2, 3, 4, and 5 times
tables and recognise that
multiplication and division
are inverse operations.
Initially, for division, use
examples that result in whole
number answers only. Then
introduce examples that
ensure learners understand
that not all quantities divide
into equal sizes and
therefore have remainders
(expressed as a whole
number).
e.g. 21 divided by 4 is 5
remainder 1
246 ÷ 6 or 246 ÷ 5
Ensure learners can
estimate simple calculations
so that they recognise when
an answer is incorrect
without a formal calculation.
For large numbers learners
can check using a calculator.
Ensure learners are secure
with all times tables facts up
to 10 x 10 and recognise that
multiplication and division
are inverse operations.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Ensure learners can
estimate simple calculations
so that they recognise when
an answer is incorrect
without a formal calculation.
For large numbers learners
can check using a calculator.
Remainders should be
expressed as a whole
number or a fraction.
Ensure learners can
estimate simple calculations
so that they recognise when
an answer is incorrect
without a formal calculation.
For large numbers learners
can check using a calculator.
Express remainders as a
fraction of the divisor when
dividing 2-digit numbers by
1-digit numbers, e.g. 97 ÷ 3
1
= 32
2
Encourage learners to look
at the question posed to
determine whether to use
mental strategies or written
methods to find the answer.
3Ni.10 Recognise
multiples of 2, 5 and 10
(up to 1000).
-
246 ÷ 6 or 246 ÷ 5 or 105 ÷ 3
Initially, do not use examples
that contain zero e.g. 105 ÷ 3
4Ni.07 Understand the
relationship between
multiples and factors.
5Ni.06 Understand and
explain the difference
6Ni.06 Understand
common multiples and
common factors.
20
between prime and
composite numbers.
Use arrays to assist learners
in finding multiples.
Ensure learners understand
that a whole number is a
multiple of its factors and
show this using multiplication
and division.
e.g. 3 and 4 are factors of 12
because 3 x 4 = 12.
12 is a multiple of 3 and 4
because 12 ÷ 3 = 4 and 12 ÷
4=3
1 group of 10, 10 groups of
1, 2 groups of 5, 5 groups of
2 etc.
2, 4, 6, 8, 10 … are multiples
of 2
5, 10, 15, 20 … are multiples
of 5
Ensure learners know that
multiples go beyond the
tenth multiple.
Ensure learners know that
factors are numbers that
divide exactly into another
number (no remainder).
Ensure learners understand
the definition of prime
number: exactly two divisors
1 and itself, that’s why 1 is
not a prime number (it only
has one divisor). A prime
number is a whole number
greater than 1.
Learners are only expected
to identify prime numbers up
to 100.
Ensure learners understand
that a common multiple is
number that is a multiple of
two or more numbers.
e.g.
The multiples of 3 are 3, 6, 9,
12, 15, 18, 21, 24…
The multiples of 4 are 4, 8,
12, 16, 20, 24 …
The common multiples of 3
and 4 are 12, 24, …
Ensure learners understand
that a common factor is a
number that is a factor of two
or more numbers, e.g. the
common factors of 12 and 15
are 1 and 3.
Include examples where
learners identify when one
number is not a multiple of
another number.
e.g. 42 is not a multiple of 8.
e.g. 25, 50 , 75, 100 are
multiples of 5.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
4Ni.08 Use knowledge of
factors and multiples to
understand tests of
divisibility by 2, 5, 10, 25,
50 and 100.
5Ni.07 Use knowledge of
factors and multiples to
understand tests of
divisibility by 4 and 8.
6Ni.07 Use knowledge of
factors and multiples to
understand tests of
divisibility by 3, 6 and 9.
Ensure learners understand
the relationship between
multiples of 2, 5, 10 and
tests of divisibility
Ensure learners understand
the relationship between
multiples of 2, 4, and 8, and
tests of divisibility.
e.g.
e.g. multiples of 2 have a
ones digit that is an even
number, and a number is
e.g. Divisible by 2 – if the
ones digit is even; divisible
by 4 if the last 2 digits of a
6 x 3 = 18, 1 + 8 = 9
4 x 3 = 12, 1 + 2 = 3
5 x 3 = 15, 1 + 5 = 6
21
divisible by 2 if the ones digit
is even.
Multiples of 5 have a ones
digit that is 5 or 0, and a
number is divisible by 5 if the
ones digit is 5 or 0.
e.g. recognise 2-digit and 3digit multiples of 2, 5 and 10
by looking at the ones digit.
number are a multiple of 4
(3728); divisible by 8 if the
last 3 digits of a number are
divisible by 8 (3728).
Learners may use a
calculator for large numbers.
The sum of the digits add up
to 3, 6, or 9 then the number
is divisible by 3.
If the number is divisible by 2
and 3, then it is divisible by
6, e.g. 1332 is even and 1 +
3 + 3 + 2 = 9 which is
divisible by 3. So 1332 is
divisible by 6.
Learners use the
relationships between factors
and multiples of 25, 50 and
100 to understand related
tests of divisibility.
5Ni.08 Use knowledge of
multiplication to recognise
square numbers (from 1
to 100).
6Ni.08 Use knowledge of
multiplication and square
numbers to recognise
cube numbers (from 1 to
125).
Ensure learners use the
notation for square numbers
(2 )
Ensure learners use the
notation for cube numbers (3)
e.g. 52 = 5 x 5 = 25 or 25 =
52 = 5 x 5 and therefore 25 is
the square of 5.
125 = 53 = 5 x 5 x 5 and
therefore 125 is the cube of
5.
Learners are not expected to
use the terminology square
root.
Make connections with cm2
and m2 in the Geometry and
Measure strand.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
e.g. 53 = 5 x 5 x 5 = 125 or
Ensure learners recognise
that 125 = 25 x 5 = 52 x 5
Learners are not expected to
use the terminology cube
root.
Use diagrams to make the
connection with cm3 and m3
in the Geometry and
Measure strand (6Gg.04).
22
Cambridge Primary Mathematics 0096 Progression Grid v1.2
23
Number
Place value, ordering and rounding
Stage 1
Stage 2
Stage 3
Stage 4
Stage 5
Stage 6
1Np.01 Understand that
zero represents none of
something.
2Np.01 Understand and
explain that the value of
each digit in a 2-digit
number is determined by
its position in that number,
recognising zero as a
place holder.
3Np.01 Understand and
explain that the value of
each digit is determined
by its position in that
number (up to 3-digit
numbers).
4Np.01 Understand and
explain that the value of
each digit in numbers is
determined by its position
in that number.
5Np.01 Understand and
explain the value of each
digit in decimals (tenths
and hundredths).
6Np.01 Understand and
explain the value of each
digit in decimals (tenths,
hundredths and
thousandths).
When talking about zero,
also use the language none,
nought, nil, nothing.
Ensure learners understand
that zero is a place holder to
record “nothing”.
Ensure learners understand
that zero is a place holder to
record “nothing”.
e.g. In 3.59 the 5 represents
0.5 or 5 tenths
e.g. in 98.745 the 5
represents 5 thousandths
Zero is an important concept
of place value that will be
covered in Stage 2.
e.g. 10 there is 1 ten and no
ones so a zero is placed in
the ones column.
e.g. five hundred and two is
represented as 502 and is 5
hundreds, no tens, and 2
ones. The zero is put in the
tens column to show that
there are no tens (otherwise
the number would be 52).
e.g. the first digit 1 in the
number 12 145 represents 1
ten thousand, whereas the
second represents 1
hundred.
Include examples of negative
numbers.
Include examples of negative
numbers.
e.g. -5.67.
e.g. -5.674
Ensure learners use
materials and group them
into tens and ones to
recognise that 10 ones are 1
ten.
In 6 235 765 the fourth digit
represents 5 thousands and
the last digit represents 5
ones.
e.g. 13 is 1 ten and 3 ones
Cambridge Primary Mathematics 0096 Progression Grid v1.2
3Np.02 Use knowledge of
place value to multiply
whole numbers by 10.
4Np.02 Use knowledge of
place value to multiply
and divide whole numbers
by 10 and 100.
5Np.02 Use knowledge of
place value to multiply
and divide whole numbers
by 10, 100 and 1000.
Ensure learners understand
that multiplying a number by
10 shifts each of its digits
one place to the left, and
does not mean adding zeros.
When dividing, use
examples that do not result
in hundredths or tenths as
decimals are not covered at
this stage.
When dividing, use
examples that do not result
in thousandths or less as
only tenths and hundredths
24
Use examples where
learners identify patterns.
1
10
100
2
20
200
3
30
300
4
40
400
....
....
....
Use a place value chart to
assist learners to identify the
pattern.
79 x 10 = 790
100s
7
10s
1s
7
9
9
0
Ensure learners understand
that multiplying a number by
10 (or 100) shifts each of its
digits one (or two) places to
the left, it does not mean
adding zeros.
Ensure learners understand
that dividing a number by 10
(or 100) shifts each of its
digits one (or two) places to
the right, it does not mean
subtracting zeros.
Use a place value chart to
assist learners.
1000s
Include examples with 1- or
2-digit numbers being
multiplied by 10 only.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
100s
10s
1s
7
9
7
9
0
0
1000s
100s
10s
1s
8
5
0
0
8
5
0
should be covered at this
stage.
Ensure learners understand
that multiplying a number by
10, 100 or 1000 shifts each
of its digits one, two or three
places to the left, it does not
mean adding zeros.
Ensure learners understand
that dividing a number by 10,
100 or 1000 shifts each of its
digits one, two or three
places to the right, it does
not mean subtracting zeros.
5Np.03 Use knowledge of
place value to multiply
and divide decimals by 10
and 100.
6Np.02 Use knowledge of
place value to multiply
and divide whole numbers
and decimals by 10, 100
and 1000.
When dividing, use
examples that do not result
in thousandths or less as
only tenths and hundredths
should be covered at this
stage.
When dividing, use
examples that do not result
in less than thousandths as
only tenths, hundredths and
thousandths should be
covered at this stage.
25
1Np.02 Compose,
decompose and regroup
numbers from 10 to 20.
2Np.02 Compose,
decompose and regroup
2-digit numbers, using
tens and ones.
3Np.03 Compose,
decompose and regroup
3-digit numbers, using
hundreds, tens and ones.
4Np.03 Compose,
decompose and regroup
whole numbers.
5Np.04 Compose,
decompose and regroup
numbers, including
decimals (tenths and
hundredths).
6Np.03 Compose,
decompose and regroup
numbers, including
decimals (tenths,
hundredths and
thousandths).
Ensure learners understand
teen numbers as tens and
ones (with understanding of
place value) and not just as
number pairs.
Compose and decompose
should focus on every
individual place value
position of numbers: 10s
(tens) and 1s (ones).
Compose and decompose
should focus on every
individual place value
position of numbers: 100s
(hundreds), 10s (tens) and
1s (ones).
Compose and decompose
should focus on every
individual place value
position of numbers: 1000s
(thousands), 100s
(hundreds), 10s (tens) and
1s (ones).
Compose and decompose
should focus on every
individual place value
position of numbers,
1
including decimals: 10s
Compose and decompose
should focus on every
individual place value
position of numbers,
1
including decimals: 10s
(tenths) and 100s (hundredths)
1
(tenths), 100s (hundredths)
only.
and 1000s (thousandths) only.
e.g. if you combine 10 and 4
you will compose the number
14. If you decompose 14 you
will get 10 + 4 (1 ten and 4
ones)
10s1s = 10s + 1s
e.g. 45 = 40 + 5
10s + 1s = 10s1s
40 + 5 = 45
Regrouping should focus on
expressing a number in
different ways to assist with
calculations.
Regrouping should focus on
expressing a number in
different ways to assist with
calculations.
e.g. 14 can be expressed as:
100s10s1s = 100s + 10s + 1s
e.g. 712 = 700 + 10 + 2 and
702 = 700 + 0 + 2
Regrouping should focus on
expressing a number in
different ways to assist with
calculations.
e.g. 35 can be expressed as:
e.g. 712 can be expressed
as:
14 = 10 + 4
35 = 32 + 3
71 tens and 2 ones
14 = 8 + 6
35 = 10 + 10 + 10 + 5 and in
many other ways
712 ones
14 = 8 + 4 + 2
14 = 8 + 2 + 4 and in many
other ways
7 hundreds, 1 ten and 2
ones
712 = 701 +11
712 = 710 + 2 and in many
other ways
e.g.
=1000s + 100s + 10s + 1s
4687 = 4000 + 600 + 80 + 7
35 903 = 30 000 + 5000 +
900 + 3
345 987 = 300 000 + 40 000
+ 5000 + 900 + 80 + 7
Regrouping should focus on
expressing a number in
different ways to assist with
calculations.
e.g. 4687 can be expressed
as:
4000 + 687
1
1
e.g.
e.g.
=10s + 1s +
1
s+
10
1
s
100
20.56 = 20 + 0 + 0.5 + 0.06
Regrouping should focus on
expressing a number in
different ways to assist with
calculations.
e.g. 20.56 can be expressed
as:
=10s + 1s +
1
s+
10
1
s+
100
1
s
1000
54.079 = 50 + 4 + 0.0 + 0.07
+ 0.009
Regrouping should focus on
expressing a number in
different ways to assist with
calculations.
20 + 0.56
e.g. 54.079 can be
expressed as:
2056 hundredths
54 + 0.079
2 tens and 56 hundredths
and in many other ways
50 + 4.079
54 ones and 79 thousandths
4650 + 37
5 tens 4,079 thousandths
4680 + 7 and in many other
ways
5407 hundredths and 9
thousandths and in many
other ways
Examples of regrouping and
decomposing negative
numbers
Cambridge Primary Mathematics 0096 Progression Grid v1.2
26
e.g.
–22 using a number line can
be regrouped as:
– 10, – 10, – 2
or
– 10, – 5, – 5, - 1,- 1
-5.67 can be decomposed
as -5, -0.6, -0.07
1Np.03 Understand the
relative size of quantities
to compare and order
numbers from 0 to 20.
2Np.03 Understand the
relative size of quantities
to compare and order 2digit numbers.
3Np.04 Understand the
relative size of quantities
to compare and order 3digit positive numbers,
using the symbols =, >
and <.
4Np.04 Understand the
relative size of quantities
to compare and order
positive and negative
numbers, using the
symbols =, > and <.
Use a number line to assist
learners in understanding the
magnitude of numbers.
Learners place numbers on
the number line.
Learners place numbers on
the number line.
e.g. when placing 23 on the
number line, learners place it
e.g. when placing 490 on the
number line, learners place it
For negative numbers use
examples that use a number
line or scale to assist
learners in understanding the
Cambridge Primary Mathematics 0096 Progression Grid v1.2
27
Learners find (or place) a
number between two given
numbers up to 20.
closer to 20 than 30 and not
any place between 20 and
30.
e.g. Learners are able to
place 15 between 10 and 20.
23
400
10
20
30
Learners use familiar
language to compare and
order numbers such as
same, more or less.
0
10
20
500
30
Ensure learners use familiar
language including the words
greater than or less than,
with or without using a
number line.
relative distance of positive
and negative numbers from
zero.
Use negative numbers in
context.
490
15
0
closer to 500 than 400 and
not any place between 400
and 500.
Ensure learners are
confident using the language
‘greater than’ and ‘less than’
before introducing the
symbols.
e.g.
e.g. a temperature of 3oC is
warmer than -5oC (3 > -5).
Learners also use the
symbols =, < and > in the
Fractions, decimals,
percentages sub-strand to
compare proper fractions.
 3 “is less than” 5
3<5
 110 “is greater than” 101
110 > 101
Learners also use the
symbols < and > in the
fractions, decimals,
percentages sub-strand to
compare unit fractions, and
fractions with the same
denominator.
1Np.04 Recognise and
use the ordinal numbers
from 1st to 10th.
2Np.04 Recognise and
use ordinal numbers.
Ensure learners know
number names: first, second,
third… tenth.
Use ordinal numbers in
context such as number of
books read. That is the
twelfth (12th) book we have
read this year.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
28
2Np.05 Round 2-digit
numbers to the nearest
10.
3Np.05 Round 3-digit
numbers to the nearest 10
or 100.
4Np.05 Round numbers
to the nearest 10, 100,
1000, 10 000 or 100 000.
5Np.05 Round numbers
with one decimal place to
the nearest whole
number.
6Np.04 Round numbers
with 2 decimal places to
the nearest tenth or whole
number.
Ensure learners understand
that rounding is used as an
approximate size of numbers
when an exact number is not
needed. Rounding is a way
of simplifying numbers to
make them easier to
understand, estimate and
calculate mentally.
Ensure learners understand
that a 3-digit number can be
rounded in two ways: to the
nearest multiple of 10, or the
nearest multiple of 100.
Ensure learners understand
that rounding can occur in
multiple places within a
number.
Ensure learners know that
they should refer to the
tenths digit and round down
for 4 tenths or less and
round up for 5 tenths or
more.
Ensure learners know that
they should refer to the
hundredths digit when
rounding to the nearest
tenth, and the tenths digit
when rounding to the nearest
whole number,
Ensure learners understand
that a 2-digit number rounds
down with 4 ones or less and
rounds up with 5 ones or
more.
e.g. 42 rounds down to 40
and 48 rounds up to 50.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
e.g. 538 rounds up to 540 (to
the nearest 10), and down to
500 (to the nearest 100).
e.g. 2 493 rounds down to 2
490 (to the nearest 10),
rounds up to 2 500 (to the
nearest 100) and rounds
down to 2 000 (to the
nearest 1 000).
Learners usually find it
difficult to round to 10 000 or
100 000 so use place value
to assist them.
e.g. round 1 234 567 to the
nearest 10 000. So, 3 is in
the ten thousand position
and represents 30 000. If the
digit to the right of the 3 is 4
or less (representing 34 000)
then round the 3 down to 30
000. If the digit to the right of
the 3 is 5 or more
(representing 35 000) then
round the 3 up to 40 000. So
in this example the number
would round down to 1 230
000.
e.g. 2.4, 2.3, 2.2, and 2.1
round down to 2, whereas
2.5, 2.6, 2.7, 2.8 and 2.9
round up to 3.
Use rounding in context.
e.g. 4.28 rounds up to 4.3 (to
the nearest tenth), and down
to 4 (to the nearest whole
number).
e.g. a sum of money to the
nearest dollar or
measurements to the
nearest centimetre.
29
Number
Fractions, decimals, percentages, ratio and proportion
Stage 1
Stage 2
Stage 3
Stage 4
1Nf.01 Understand that
an object or shape can be
split into two equal parts
or two unequal parts.
2Nf.01 Understand that
an object or shape can be
split into four equal parts
or four unequal parts.
3Nf.01 Understand and
explain that fractions are
several equal parts of an
object or shape and all
the parts, taken together,
equal one whole.
4Nf.01 Understand that
the more parts a whole is
divided into, the smaller
the parts become.
Learners find half of shapes
by folding or shading.
Ensure learners can interpret
fractions as comparing a part
of an object (part-whole
continuous).
Ensure learners can interpret
fractions as comparing a part
of an object (part-whole
continuous). A fraction is
always a fraction of
something and learners need
to be able to describe the
whole (the ‘something’) as
well as the parts.
Ensure learners can interpret
fractions as comparing a part
of an object (part-whole
continuous).
Ensure learners can interpret
fractions as comparing a part
of an object (part-whole
continuous).
e.g. Cut this shape into
quarters so that each piece
is the same size.
Stage 5
Stage 6
Learners continue to work with fractions to solve problems in
a range of contexts such as fractions of a turn, time etc.
Understand the relative size
of unit fractions - the greater
the denominator the smaller
each piece will be.
e.g.
Learners understand that
one quarter or
1
4
of each
shape is shaded.
These shapes were cut up
into equal parts like this.
What fraction are these
parts?
1
This is of a shape, what is
6
Ensure learners understand
that an object or shape is
only considered a half when
it is divided into two equal
parts, and some things
e.g. If this is one-quarter of a
shape, what is the shape?
There may be several
presentations of solutions to
this so discuss this with
learners.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
the shape? There may be
several presentations of
solutions to this so discuss
this with learners.
If two positive fractions have
the same numerator, then
the fraction with the smaller
denominator is the larger
fraction.
e.g.
1
The denominator for is 8
8
and the denominator for
2. So
1
2
1
2
is
1
is larger than .
8
Ensure learners understand
the role of the whole.
30
cannot be divided in half
(people, animals, etc.).
In the parts-of-a-whole
interpretation, the fractional
parts do not have to be
identical in shape (i.e.,
congruent), but they must be
equivalent in size
Relate to time in Geometry
and Measure strand – half
past, quarter past and
quarter to the hour.
Relate to time in Geometry
and Measure strand (half
past the hour).
Ensure learners understand
what each part of the fraction
represents: The denominator
is the bottom number and
shows in how many equal
parts the whole was divided
into. The numerator is the
top number and shows how
many parts we have.
Introduce
3
4
as the first non-
e.g. In both of these shapes
the whole is the same size.
2
In the first shape, of the
5
3
shape is shaded and is
5
unshaded. In the second
2
2
shape is shaded and is
4
4
2
unshaded. So is greater
4
2
than .
5
unit fraction. Use thirds, fifths
and tenths as other non-unit
2 2
fractions, e.g. , ,
3
3 5 10
and
link to known times tables,
e.g.
1
10
is one tenth or 1 part
out of 10 equal parts,
3
4
is
three quarters or 3 parts out
of 4 equal parts.
e.g.
3
4
of the jug is filled with
water, so
1
4
of the jug is filled
In the next shapes, the
whole is a different size.
Although the shaded blocks
have the same size, it
represents
1
4
1
in the first
shape and in the second
5
shape.
with air (empty).
Use examples that use the
same numerator but different
denominators
e.g.
3
5
3
3
7
12
and and
3Nf.02 Understand that
the relationship between
the whole and the parts
depends on the relative
size of each, regardless of
their shape or orientation.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
31
e.g. shape A is larger than
shape B, and shape C is not
the same shape as A or B,
but the shaded part of each
1
shape is of the whole
4
shape.
Shape A
Shape B
Shape C
1Nf.02 Understand that a
half can describe one of
two equal parts of a
quantity or set of objects.
2Nf.02 Understand that a
quarter can describe one
of four equal parts of a
quantity or set of objects.
3Nf.03 Understand and
explain that fractions can
describe equal parts of a
quantity or set of objects.
Ensure learners can interpret
fractions as comparing a part
of a set of objects (partwhole discrete).
Ensure learners can interpret
fractions as comparing a part
of a set of objects (partwhole discrete).
Include activities that include
half of sets of objects
(discrete whole)
Ensure learners understand
that parts of a set can be put
back together to make a
whole set.
Ensure learners can interpret
fractions as comparing a part
of a set of objects (partwhole discrete). A fraction is
always a fraction of
something and learners need
to be able to describe the
whole (the ‘something’) as
well as the parts.
Learners should be able to
find half of any even number
of objects between 0 and 20,
e.g. half of 8 is 4.
e.g. this is one-quarter of a
set of balls. How many balls
are in the set?
e.g.
1
4
of the marbles are
blue, so
3
4
of the marbles are
white.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
32
You have some marbles and
you pick up 3 marbles and
that is one third. How many
marbles do you have?
2Nf.03 Understand that
one half and one quarter
can be interpreted as
division.
3Nf.04 Understand that a
fraction can be
represented as a division
of the numerator by the
denominator (half, quarter
and three-quarters).
4Nf.02 Understand that a
fraction can be
represented as a division
of the numerator by the
denominator (unit
fractions and threequarters).
5Nf.01 Understand that a
fraction can be
represented as a division
of the numerator by the
denominator (unit
fractions, three-quarters,
tenths and hundredths).
6Nf.01 Understand that a
fraction can be
represented as a division
of the numerator by the
denominator (proper and
improper fractions).
Ensure learners can interpret
fractions as division.
Ensure learners can interpret
fractions as division.
Ensure learners can interpret
fractions as division.
Ensure learners can interpret
fractions as division.
Ensure learners can interpret
fractions as division.
e.g. There are 12 sweets. If
you are given one half of
them, how many sweets will
Ensure learners know that
the denominator is the
bottom number and shows in
how many equal parts the
whole was divided into. The
numerator is the top number
and shows how many parts
we are considering.
Ensure learners understand
that 1 ÷ 3 means that one
whole part is divided into 3
equal parts and can be
Ensure learners understand
e.g.
you get? 6 sweets or
1
2
the sweets
of
e.g.
𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟
𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
=
3
4
represented as
5
=1÷5
10
is the result of dividing 1
÷ 10 e.g.
1
3 ÷ 10 can be represented
3
as
Five people share one
biscuit. How much of a
biscuit does each person get
when they share equally?
1
1
3
10
17 ÷ 100 can be represented
as
17
100
3 ÷ 8 is
3
8
1 ¼ can be represented as
5÷4
50 ÷ 40 can be represented
as
50
40
or 1 and
10
40
. Some
learners may be able to
simplify this answer to 1 and
1
4
12 ÷ 2 = 6
Cambridge Primary Mathematics 0096 Progression Grid v1.2
33
There are now 12 sweets for
4 children, how many sweets
do they each receive?
If there are 3 strips of paper,
and 4 people want an equal
share then each person
Each child receives 3 sweets
or one quarter.
receives
3
of a strip of
4
paper.
1
2
3
1
2
4
1
3
4
2
3
4
12 ÷ 4 = 3
There are 3 cakes and 4
people who want an equal
amount. Each person
receives
3
4
1
4
of each cake, so
each in total.
e.g. There are 8 sweets. You
take 2 of them, What fraction
of the sweets did you take? 2
out of 8 = 2÷ 8 =
2
8
=
1
4
𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟
2
1
= =
𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 8
4
Cambridge Primary Mathematics 0096 Progression Grid v1.2
34
1Nf.03 Understand that a
half can act as an
operator (whole number
answers).
2Nf.04 Understand that
fractions (half, quarter and
three-quarters) can act as
operators.
3Nf.05 Understand that
fractions (half, quarter,
three-quarters, third and
tenth) can act as
operators.
4Nf.03 Understand that
unit fractions can act as
operators.
In examples start by using
the word half and only move
Use examples that use
diagrams
Find halves, thirds, quarters
and tenths of numbers. In
examples use the fraction
e.g. Learners find
e.g.
notation
to the symbol
1
2
when
learners are secure with the
concept.
e.g. half of 8 is 4
In this example the fraction
,
2
1
,
3
1
,
4
e.g. Learners find
1
2
(half) is operating on 8. The
operator, one half,
decreases the original value
from 8 to 4.
1
Learners find
1
4
1
5
of this
shape
1
3
of this
3
4
of these marbles
Use
3
4
as the only non-unit
fraction as it was covered in
previous stages.
Learners should be able to
find half of any even number
from 0 to 20
What is one half of six?
marbles.
1
2
e.g.
e.g.
Find
Learners find
Initially use examples with
numbers that are easy to
calculate (tenths).
shape
of the above
shape
Fractions as operators means
“fractions of” or half of.
6Nf.02 Understand that
proper and improper
fractions can act as
operators.
of the above
Learners should be able to
find quarter and half of
numbers from 1 to 20. Do
not include examples that
result in a mixed or improper
fraction.
e.g. half of 6 = 3
quarter of 12 = 3
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Fraction as operator: a unit
fraction is understood to be a
number that acts on another
number in the sense of
shrinking the magnitude of
the number.
e.g. Find
1
10
of 100. The
answer is 10.
The operator,
1
10
, decreases
the original value from 100 to
10.
3
2
of 6 is equal to 9.
Ensure learners understand
that operators are
multiplicative rather than
additive.
10
1
5Nf.02 Understand that
proper fractions can act
as operators.
3
10
of 100m is 30m
Ensure learners understand
that to solve this example
several combinations of
operations could occur:
-
Divide100m by 10 then
multiply by 3 or
Multiply 100m by 3 then
divide by 10
The answer 30m is less than
100m because 100m was
multiplied by a fraction less
than 1
Ensure learners understand
that they can multiply a
quantity that represents a
fraction to find the whole
quantity
e.g. If
1
4
of a length is
36cm, then the whole length
is 36 × 4 = 144cm.
35
2Nf.05 Recognise the
1
1
3
4
2
4
relative size of , , and
1, and the equivalence of
1
2
2
2
4
4
2
4
and , and , and 1.
Use diagrams and number
lines to assist learners in
understanding equivalence
of fractions
3Nf.06 Recognise that
two fractions can have an
equivalent value (halves,
quarters, fifths and
tenths).
4Nf.04 Recognise that
two proper fractions can
have an equivalent value.
5Nf.03 Recognise that
improper fractions and
mixed numbers can have
an equivalent value.
6Nf.03 Use knowledge of
equivalence to write
fractions in their simplest
form.
Use examples where the
denominator and numerators
are in the 1, 2, 4, 5, or 10
times tables.
Initially use examples that
are easy for learners to
understand the concept.
e.g. 72 = 3 12
Use examples of writing in
e.g.
1
2
1
4
1
5
=
=
1
2
=
4
2
=
8
2
10
=
2
20
5
1
10
7
3
12
=
4
20
=
5
50
Use diagrams to illustrate
equivalences
e.g.
1
2
is equivalent to
4
8
,
4
16
etc.
=
10
e.g.
1
2
=
5
10
=
Use diagrams to show the
equivalence between
improper fractions and mixed
number, e.g.
2
5
14
4
Recognise that one whole is
equivalent to any fraction
which has the same
numerator and denominator
and use this to identify
simple fractions with a total
of 1
1
=1
4
simplest form where this is
1
,
,
4
3
4
1
2
or a number of fifths
or tenths.
e.g.
4
=
20
3
4
10
4
20
=
2
5
1
5
=3
1
5
3 4
e.g. ,
3 4
Use examples that include
diagrams (fraction wall),
numbers lines and table
squares to identify patterns
of equivalent fractions.)
×
1
2
3
4
5
1
1
2
3
4
5
2
2
4
6
8
10
3
3
6
9
12
15
4
4
8
12
16
20
5
5
10
15
20
25
1
2
2
4
e.g. =
Cambridge Primary Mathematics 0096 Progression Grid v1.2
=
3
6
=
4
8
=
5
10
36
5Nf.04 Recognise that
proper fractions, decimals
(one decimal place) and
percentages can have
equivalent values.
6Nf.04 Recognise that
fractions, decimals (one
or two decimal places)
and percentages can
have equivalent values.
When learners have
mastered equivalent
fractions introduce them to
the equivalence of fractions,
decimals (place value) and
percentage, initially using ½
and 1 only, then progressing
to tenths and hundredths
(one decimal place only).
Include equivalences of
fractions, decimals and
percentages for hundredths
(one or two decimal places).
e.g.
100
50
100
100
100
10
100
40
100
is 50% =
1
2
= 0.5
is 100% = 1
=
1
10
=
4
10
e.g.
60
100
25
100
72
6
=
10
=
1
4
=
3
5
= 60% = 0.6
= 25% = 0.25
= 72% = 0.72
Use examples with mixed
numbers
1
e.g. 1
= 1.25
4
= 10% = 0.1
= 40% = 0.4
1Nf.04 Understand and
visualise that halves can
be combined to make
wholes.
2Nf.06 Understand and
visualise that wholes,
halves and quarters can
be combined to create
new fractions.
3Nf.07 Estimate, add and
subtract fractions with the
same denominator (within
one whole).
4Nf.05 Estimate, add and
subtract fractions with the
same denominator.
5Nf.05 Estimate, add and
subtract fractions with the
same denominator and
denominators that are
multiples of each other.
6Nf.05 Estimate, add and
subtract fractions with
different denominators.
In examples start by using
the words one half and only
At this stage do not use the
fraction notation for three
In examples use fraction
notation.
Use examples that add and
subtract proper fractions with
proper fractions (same
denominator). Learners use
diagrams to add and subtract
fractions.
Use examples that add and
subtract proper fractions with
proper fractions (same
denominators and
denominators that are
multiples of each other).
Use examples that add and
subtract proper and improper
fractions with different
denominators. Do not use
examples that include mixed
numbers in calculations:
move to the symbol
1
2
when
learners are secure with the
concept.
3
quarters ( )
4
e.g.
1
5
+
2
5
=
3
5
(answer
within one whole)
Use diagrams to combine:
3
7
- quarters to make 3 quarters
Cambridge Primary Mathematics 0096 Progression Grid v1.2
+?=1
e.g.
2
1
3
+3
1
5
37
Use diagrams to show that
one half and one half is 1
whole.
1
4
One
quarter
One
quarter
One
quarter
one
half
Three quarters
- halves to make one and a
half
One
half
1 whole
One
half
One
half
+
8
5
5
=
3
5
1
1
1
1
5
5
5
5
1
+
8
one
half
one
half
2
3
+
8
=
3
5
- one quarter with one half to
make 3 quarters
One
quart
er
One half
−
1
5
2
8
8
−
3
10
=
1
5
5
8
1
+
8
1
1
1
4
4
4
10
8
2
3
5
4
24
3
1
5
8
7
5
1
6
6
2
5
=
4
=
8
+
=
1
=
8
5
8
7
8
3
+
5
3
+
5
=1
When adding and
subtracting fractions,
learners express answers
greater than one as improper
fractions. They are not
required to simplify or
convert to a mixed number.
3
8
1
8
10
=
1
+
When adding fractions,
learners express answers
greater than one as an
improper fraction and a
mixed number.
1
+
4
Three quarters
1
+
4
6
5
1 whole
2
wholes
Learners use diagrams to
add and subtract fractions.
8
4
Learners use diagrams to
add and subtract fractions.
and
one
half
4
e.g.
1
4
one
half
=
8
4
3
9
4 halves is 2 wholes.
3
1
1-=
e.g. +
one
half
1
+=1
4
8
1
+
4
8
2
4
8
8
=
=
or 1
5
4
12
8
1
2
and not 1
and not
3
2
1
4
or
+
3
+
32
=
8
12
6
8
=
32
or 1
3
4
1
=
6
4
10
35
25
+
35
35
=
31
35
46
=
35
35
simplest form where this is
8
=
or
8
9
8
.
and not 1
2
4
,
1
,
4
3
4
1
2
or a number of fifths
or tenths.
or
e.g.
2
15
+
2
3
=
2
15
+
10
15
=
12
15
=
4
5
3
2
2
5Nf.06 Estimate, multiply
and divide unit fractions
by a whole number.
6Nf.06 Estimate, multiply
and divide proper
fractions by whole
numbers.
Use diagrams to assist
learners.
Use diagrams to assist
learners.
e.g.
1
2
÷4=
1
8
e.g. 3 x
Cambridge Primary Mathematics 0096 Progression Grid v1.2
+
35
21
32
+
9
When adding and
subtracting fractions,
learners express answers
greater than one as improper
fractions They are not
required to simplify or
convert to a mixed number
+
=
7
11
21
36
the equivalence to
4
=
7
5
When adding or subtracting
fractions, ensure learners
can reduce fractions to their
3
Ensure learners understand
3
2
2
3
6
= =2
3
38
1
8
1
5
x4
3
4
=
3
1
4
1
4
1
4
1
4
1
4
3
4
Ensure learners understand
that when the numerator and
denominator are the same
number, effectively you are
multiplying by 1.
3
e.g. 15 x = 15 x 1 = 15
3
Cambridge Primary Mathematics 0096 Progression Grid v1.2
4Nf.06 Understand
percentage as the number
of parts in each hundred,
and use the percentage
symbol (%).
5Nf.07 Recognise
percentages of shapes,
and write percentages as
a fraction with
denominator 100.
6Nf.07 Recognise
percentages (1%, and
multiples of 5% up to
100%) of shapes and
whole numbers.
Ensure learners understand
the relationship of
percentage as hundredths of
one whole or per cent is
another way of expressing
fractions in terms of
hundredth.
Ensure learners know that 1
per cent means 1 per 100 or
1 hundredth = 0.01 = (1%)
e.g. find 15% of 4 kg
Learners express tenths and
hundredths as percentages.
Ensure learners make the
connection between fractions
and percentages
e.g.
1
25% of 60 = of 60 = 15 or
4
39
Ensure learners understand
that 100% is equivalent to 1
e.g. Shade 10% of the
square
1
whole, 50% is half, 25% is ,
4
3
75% is , and 1% is 1
4
hundredth or 1 per hundred
10%
If I have a block of wood that
is 20 centimetres long and I
cut a piece from it that is 5
centimetres long, what
percentage did I cut?
Learners use their
knowledge of equivalence to
1
find out 5cm is of 20 and
4
therefore 25%.
Use knowledge of place
value to assist learners.
e.g.
1s
1
10
s
1
100
s
0.09 is the same as 9
hundredths =
9
100
= 9%
e.g. e.g. if an item is initially
priced at $200 and the price
increases by 10%, then the
increase is $20, and the new
price will be $220.
Link with percentages,
angles and fractions of pie
charts
3Nf.08 Use knowledge of
equivalence to compare
and order unit fractions
and fractions with the
same denominator, using
the symbols =, > and <.
4Nf.07 Use knowledge of
equivalence to compare
and order proper
fractions, using the
symbols =, > and <.
5Nf.08 Understand the
relative size of quantities
to compare and order
numbers with one decimal
place, proper fractions
with the same
denominator and
percentages, using the
symbols =, > and <.
6Nf.08 Understand the
relative size of quantities
to compare and order
numbers with one or two
decimal places, proper
fractions with different
denominators and
percentages, using the
symbols =, > and <.
e.g. order from smallest to
largest
Use examples where one
denominator is multiple of
the other
e.g. Order from smallest to
largest:
Use examples where the
denominators are limited to
10 or less.
1 1
, ,
1
2 5 10
1
,
5
,
or
3
7
1 5 3 7
5
10
8 8 8 8
e. g. and
10 10 10
In the sub-strand ‘Place
value, ordering and rounding’
Cambridge Primary Mathematics 0096 Progression Grid v1.2
2.3, 5.4, 2.4, 1.9 and 5.3
3
, , ,
10%,
2
5
, 0.3, 20%,
3
5
Use equivalence to help
order fractions
5 1 7
3
8 4 8
4
e.g. , , and where
40
Ensure learners understand
the relative size of unit
fractions - the larger the
denominator the smaller
each piece will be.
1
1
5
4
e.g. is smaller than
because the denominator 5
is larger than the
denominator 4.
Ensure learners understand
that fractions with the same
denominator, the numerator
determines its size.
1
5
5
1
4
2
3
8
4
= and
=
6
8
Ensure learners are
confident ordering and
comparing numbers with the
same number of decimal
places before progressing to
numbers with different
number of decimal places.
e.g. 4.56, 4.65, 5.07, 5.70;
4.56, 4.06, 5.1, 5.70
Learners often
misunderstand the value of
decimals
e.g. 0.37 is smaller than 0.4
e.g. is smaller than
3
learners use these symbols
to order and compare
positive and negative
numbers.
because both fractions
have the same denominator
Use known facts to find
1 1 1
1
equivalent fractions of , , ,
5
and the numerator for is 1
2 4 5
3
1
e.g. ¼=0.25, so ¾ =0.75
5
5
1
and for is 3 so is smaller
3
than .
5
5
2
5
= 0.2
= 0.4
Learners use the symbols <
or > to compare and order
values
e.g.
3
5

1
5
In the sub-strand ‘Place
value, ordering and rounding’
learners use these symbols
to order and compare 3-digit
positive numbers.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
41
5Nf.09 Estimate, add and
subtract numbers with the
same number of decimal
places.
6Nf.09 Estimate, add and
subtract numbers with the
same or different number
of decimal places.
e.g. Calculations to involve
tenths or hundredths. Both
numbers with 1 decimal
place (tenths) 23.1 + 35.3 =
58.4 or both numbers with 2
decimal places (hundredths)
4.83 - 2.78 = 2.05
Calculations to involve
tenths, hundredths or
thousandths.
Ensure learners use
knowledge of place value.
123.56 + 23.745
23.1 - 4.237 = 18.863
Ensure learners use
knowledge of place value.
5Nf.10 Estimate and
multiply numbers with one
decimal place by 1-digit
whole numbers.
6Nf.10 Estimate and
multiply numbers with one
or two decimal places by
1-digit and 2-digit whole
numbers.
e.g.
4.6 x 9,
e.g. 4.6 x 9, 16.5 x 3 and
114.3 x 5
13.6 × 7
6.37 x 8 and 15.21 x 5
7.3 x 12, 25.7 x 15 and
125.6 x 18
9.84 x 36 and 12.11 x 15
6Nf.11 Estimate and
divide numbers with one
or two decimal places by
whole numbers.
Use examples that are easy
for learners to recognise and
calculate
23.46 ÷ 23 instead of 23.56 ÷
23 as 56 is not multiple of 23
20.05 ÷ 5
Cambridge Primary Mathematics 0096 Progression Grid v1.2
42
5Nf.11 Understand that:
- a proportion compares
part to whole
- a ratio compares part to
part of two or more
quantities.
When discussing proportion
use the language “in every”
or “out of”. When discussing
ratio use the language “for
every”
e.g. imagine a row with a
repeating pattern of 3 white
squares and 1 grey square.
Etc.
Proportion: 1 in every 4
squares is grey
Ratio: For every 1 grey
square there are 3 white
squares
Ensure learners understand
that the order of the numbers
is important in a ratio.
e.g. in a bag there are 4 red
and 5 blue counters. The
ratio of red to blue is 4:5 not
5:4
Ensure learners understand
how to write proportion and
ratio (including using the
notation ‘:’) for a given
situation and write proportion
in different ways using
knowledge of equivalence of
Cambridge Primary Mathematics 0096 Progression Grid v1.2
6Nf.12 Understand the
relationship between two
quantities when they are
in direct proportion.
Ensure learners understand
what is meant by “in
proportion”.
e.g. a model is in proportion
to a real dog. The dog is 9
times as big as the model. If
the model is 4cm tall, the
real dog will be 36cm tall (9 x
4 = 36). If the real dog’s tail
is 18cm long, the tail on the
model will be 2cm long (9 x 2
= 18)?
Ensure learners understand
that when one quantity
increases (or decreases) the
other quantities increase (or
decrease) in the same ratio.
E.g. A photocopy is in
proportion to the original. If
the original is 30cm by 40cm.
What sizes can be the
photocopies?
Use simple recipe examples
e.g. to adapt a recipe for 6
people to one for 3 or 12
people
43
fractions and percentages
(multiples of 10).
e.g. in a bag there are 4 red,
3 green counters and 3 blue
counters. The ratio of red to
green to blue counters is
4:3:3. The proportion of red
is
4
10
which is also the same
as 40%.
6Nf.13 Use knowledge of
equivalence to
understand and use
equivalent ratios.
e.g. the following ratios are
equivalent
e.g. a builder uses sand and
cement. He uses 3 bags of
sand for every 2 bags of
cement. If there are 10 bags
of cement, how many bags
are sand?
Use a table or diagram to
assist learners.
Sand
Cambridge Primary Mathematics 0096 Progression Grid v1.2
3
15
Cement 2
10
44
When discussing ratio,
ensure learners understand
that a ratio shows the
relationship between two or
more quantities, so a single
number cannot express a
ratio.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
45
Geometry and Measure
Time
Stage 1
Stage 2
Stage 3
Stage 4
Stage 5
1Gt.01 Use familiar
language to describe units
of time.
2Gt.01 Order and
compare units of time
(seconds, minutes, hours,
days, weeks, months and
years).
3Gt.01 Choose the
appropriate unit of time for
familiar activities.
4Gt.01 Understand the
direct relationship
between units of time, and
convert between them.
5Gt.01 Understand time
intervals less than one
second.
Daily routines (bedtime
stories; yesterday, today,
tomorrow; morning,
afternoon and evening).
Learners should understand
relationships such as: a
second is less than a minute,
an hour is more than a
minute, etc.
e.g. age is measured in
years, we sleep for
approximately 8 hours, a
football match lasts 90
minutes.
Relationships such as
Match the activity to its likely
time span: blink of an eye,
boil an egg, run 25m, walk
100m.
Learners need to know that
there are 60 minutes in an
hour to read a clock. They do
not need to know that there
are 60 seconds in a minute
or 24 hours in a day.
Introduce activities that allow
learners to estimate how
many times they can do an
activity in one minute, one
hour, etc.
Recognise the everyday
language used to describe
familiar activities related
to time e.g. your birthday
happens once a year, we
play the same sport every
day or every week.
Learners do not need to
understand the relationship
between units of time.
Learners should be able to
order the days of the week
and the months of the year
by name with or without the
aid of a calendar
e.g. Wednesday comes
before Thursday.
 60 seconds(s) in a minute
(min)
 60 minutes in an hour (h)
 24 hours in a day
 number of days in each
month (including leap
years)
 52 weeks in a year
 12 months in a year
Stage 6
Likely time span: 0.5sec,
5min, 5sec, 25sec
Use whole numbers only
(e.g. 100 minutes is one hour
and 40 minutes).
In Stage 5 learners are
introduced to decimals in the
Number strand when adding
and subtracting numbers.
However, do not use
examples involving time in
decimals such as 1.5 hours
as learners often misinterpret
this as 1 hour and 50
minutes instead of 1 hour
and 30 minutes.
1Gt.02 Know the days of
the week and the months
of the year.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
46
1Gt.03 Recognise time to
the hour and half hour.
2Gt.02 Read and record
time to five minutes in
digital notation (12-hour)
and on analogue clocks.
3Gt.02 Read and record
time accurately in digital
notation (12-hour) and on
analogue clocks.
4Gt.02 Read and record
time accurately in digital
notation (12- and 24-hour)
and on analogue clocks.
5Gt.02 Compare times
between time zones in
digital notation (12- and
24-hour) and on analogue
clocks.
e.g. ten o’clock in the
morning, half past three in
the afternoon.
e.g. twenty-five past one in
the afternoon (1:25), twenty
to ten in the morning (9:40),
quarter past in the evening
(10:15), half past three in the
afternoon (3:30), quarter to
nine (8:45) in the evening.
e.g. sixteen minutes past
one in the afternoon (1:16),
9:40 can be read as 40
minutes past 9, twenty to ten
in the morning or twenty to
ten in the evening.
e.g. 3:30 in the afternoon
can be recorded as 15:30 or
3:30pm, and 3:30 in the
morning as 3:30 or 3:30am.
e.g. a quarter to four in the
afternoon is later than 15:40.
Ensure learners understand
that when 24 hours is
reached, they have reached
a new day and must go back
to zero with their counting.
Ensure learners understand
that the world is divided into
24 time zones but the
comparison between time
zones will depend on the
time of year.
Learners continue to read,
record and compare times in
context (12- and 24-hour
clocks).
Ensure learners understand
that clocks are usually set
one hour apart in adjacent
time zones. Some countries
have more than one time
zone.
2Gt.03 Interpret and use
the information in
calendars.
3Gt.03 Interpret and use
the information in
timetables (12-hour
clock).
4Gt.03 Interpret and use
the information in
timetables (12- and 24hour clock).
Ensure learners understand
that calendars are used to
organise time in days, weeks
and months of a particular
year.
Ensure learners understand
that timetables are a plan of
times at which events are
scheduled to take place
usually organised in hours
and minutes.
Ensure learners understand
that timetables often use a
24-hour clock to differentiate
between morning, afternoon
and evening times.
Learners continue to interpret and use calendars and
timetables to calculate times (12- and 24-hour clocks).
3Gt.04 Understand the
difference between a time
and a time interval. Find
time intervals between the
same units in days,
weeks, months and years.
4Gt.04 Find time intervals
between different units:
5Gt.03 Find time intervals
in seconds, minutes and
hours that bridge through
60.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
- days, weeks, months
and years
47
- seconds, minutes and
hours that do not bridge
through 60.
Ensure learners understand
that the difference between
being 5 years old and the
interval 5 years: a time
interval measures the length
of time between two given
times.
e.g. A journey that starts at
7:00 on February 15th and
ends at 7:30 on February
16th has a time interval of 1
day and 30 minutes.
Ensure learners can bridge
through 60
e.g. a digital clock that
displays 5:57 in five minutes
will display 6:02 not 5:62
e.g. If an project runs from
February to June, it
represents a time interval of
4 months. An activity
happening in February,
happens 2 months earlier
than an activity in April.
Use examples that use the
same units only, so that
learners do not need to
convert between units.
5Gt.04 Recognise that a
time interval can be
expressed as a decimal,
or in mixed units.
6Gt.01 Convert between
time intervals expressed
as a decimal and in mixed
units.
e.g. know that 0.5 hours
corresponds to 30 minutes or
0.5 minutes corresponds to
30 seconds or 1.5 days is
equivalent to 1 day and 12
hours not 1 day and 5 hours,
so that learners can
calculate time intervals
represented in a decimal
format.
Start with examples that are
easy recognisable and easy
to calculate
e.g. 5.5 hours is equivalent
to 5 hours and 30 minutes.
3.25 hours is equivalent to 3
hours and 15 minutes (0.25
1
1
is 4 and 4 of an hour is 15
minutes)
Learners should understand
that time can be represented
Cambridge Primary Mathematics 0096 Progression Grid v1.2
48
in decimal format (usually as
the result of a calculation)
and that it can be converted
to hours and minutes, and
even parts of a minute.
e.g. 1.5 hours is equivalent
to 1 hour and 30 minutes not
1 hour and 50 minutes
Tenths can be converted
easily
0.1
min
0.2
min
0.3
min
6s
12 s
18 s
0.1 h
0.2 h
0.3 h
6 min
12
min
18
min
e.g. convert 3.7 hours into
hours and minutes
0.7 x 60 = 42 minutes
3 hours and 42 minutes
Do not include examples
where learners need to
convert from whole numbers
to decimals.
e.g. 11 seconds into minutes
Cambridge Primary Mathematics 0096 Progression Grid v1.2
49
Geometry and Measure
Geometrical reasoning, shapes and measurements
Stage 1
Stage 2
Stage 3
Stage 4
Stage 5
Stage 6
1Gg.01 Identify, describe
and sort 2D shapes by
their characteristics or
properties, including
reference to number of
sides and whether the
sides are curved or
straight.
2Gg.01 Identify, describe,
sort, name and sketch 2D
shapes by their
properties, including
reference to regular
polygons, number of sides
and vertices. Recognise
these shapes in different
positions and orientations.
3Gg.01 Identify, describe,
classify, name and sketch
2D shapes by their
properties. Differentiate
between regular and
irregular polygons.
4Gg.01 Investigate what
shapes can be made if
two or more shapes are
combined, and analyse
their properties, including
reference to tessellation.
5Gg.01 Identify, describe,
classify and sketch
isosceles, equilateral or
scalene triangles,
including reference to
angles and symmetrical
properties.
6Gg.01 Identify, describe,
classify and sketch
quadrilaterals, including
reference to angles,
symmetrical properties,
parallel sides and
diagonals.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
50
Emphasise the properties
(number of sides),
characteristics (colours, size
and type of material) of
shapes rather than just their
names.
Introduce learners to regular
polygons only.
e.g. pentagons, hexagons
and octagons
Identify and recognise that
squares, circles, triangles
and rectangles are 2D
shapes.
Learners continue to use
shapes to make patterns
using physical equipment
including repeating a shape
to see if it will fit together
(tessellation).
Familiarise learners with
regular and irregular
polygons.
e.g. combine two triangles to
make a larger triangle or
square
Include:
e.g. combine two
parallelograms to make a
larger parallelogram. Further
parallelograms can be added
to form a tessellating pattern.
 Semi-circles and circles
 relevant information
(properties)
 irrelevant information (e.g.
characteristics such as
colour)
 non-examples (e.g. dice).
 shapes in a range of
different orientations
 reference to number of
sides, number of vertices,
curved, straight edges.
Ensure that learners identify
and sketch examples of 2D
shapes in patterns, art and
architecture
e.g.
Learners should be able to
identify non-examples,
relevant and irrelevant
information.
Include reference to number
of sides, number of vertices,
curved, straight edges, right
angles, parallel edge.
e.g. an isosceles triangle has
two equal angles, 2 equal
sides and one line of
symmetry.
Ensure learners understand
that all triangles will
tessellate
Include parallelogram,
rhombus, trapezium and kite.
e.g. a parallelogram can be
decomposed into two
triangles and a rectangle.
Ensure learners understand
that if line a is parallel to b
and b is parallel to c, then a
is parallel to c.
a
b
c
Ensure learners understand
that all quadrilaterals will
tessellate
Ensure learners understand
that a 2D shape with a
curved side is not a polygon
and use this to classify
shapes as a polygon or not.
2Gg.02 Understand that a
circle has a centre and
any point on the boundary
is at the same distance
from the centre.
6Gg.02 Know the parts of a
Learners identify the centre
of a circle practically, for
example, by folding a paper
circle in half and half again to
create quadrants. Learners
Ensure learners understand
that the diameter is twice the
radius.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
circle:
- centre
- radius
- diameter
- circumference.
Ensure learners know that
perimeter of a circle is called
51
measure the folds created to
understand that at any point
on the boundary is the same
distance from the centre.
a circumference, and that
any length inside the circle
that does not pass through
the centre is not a diameter.
1Gg.02 Use familiar
language to describe
length, including long,
longer, longest, thin,
thinner, thinnest, short,
shorter, shortest, tall,
taller and tallest.
2Gg.03 Understand that
length is a fixed distance
between two points.
Estimate and measure
lengths using nonstandard or standard
units.
3Gg.02 Estimate and
measure lengths in
centimetres (cm), metres
(m) and kilometres (km).
Understand the
relationship between
units.
Learners should also
understand that height and
distance are lengths.
Ensure learners understand
that two lengths can be
added together to give a
longer length or subtracted
to find their difference.
Ensure learners can
compare the relative sizes of
cm, m and km.
Learners should discuss
measurements using
language in local contexts.
Ensure that learners know
why it is better to measure
length in standard units
rather than non-standard
units.
Learners continue to use length in context.
Which is the longest
measurement out of the
following?
a)
3 m, 3 km, 3 cm
b)
5 km, 1 m, 50 cm
c)
15 cm, 10 km, 7 m
Only introduce centimetres
and metres, and ensure
learners know that
centimetres are used to
measure short lengths and
metre for longer lengths.
3Gg.03 Understand that
perimeter is the total
distance around a 2D shape
and can be calculated by
adding lengths, and area is
how much space a 2D shape
occupies within its boundary.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
4Gg.02 Estimate and
measure perimeter and
area of 2D shapes,
understanding that two
areas can be added
together to calculate the
area of a compound
shape.
5Gg.02 Estimate and
measure perimeter and
area of 2D shapes,
understanding that
shapes with the same
perimeter can have
different areas and vice
versa.
52
Ensure learners understand
that to find the perimeter of a
shape they measure the
length of each side and find
the total.
Use whole numbers in a
single metric unit (e.g. either
metres or centimetres, not
both together).
2Gg.04 Draw and
measure lines, using
standard units.
3Gg.04 Draw lines,
rectangles and squares.
Estimate, measure and
calculate the perimeter of
a shape, using
appropriate metric units,
and area on a square
grid.
4Gg.03 Draw rectangles
and squares on square
grids, and measure their
perimeter and area.
Derive and use formulae
to calculate areas and
perimeters of rectangles
and squares.
5Gg.03 Draw compound
shapes that can be
divided into rectangles
and squares. Estimate,
measure and calculate
their perimeter and area.
6Gg.03 Use knowledge of
area of rectangles to
estimate and calculate the
area of right-angled
triangles.
Ensure learners understand
that when making
measurement using a ruler
they should start from zero.
Include shapes that cover
half squares.
What is the perimeter and
area of this shape?
e.g. if the area of this
rectangle is 8cm2
Include lines that can be
measured in cm or m.
Know the meaning of ‘kilo’,
‘centi’ and ‘milli’
Ensure learners discover for
themselves that the area of a
square or rectangle can be
found by multiplying one side
length by the other side
length.
1 m = 100 cm
1 km = 1000 m
For area use the terminology
‘square units’ rather than
cm2, m2
e.g. The area of the square
below is 16 square units
Cambridge Primary Mathematics 0096 Progression Grid v1.2
e.g. a rectangle has a
perimeter of 32 cm, what is
the area of the rectangle?
Why?
Ensure learners use the
notation for area, square
centimetres (cm2) and
square metres (m2).
- perimeter using millimetre
(mm), centimetre (cm), metre
(m) and kilometre (km) and
understand their
relationships
- area using square
centimetres (cm2) and
square metres (m2) and
square kilometres (km2).
4cm
2cm
(Perimeter 30cm, Area
29cm2)
Then, the area of each right
angle triangle is 4cm2
2cm
4cm
53
4Gg.04 Estimate the area
of irregular shapes on a
square grid (whole and
part squares).
Start with rectilinear shapes
and then irregular shapes
with curved sides.
1Gg.03 Identify, describe
and sort 3D shapes by
their properties, including
reference to the number
of faces, edges and
whether faces are flat or
curved.
2Gg.05 Identify, describe,
sort and name 3D shapes
by their properties,
including reference to
number and shapes of
faces, edges and vertices.
3Gg.05 Identify, describe,
sort, name and sketch 3D
shapes by their
properties.
4Gg.05 Identify 2D faces
of 3D shapes, and
describe their properties.
5Gg.04 Identify, describe
and sketch 3D shapes in
different orientations.
6Gg.04 Identify, describe
and sketch compound 3D
shapes.
Learners are expected to
identify whether a 3D shape
has flat faces or curved
surfaces. They are not
expected to use the
terminology ‘curved surface’.
e.g. Circles on a cylinder,
triangle on a pyramid.
e.g. compare the similarities
and differences between
pyramids and prisms
e.g. compare the similarities
and differences between
squares, rectangles, cubes
and cuboids.
Use isometric paper or other
resources to assist in
sketching 3D shapes. Sketch
rather than accurately draw.
e.g. find the least number of
centimetre cubes needed to
turn this shape into a cuboid:
Emphasise the properties of
shapes rather than just their
names.
Ensure learners use and
combine 3D shapes to make
patterns and other familiar
3D shapes, e.g. the 3D
shapes
Learners continue to use
shapes to make patterns.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Ensure that learners identify
examples of 3D shapes in
patterns, art, architecture,
and the environment, such
as tables, car wheels, coins,
boxes, dice, food etc.
Answer: 9 cm3
Link to Number strand
learning objective 6Ni.08.
54
can be combined to form a
3D shape that looks like a
house:
1Gg.04 Use familiar
language to describe
mass, including heavy,
light, less and more.
1Gg.05 Use familiar
language to describe
capacity, including full,
empty, less and more.
2Gg.06 Understand that
mass is the quantity of
matter in an object.
Estimate and measure
familiar objects using nonstandard or standard
units.
3Gg.06 Estimate and
measure the mass of
objects in grams (g) and
kilograms (kg).
Understand the
relationship between
units.
Standard units such as
grams and kilograms and
any other units used in local
contexts.
1kg =1000 g
2Gg.07 Understand that
capacity is the maximum
amount that an object can
contain. Estimate and
measure the capacity of
familiar objects using nonstandard or standard
units.
3Gg.07 Estimate and
measure capacity in
millilitres (ml) and litres (l),
and understand their
relationships.
Use liquids only.
1 litre = 1000 ml
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Learners continue to use mass in context.
6Gg.05 Understand the
difference between
capacity and volume.
Learners continue to use capacity in context.
Volume is the amount of
space taken up by an object,
while capacity is the
measure of an object's ability
to hold a substance, like a
solid, a liquid or a gas.
55
e.g. a flask can have a
capacity of 1 litre but be filled
with 0.5 litre of water. So, the
volume of water is 0.5 litre.
1Gg.06 Differentiate
between 2D and 3D
shapes.
2Gg.08 Identify 2D and
3D shapes in familiar
objects.
3Gg.08 Recognise
pictures, drawings and
diagrams of 3D shapes.
4Gg.06 Match nets to
their corresponding 3D
shapes.
5Gg.05 Identify and
sketch different nets for a
cube.
6Gg.06 Identify and
sketch different nets for
cubes, cuboids, prisms
and pyramids.
The bottom of a glass looks
like a circle.
e.g. drawings of cylinders
e.g. unfold packets to identify
their nets or shapes (cubes,
cuboids, cylinders and cones
etc.)
e.g. different nets of an open
or closed cube
Ensure learners have the
opportunity to make nets
using cut paper.
The top of the box looks like
a square.
Ensure that learners identify
examples of familiar 2D and
3D shapes in the
environment, such as
football, clock, computer
screen, window
is a sphere
Include reference to the
number and shapes of faces.
Ensure learners identify nets
that will not produce a cube.
Ensure learners have the
opportunity to make nets
using cut paper.
Include reference to their
properties, e.g. a cube has 6
faces and the net is made up
of six squares.
Use examples that allow
learners the opportunity to
create shapes
e.g. create the shape in the
picture below using blocks or
other generic maths
equipment
6Gg.07 Understand the
relationship between area
of 2D shapes and surface
area of 3D shapes.
Link surface area to work
on nets.
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56
1Gg.07 Identify when a
shape looks identical as it
rotates.
2Gg.09 Identify a
horizontal or vertical line
of symmetry on 2D
shapes and patterns.
3Gg.09 Identify both
horizontal and vertical
lines of symmetry on 2D
shapes and patterns.
4Gg.07 Identify all
horizontal, vertical and
diagonal lines of
symmetry on 2D shapes
and patterns.
5Gg.06 Use knowledge of
reflective symmetry to
identify and complete
symmetrical patterns.
6Gg.08 Identify rotational
symmetry in familiar
shapes, patterns or
images with maximum
order 4. Describe
rotational symmetry as
‘order 𝑥’.
e.g.
Using a mirror or folding to
confirm.
Using a mirror or folding to
confirm.
e.g. a sheet of paper folded
in half (line of symmetry); a
sheet of paper folded
unevenly (no line of
symmetry).
Ensure that learners
understand that the same
shape or pattern can have
more than one line of
symmetry.
e.g. all lines of symmetry of
squares, rectangles,
pentagons, octagons,
parallelograms
e.g. colour three more
squares so that this pattern
has 2 lines of symmetry
e.g. an equilateral triangle
has rotational symmetry
order 3, a square has
rotational symmetry order 4;
the letters A and T do not
have rotational symmetry but
they do have lines of
symmetry
Learners can use turn and
rotate interchangeably
This includes identifying
examples in the
environment.
e.g. a picture of a butterfly
showing the mirror line or
fold line and looks identical
only once in a full turn.
Ensure learners recognise
examples of vertical and
horizontal lines of symmetry
in the environment and art.
e.g.
e.g. draw all 8 lines of
symmetry on a regular
octagon
Ensure learners recognise
examples of horizontal,
vertical and diagonal lines of
symmetry in the environment
and art.
Include diagonal lines of
symmetry
e.g. colour two more squares
so that this pattern has 2
lines of symmetry
Also include examples with
no lines of symmetry.
2Gg.10 Predict and check
how many times a shape
looks identical as it
completes a full turn.
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57
2Gg.11 Understand that
an angle is a description
of a turn, including
reference to the terms
whole, half and quarter
turns, both clockwise and
anticlockwise.
3Gg.10 Compare angles
with a right angle.
Recognise that a straight
line is equivalent to two
right angles or a half turn.
4Gg.08 Estimate,
compare and classify
angles, using geometric
vocabulary including
acute, right and obtuse.
5Gg.07 Estimate,
compare and classify
angles, using geometric
vocabulary including
acute, right, obtuse and
reflex.
6Gg.09 Classify,
estimate, measure and
draw angles.
Identify right angles in 2D
shapes and in the
environment.
Ensure learners recognise
that a right angle is a quarter
turn.
Learners identify whether
angles are greater than or
less than a right angle.
Do not measure angles,
instead use benchmarks 90
degrees, 180 degrees to
identify less than or more
than 90 or 180 degrees.
Know that a reflex angle is
greater than 180º but less than
360º.
Use full circle protractors to
draw or measure angles.
No need to draw or measure
angles.
123º
247º
Ensure learners know that:
 an angle less than a right
angle is called an acute
angle
 an angle greater than a
right angle and less than a
straight line is called an
obtuse angle
 a quarter turn is 90
degrees
 a half turn is 180 degrees
 a three-quarter turn is 270
degrees
 a full turn is 360 degrees
Cambridge Primary Mathematics 0096 Progression Grid v1.2
e.g.36º.
Obtuse angle
Reflex angle
5Gg.08 Know that the
sum of the angles on a
straight line is 180º, and
use this to calculate
missing angles on a
straight line.
6Gg.10 Know that the
sum of the angles in a
triangle is 180º, and use
this to calculate missing
angles in a triangle.
e.g. What is the size of
angles a and b?
Learners should measure or
use paper folding to find the
sum of angles and to find
58
missing interior angles for all
types of triangle.
e.g.
Include examples where
learners have to apply their
knowledge of the properties
of equilateral and isosceles
triangles.
e.g.
Find angle b.
180-40 = 140
140 ÷ 2 = 70°
So angle b is 70°
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59
1Gg.08 Explore
instruments that have
numbered scales, and
select the most
appropriate instrument to
measure length, mass,
capacity and temperature.
2Gg.12 Understand a
measuring scale as a
continuous number line
where intermediate points
have value.
3Gg.11 Use instruments
that measure length,
mass, capacity and
temperature.
4Gg.09 Use knowledge of
fractions to read and
interpret a measuring
scale.
At this stage learners are
exploring non-standard
lengths so introduce them to
instruments that have scales:
rulers, balance scales to
measure mass, jugs to
measure capacity and
thermometers to measure
temperature.
 read from numbered
scales starting at zero
 use language of
approximation.
 estimate first and then
measure
 round up if the
measurement is past or
equal the half-way point
between readings
Ensure that learners use
knowledge of fractions to
read scales: half way,
quarter of the way.
e.g. use rulers to measure
length, balance scale to
measure mass, jugs to
measure capacity and
thermometers to measure
temperature.
Read scales with fully
numbered divisions and
interpret the values that lie
between them, using
language of approximation,
e.g. part way between 3 and
4, slightly more than 1, more
than 3 but less than 4.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
round down if the
measurement is less than
the half-way point between
readings.
Learners continue to read and interpret a measuring
scale in context.
Read scales with partially
numbered divisions and
interpret values to the
nearest division or half
division.
Interpret values that lie
between divisions on
numbered and partially
numbered scales, rounding
up or down to the nearest
labelled division.
60
6Gg.11 Construct circles
of a specified radius or
diameter.
Using a ruler and compass
or digital technology.
Ensure learners understand
that a circle is a set of points
that are the same distance
from the centre.
e.g. draw the set of points
that are exactly 3cm from the
point A.
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61
Geometry and Measure
Position and transformation
Stage 1
Stage 2
Stage 3
Stage 4
1Gp.01 Use familiar
language to describe
position and direction.
2Gp.01 Use knowledge of
position and direction to
describe movement.
3Gp.01 Interpret and
create descriptions of
position, direction and
movement, including
reference to cardinal
points.
4Gp.01 Interpret and
create descriptions of
position, direction and
movement, including
reference to cardinal and
ordinal points, and their
notations.
Language such as left, right,
up, down, under, above,
below, in front of, behind.
This includes:
This includes:
 clockwise and anticlockwise.
 equivalent descriptions
(e.g. a quarter of a turn
clockwise and another
quarter of a turn clockwise
is equivalent to a half turn
clockwise)
 reverse descriptions (e.g.
two steps forward, two
steps backwards)
 clockwise, anti-clockwise
 up, down, above, below,
next to, between, under,
right, left, straight on
Emphasise written
instructions as well as oral.
Ensure learners understand
that ordinal points [northeast
(NE), southeast (SE),
southwest (SW) and
northwest (NW)] are halfway
between cardinal points
[north (N), east (E), south
(S), west (W)] on a compass.
Ordinal points represent
angles less than 90º.
Emphasise oral descriptions
rather than reading and
writing them.
Learners start creating and
interpreting simple grid
maps.
e.g. Imagine you are facing
south. Write the instructions
for the route from start to
finish. Start with: Move south
1 square, turn right ……
Stage 5
Stage 6
e.g. describe all the different
routes from A to B, travelling
only northeast or northwest
Start

N
Use simple scales, legends
and directions to interpret
information contained on a
map.
Finish
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62
4Gp.02 Understand that
position can be described
using coordinate notation.
Read and plot coordinates
in the first quadrant (with
the aid of a grid).
5Gp.01 Compare the
relative position of
coordinates (with or
without the aid of a grid).
6Gp.01 Read and plot
coordinates including
integers, fractions and
decimals, in all four
quadrants (with the aid of
a grid).
Ensure learners can draw a
pair of coordinate axes for
the first quadrant and
understand that the axes
represent two number lines.
Know that the areas of the
graph between axes are
called quadrants.
First quadrant only.
Ensure learners understand
that coordinates can be
represented by both negative
and positive values, and
fractions and decimals.
Identify points on a 2D grid
using coordinates (the first
number represents the
movement in the horizontal
direction and the second
number the vertical
direction). Start to use the
language: the first number
refers to the x coordinate
and the second number
refers to the y coordinate,
referring to x-axis and y-axis.
e.g. Point (2,6) is further
away from y-axis than point
(1,3).
This is point (5, 5). Estimate
the position of (1,3).
(5, 5)
e.g.
negative and positive values
(1, 1), (-2, 3), (1, -2), (-3, -4),
decimals or fractions (1, 1.5),
1
(-2.5, 3), ( , -2),
2
9
1
3
2
2
4
(-3, - ) ( , 2), (1, - ).
e.g., (3, 1) describes a point
starting at the origin and
moving 3 squares horizontal
and 1 square vertical so (3,
1) and (1, 3) describe
different points
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63
5Gp.02 Use knowledge of
2D shapes and
coordinates to plot points
to form lines and shapes
in the first quadrant (with
the aid of a grid).
6Gp.02 Use knowledge of
2D shapes and
coordinates to plot points
to form lines and shapes
in all four quadrants.
Ensure learners can use
geometric information to find
a missing vertex.
Ensure learners can use
geometric information to find
a missing vertex or a second
point on a line.
In the image below, if (5, 5)
is point A of the square, what
are the other points?
e.g. plot the points A(1, 4),
B(–2, 3), C(–1, 4) ABCD is a
parallelogram, find two
possible coordinates for D
If you draw a line between
(1,1) and (5, 1), this forms
one side of a square, draw
the other sides of the square
(in the first quadrant).
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64
5Gp.03 Translate 2D
shapes, identifying the
corresponding points
between the original and
the translated image, on
square grids.
6Gp.03 Translate 2D
shapes, identifying the
corresponding points
between the original and
the translated image, on
coordinate grids.
Ensure learners can
describe and perform a
translation on a square grid
using up, down, left, right or
a combination of horizontal
and vertical movements in
the first quadrant
Ensure learners can
describe and perform a
translation on a first quadrant
and all four quadrant
coordinate grid using up,
down, left, right.
e.g. A square ABCD has
been translated 3 squares to
the right.
e.g. Translate the blue
square 7 squares up.
Learners are not expected to
identify points using
coordinates. They should
use their geometrical
knowledge. Coordinates are
a separate concept that is
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65
covered in another learning
objective.
Ensure that learners
understand translation as
movement along a straight
line whilst maintaining its
size, shape and orientation
(every vertex moves in the
same direction by the same
amount).
Reflection and rotation of
shapes should be on
squared paper only at this
stage, whereas translation
can be done using
coordinates.
Learners should join the
corresponding corners of a
pair of translated shapes
together to show the lines
formed are parallel and the
same length (in comparison
to reflection where the lines
are parallel but not equal
length).
2Gp.02 Sketch the
reflection of a 2D shape in
a vertical mirror line,
including where the mirror
line is the edge of the
shape.
3Gp.02 Sketch the
reflection of a 2D shape in
a horizontal or vertical
mirror line, including
where the mirror line is
the edge of the shape.
4Gp.03 Reflect 2D
shapes in a horizontal or
vertical mirror line,
including where the mirror
line is the edge of the
shape, on square grids.
Learners should sketch the
shapes on plain paper rather
than on grids because it is
the concept of reflection that
is important rather than
accuracy.
Learners should sketch the
shapes on plain paper rather
than on grids because it is
the concept of reflection that
is important rather than
accuracy.
Ensure learners visualise
and sketch the result of
reflecting a shape along one
edge to create new shapes.
This includes examples in
the environment.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
5Gp.04 Reflect 2D
shapes in both horizontal
and vertical mirror lines to
create patterns on square
grids.
6Gp.04 Reflect 2D
shapes in a given mirror
line (vertical, horizontal
and diagonal), on square
grids.
Include examples where the
sides of the shape are not
Include examples where the
sides of the shape are not
e.g. when you reflect a
square, the new shape
(adding both squares) is a
rectangle.
Learners should sketch the
shapes on square grids so
66
e.g. a picture of a butterfly
reflected over the dotted line
count number of squares
which will assist them in
understanding the concept of
reflection.
parallel or perpendicular to
the mirror line.
parallel or perpendicular to
the mirror line.
e.g.
Learners should join the
corresponding corners of a
pair of reflected shapes
together to show parallel
lines formed.
6Gp.05 Rotate shapes
90º around a vertex
(clockwise or
anticlockwise).
Learners should join the
corresponding corners of a
pair of rotated shapes
together to show the lines
formed are not parallel (in
comparison to reflection and
translation where the lines
are parallel).
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67
Statistics and Probability
Statistics
Stage 1
Stage 2
Stage 3
Stage 4
Stage 5
Stage 6
1Ss.01 Answer nonstatistical questions
(categorical data).
2Ss.01 Conduct an
investigation to answer
non-statistical and
statistical questions
(categorical data).
3Ss.01 Conduct an
investigation to answer
non-statistical and
statistical questions
(categorical and discrete
data).
4Ss.01 Plan and conduct
an investigation to answer
statistical questions,
considering what data to
collect (categorical and
discrete data).
5Ss.01 Plan and conduct
an investigation to answer
a set of related statistical
questions, considering
what data to collect
(categorical, discrete and
continuous data).
6Ss.01 Plan and conduct
an investigation and make
predictions for a set of
related statistical
questions, considering
what data to collect
(categorical, discrete and
continuous data).
Learners do not need to
know formal definitions such
as “categorical data”.
Learners do not need to
know formal definitions such
as “categorical data”.
Categorical data refers to
characteristics such as
colour, names, personal
preferences, etc. where
there is only one answer.
Ask questions such as:
Learners do not need to
know formal definitions such
as “categorical and discrete
data”.
Learners do not need to
know formal definitions such
as “categorical and discrete
data”.
Learners do not need to
know formal definitions such
as “categorical, discrete and
continuous data”.
Learners do not need to
know formal definitions such
as “categorical, discrete and
continuous data”.
Discrete data refers to data
that can be counted and has
a finite number of possible
values in a given range, such
as number of siblings, how
many books they have read
this month etc.
Include examples where
learners need to decide what
data to collect in order to
answer the question
Continuous data refers to
data that can be measured
and has an infinite number of
possible values within a
selected range, e.g. mass,
height, temperature.
Ensure learners make
predictions before
conducting their
investigation.
Ask questions (on topics
familiar and of interest to
learners).
e.g.
What is your favourite fruit?
Questions can be cross
curricular, e.g. if reading The
Very Hungry Caterpillar:
Which food did the caterpillar
eat the most?
What is your favourite book?
(non-statistical)
What is the favourite genre
of book of people in this
class? (statistical)
Discuss the difference
between a statistical and
non-statistical question with
learners so they are familiar
with these terms.
A non-statistical
question is one with a
deterministic answer (it has a
single answer), whereas a
statistical question is one
that will have variable
answers so collecting data is
necessary for it to be
answered.
Ask questions such as:
How many 3-letter words are
on this page? (nonstatistical)
What length are the words in
children’s books? (statistical)
e.g.
Which of these two children’s
books is easier to read?
For this question learners
could suggest a number of
different measures to
investigate such as:
 word length
 number of pictures
 number of pages
 words per page.
Include examples where
learners need to decide what
data to collect in order to
answer the question.
Learners should investigate
a range of these ideas,
rather than just one.
e.g.
Do 10-year olds have larger
body measurements than 9year olds?
For this question learners
could suggest a number of
e.g.
“I think my data will show
that 10-year olds have a
larger shoulder width and
shoe size than 9-year olds”
Ask questions that allow
learners to collect more than
two variables including
categorical per observation,
to allow comparison of subgroups.
e.g. data collected for height
and gender could be split
into male heights and female
heights and compared
e.g.
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68
different measures to
investigate such as:
 height
 hand span
 leg length
 arm span
 shoulder width
 shoe size
Learners may decide to
investigate height,
shoulder width and shoe
size to answer the original
question.
Is there a connection
between a person’s height
and their other body
measurements?
Learners may decide to
investigate whether there is
a link between height and
hand span, or height and
shoe size. This relationship
is best analysed using
scatter graphs.
Stage 1
Stage 2
Stage 3
Stage 4
Stage 5
Stage 6
1Ss.02 Record, organise
2Ss.02 Record, organise
3Ss.02 Record, organise
4Ss.02 Record, organise
5Ss.02 Record, organise
6Ss.02 Record, organise
and represent categorical
data using:
and represent categorical
data. Choose and explain
which representation to
use in a given situation:
and represent categorical
and discrete data. Choose
and explain which
representation to use in a
given situation:
and represent categorical
and discrete data. Choose
and explain which
representation to use in a
given situation:
and represent categorical,
discrete and continuous
data. Choose and explain
which representation to
use in a given situation:
and represent categorical,
discrete and continuous
data. Choose and explain
which representation to
use in a given situation:
- Venn and Carroll
diagrams
- tally charts and
frequency tables
- pictograms and bar
charts.
- Venn and Carroll
diagrams
- tally charts and
frequency tables
- pictograms and bar
charts
- dot plots (one dot per
count).
- Venn and Carroll
diagrams
- tally charts and
frequency tables
- bar charts
- waffle diagrams
- frequency diagrams for
continuous data
- line graphs
- dot plots (one dot per
data point).
-
- practical resources and
drawings
- lists and tables
- Venn and Carroll
diagrams
- block graphs and
pictograms.
- lists and tables
- Venn and Carroll
diagrams
- tally charts
- block graphs and
pictograms.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
-
Venn and Carroll
diagrams
tally charts and
frequency tables
bar charts
waffle diagrams and
pie charts
frequency diagrams
for continuous data
line graphs
scatter graphs
dot plots.
69
Lists, tables,
tally
Record and organise
answers to non-statistical
questions only.
Ensure learners can
correctly use tallies to
record categorical data.
e.g. each learner asks a
peer “What is your
favourite fruit?” and
places a picture of the
fruit next to their name:
e.g. Learners ask their
friends “What is your
favourite colour?”.
Record using a tally chart
and include a column to
present frequencies
Continue to use tally
charts and frequency
tables where appropriate
and explain choice of data
representation.
Include frequency tables
with percentages to cover
the idea of frequency as a
proportion of the whole
population
Representing grouped
discrete data in a
frequency table
e.g.
e.g.
Eva
Record discrete data, e.g.
Representing continuous
data in a frequency table
(not using ≤, < until later
stages)
Pierre
Carlos
Learners organise
information into lists or
tables:
Apple
Banana
Eva
Pierre
They should explain the
advantages and
disadvantages of using a
list, table or tally chart, to
organise information.
Ensure learners discuss
how to record a mass of
exactly 50kg, or 100kg.
Carlos
Venn and
Carroll
Use Venn or Carroll
diagrams to sort numbers
or objects using one
criterion; explain choices
using appropriate
language including ‘not’.
e.g.
Students can select their
own groupings for
discrete or continuous
data
Use Venn or Carroll
diagrams to sort numbers
or objects using one
criterion or two criteria;
explain choices using
appropriate language
including ‘not’.
e.g. sorting shapes by
colour (red and not red,
circles and not circles).
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Continue to use Venn and
Carroll diagrams with one
or two criterion where
appropriate and explain
choice of data
representation.
For Venn diagrams,
introduce the universal set
and entries outside the
chosen sets.
Use Venn diagrams or
Carroll diagrams to sort
data and objects using up
to three criteria.
e.g. use a Venn diagram
to compare characteristics
of animals.
Continue to use Venn and
Carroll diagrams where
appropriate and explain
choice of data
representation.
Continue to use Venn and
Carroll diagrams where
appropriate and explain
choice of data
representation.
For 2 sets learners can
create Carroll diagrams
from Venn diagrams and
vice versa.
70
Block graph,
pictogram,
bar chart
Use pictograms first and
then show how this data
can be represented in
block graphs where one
object or drawing
represents one data value
Draw block graphs
directly from information
presented in tally charts
e.g.
Use pictogram where one
object or drawing
represents one or two
data values.
e.g. each image
represents two cars
e.g.
Introduce the terminology
of axes and initially use
examples that use words
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Use examples that record
data in bar charts
(discrete data), and do not
use histograms
(frequency diagrams for
continuous data) as this
requires knowledge of
continuous data.
Ensure learners know the
difference between bar
charts (discrete data) and
frequency diagrams, or
histograms, (continuous
data) and can explain
which representation to
use in a given situation.
Use bar chart scales in
1s, 2s, 5s, 10s and 20s.
Use bar chart scales in
1s, 2s, 5s, 10s, 20s and
100s.
Introduce bar charts with
grouped discrete data
represented in groups of 2
(1 – 2, 3 – 4 etc.), 5 (1 –
5, 6 – 10 etc.) and 10 (1 –
10, 11 – 20 etc.)
e.g.
Ensure learners
understand the impact of
representations where
scales have different
intervals, e.g. comparing
71
rather than numbers on x
axis. Ensure learners
understand that a bar
chart of discrete data
includes a gap between
each bar, e.g.
They should explain the
advantages and
disadvantages of using a
pictogram or block graph
to represent information.
Ask learners to choose
suitable equal class
intervals where
appropriate.
and
At this stage do not use
examples that require
histograms (frequency
diagrams for continuous
data) as this requires
knowledge of continuous
data.
Use bar chart scales in 1s
and 2s.
Dot plots
Use dot plots to record
data, where each dot
represents 1 count.
Use dot plots to record
data, where each dot
represents one data point
rather than one dot per
count.
e.g.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Number of
pets
0
1
2
3
Frequency
6
2
3
5
Continue to use dot plots
where appropriate and
explain choice of data
representation.
e.g.
Number of
pets
0
1
2
3
Frequency
6
2
3
5
72
Waffle
diagrams
and pie
charts
Use diagrams that
represent proportions in
data, e.g. waffle
diagrams, to assist
learners in understanding
percentage and
proportions of the whole
sample or population.
e.g.
waffle diagrams:
or
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Use examples where the
total frequency is 4, 5, 10
or 20. If using other
frequencies, ensure
learners are provided with
a pre-divided pie chart
using dots around the
edge of a circle. For
example, for a total
frequency of 12:
Record data in waffle
diagrams with 100
squares and related pie
charts to assist learners in
understanding the
proportion of a population.
e.g.
73
waffle diagram:
pie chart:
Frequency
diagrams
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Ensure learners know the
difference between bar
charts (discrete data) and
frequency diagrams, or
histograms, (continuous
data).
Continue to use frequency
diagrams for continuous
data (histograms) where
appropriate and explain
choice of data
representation.
Provide learners with the
scales and a partially
complete diagram. Ensure
learners can complete
and add data to frequency
diagrams for continuous
data (histograms) with
equal class intervals.
Use scales for frequency
such as 1s, 2s, 5s and
10s.
74
Use simple scales for
frequency such as 1s.
Line graphs
Use line graphs to
represent continuous
data, e.g. temperature
over time
Continue to use line
graphs where appropriate
and explain choice of data
representation.
Use examples that require
learners to read between
grid lines.
Use examples that
include grid lines
Scatter
graphs
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Use examples that record
data in scatter graphs to
draw a line of best fit as
learners will use these in
science.
75
Use simple scales, for
example 1s or 2s.
Stage 1
Stage 2
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Stage 3
Stage 4
Stage 5
Stage 6
5Ss.03 Understand that
the mode and median are
ways to describe and
summarise data sets.
Find and interpret the
mode and the median,
and consider their
appropriateness for the
context.
6Ss.03 Understand that
the mode, median, mean
and range are ways to
describe and summarise
data sets. Find and
interpret the mode
(including bimodal data),
median, mean and range,
and consider their
appropriateness for the
context.
76
e.g. Ana’s last five marks out
of 10 were
1, 1, 5, 6, 7
Median: 5
Mode: 1
Ensure learners understand
that in this situation the
mode is not an appropriate
measure as most of Ana’s
marks (3 out of 5) were
above 5. In this case,
therefore, they should
choose the median.
The mode represents the
marks that occurred the most
and the median is the value
that leaves the same number
of data above and below it (2
marks below 5 and 2 marks
above 5).
Introduce median of an odd
number of events so that the
median is a whole number.
First review median of odd
number of events and then
introduce median of even
numbers.
e.g. Becky’s last six marks
out of 10 were
1, 1, 5, 7, 8, 8
Median: (5 + 7) = 12 = 6
2
2
Mode: 1 and 8
Mean = 5
In the example above,
learners should recognise
that there are three marks
below the median and three
marks above the median
1, 1, 5  below 6
7, 7, 8  above 6
If a shop manager wants to
find out which size people
buy on average, they should
look into the mode as this
represents the size they sell
the most.
If a company wants to report
on the average salaries of
their employees, they should
use median as it will not be
affected by the very high and
very low salaries.
If a student has had 1, 1, 1,
1, 2 and 3 as the last six
Cambridge Primary Mathematics 0096 Progression Grid v1.2
77
marks, the mean would be
more representative as it
would be above 1 and would
show that the student got
some marks above 1.
1Ss.03 Describe data,
using familiar language
including reference to
more, less, most or least
to answer non-statistical
questions and discuss
conclusions.
2Ss.03 Describe data,
identifying similarities and
variations to answer nonstatistical and statistical
questions and discuss
conclusions.
3Ss.03 Interpret data,
identifying similarities and
variations, within data
sets, to answer nonstatistical and statistical
questions and discuss
conclusions.
4Ss.03 Interpret data,
identifying similarities and
variations, within and
between data sets, to
answer statistical
questions. Discuss
conclusions, considering
the sources of variation.
5Ss.04 Interpret data,
identifying patterns, within
and between data sets, to
answer statistical
questions. Discuss
conclusions, considering
the sources of variation.
6Ss.04 Interpret data,
identifying patterns, within
and between data sets, to
answer statistical
questions. Discuss
conclusions, considering
the sources of variation,
and check predictions.
Questions should be on
topics that are familiar and of
interest to learners.
Within data refers to data
collected about the preferred
book genre of all learners in
a class:
Within data refers to data
collected about word length
of all words on one page of
one children’s book:
Between data refers to data
collected about word length
of all words on one page of
two children’s books:
Learners identify patterns
within and between the data
sets.
Learners check whether their
predictions were correct or
incorrect and give possible
reasons for this.
The Very Hungry Caterpillar
example:
Use the diagrams to
compare quantities, order
items from most eaten to
least eaten etc., and explain
reasoning.
Genre
Number
Adventure
12
Fact book
5
e.g. “The food that the
caterpillar ate the most of
was oranges. He ate more
plums than apples. Maybe
the caterpillar likes plums
more than apples.”
Scary
stories
9
Word
length
1
2
3
4
5
6
Number
10
11
13
9
7
2
Children’s book A
Word
length
1
2
3
4
5
6
Number
10
11
13
9
7
2
Children’s book B
Word
length
1
2
3
4
5
6
7
Number
6
6
9
8
7
4
2
Book A
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Book B
Book A
Book B
e.g. “Both bar charts show
the same bump. They go up
and then down again. This is
because they both have the
most 3-letter words. The
mode word length for both
books is 3 letters.”
e.g. “We thought there would
be the most 1-letter and 2letter words in children’s
books. Actually there were
more 3-letter words. This
might be because the words
‘and’ and ‘the’ are both 3letter words that come up a
lot.”
Use examples that cover the
idea of frequency as a
proportion of the whole
population.
e.g.
“The bars are more similar
heights in the bar chart for
book B than book A. The
bump isn’t as steep.”
78
Ensure learners interpret the
data in context (presented in
tables, bar charts,
pictograms etc.)
e.g. Learners should not say
“the shortest bar is 6-letter
words” instead they should
say “The bar chart shows
that there were fewest 6letter words. There were only
two 6-letter words on the
page”
They should identify
similarities and variations
within the data set.
e.g. “There were two more 4letter words than 5-letter
words”
Learners describe the data
presented in tables, block
graphs, pictograms etc.
e.g. “The highest column on
the block graph is adventure”
“The most popular genre
was adventure books”
“The second column is
shorter than the first column”
Cambridge Primary Mathematics 0096 Progression Grid v1.2
Learners notice similarities
and variations within data
sets.
e.g. “There were the same
number of 1-letter and 2letter words in book B”
They also make
comparisons between data
in tables, pictograms, bar
charts, dot plots etc.
“Book B had less words on
the page than book A, but
they were a bit longer. This
might be because it was a
fact book, not a story book”
“About 50% of words on the
page have length 2-letters,
3-letters or 4-letters”
e.g. “The bar charts show
both books had the most 3letter words”
“Book B had two 7-letter
words, but book A didn’t
have any 7-letter words”
Learners consider the
sources of variation. They
explain why the data shows
variations and give reasons
for the differences in the data
they collected for each book.
e.g. “The data I collected for
book A and book B is
different. This might be
because Book A is a story
book, but book B is a fact
book. Also the fact book
contains more pictures on
the page. The fact book
includes longer words, it is
more complicated to
understand”
79
Statistics and Probability
Probability
Stage 1
Stage 2
Stage 3
Stage 4
Stage 5
Stage 6
2Sp.01 Use familiar
language associated with
patterns and randomness,
including regular pattern
and random pattern.
3Sp.01 Use familiar
language associated with
chance to describe
events, including ‘it will
happen’, ‘it will not
happen’, ‘it might happen’.
4Sp.01 Use language
associated with chance to
describe familiar events,
including reference to
maybe, likely, certain,
impossible.
5Sp.01 Use the language
associated with likelihood
to describe and compare
likelihood and risk of
familiar events, including
those with equally likely
outcomes.
6Sp.01 Use the language
associated with probability
and proportion to describe
and compare possible
outcomes.
e.g. When observing
Classify and make
judgements on familiar
events and explain why.
e.g. discuss statements
using the vocabulary: no
chance, poor chance, even
chance, good chance and
certain:
Compare two or more events
using vocabulary: most
likely, less likely, equally
likely (even chance),
impossible, certain.
Learners are not expected to
calculate probabilities. They
should be using the
language only.
 I will watch television
tonight
 It will get dark tonight
 I will see a penguin on my
way home from school.
Learners position events on
a likelihood scale, e.g.
RGBRGTRGBRGSR
GT
learners are able to make
comments like “every third
letter is an R” or ”G always
comes after an R”.
This also includes identifying
when there appears to be no
pattern.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
e.g. using fractions: 1 out of
4 chance; using
percentages: 25% chance
5Sp.02 Recognise that
some outcomes are
equally likely to happen
and some outcomes are
more (or less) likely to
happen, when doing
practical activities.
6Sp.02 Identify when two
events can happen at the
same time and when they
cannot, and know that the
latter are called 'mutually
exclusive'.
e.g. from a pack of 52
playing cards:
Ensure learners understand
the term ‘mutually exclusive’,
e.g. turning left and turning
right are mutually exclusive
80
 you are equally likely to
choose a red card or a
black card
 you are more likely to
choose a number card
than a picture card
 you are less likely to
choose a king or queen
than an even numbered
card.
(you can't do both at the
same time); whereas turning
left and scratching your head
can happen at the same
time.
Ensure learners recognise
that some probabilities
cannot be calculated by
using equally likely outcomes
but can be modelled through
experiments involving a large
number of trials.
6Sp.03 Recognise that
some probabilities can
only be modelled through
experiments using a large
number of trials.
Use probability examples
that require a large number
of trials, e.g. roll a pair of sixsided dice and observe the
sum of the numbers on the
uppermost face: which
total(s) occur the most often/
least often?
2Sp.02 Conduct chance
experiments with two
outcomes, and present
and describe the results.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
3Sp.02 Conduct chance
experiments, and present
and describe the results.
4Sp.02 Conduct chance
experiments, using small
and large numbers of
trials, and present and
describe the results using
5Sp.03 Conduct chance
experiments or
simulations, using small
and large numbers of
trials, and present and
describe the results using
6Sp.04 Conduct chance
experiments or
simulations, using small
and large numbers of
trials. Predict, analyse
and describe the
frequency of outcomes
81
Use resources that only have
two outcomes such as, coins
(head or tails), selecting two
items from a jar, spinners
with two colours.
Use resources that have
more than two outcomes
such as a pack of 52 playing
cards, a spinner with ten
colours.
Learners realise that if there
are more equally likely
outcomes they are less likely
to happen.
e.g. winning a game of
heads/tails or choosing the
ace of diamonds from a pack
of playing cards. Which is
more likely? Why?
the language of
probability.
the language of
probability.
using the language of
probability.
If possible, use digital
resources such as chance
generators that model realworld situations, e.g. model
flipping a coin by using a
random number generator
on a computer, or assigning
even and odd numbers on a
dice.
Use examples that include
different coloured beads in a
bag so that learners cannot
see how many of each
colour are in the bag, so that
they need to predict the
results.
Understand that randomness
has uncertain individual
outcomes but exhibit regular
patterns of outcomes over
many repetitions.
Also include examples with
spinners and coins to
encourage learners to use
the language of probability to
describe the outcomes of
experiments and games with
random generators.
Ensure learners understand
that experimental probability
is random (has uncertain
individual outcomes but
exhibit regular patterns of
outcomes over many
repetitions) and
unpredictable (the next
outcome is not predictable).
This will help to avoid the
misconception that the
theoretical probability value
is precise (e.g. I will get a 3
on a dice every 6 rolls).
Investigate through
discussion and
experimentation two
outcomes that are equally
likely, outcomes that are
more or less likely.
Cambridge Primary Mathematics 0096 Progression Grid v1.2
82
Version 1.2, published November 2022
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