Level 2
Read, write,
understand
fractions
Recognise, name
and write fractions
1/2, 1/3, 1/4 of a
length, shape, set
of objects or
quantity
Recognise, name
and write fractions
2/4 and 3/4 of a
length, shape, set
of objects or
quantity
Counting
fractions
Count in halves
and quarters
including
representing
pictorially and on
numberlines
Low
Recognise and
use fractions as
numbers: unit
fractions with
small
denominators
Recognise that
tenths arise from
dividing an
object into 10
equal parts and
in dividing onedigit numbers or
quantities by 10
Count in small
denominator
fractions
including
representing
pictorially and on
numberlines
Level 3
High
Recognise and
use non-unit
fractions with
small
denominators
Recognise that
hundredths arise
when dividing an
object by one
hundred
e.g. 5/6, 3/8, 6/10
(The above
objective has
been split over
high 3 and low 4)
Combine tenths
of shapes,
objects,
quantities or
measures to find
2/10, 3/10
Count up and
down in
hundredths
Ext: Counting in
hundredths that
crosses
boundaries e.g.
99/100
100/100
101/100
Count up and
down in tenths to
one whole
Compare
and order
fractions
Which is larger, ½
or ¼ and why?
Identify the larger
of 1/3 and 1/5
with supporting
diagrams.
Equivalent
fractions
and
converting
Count in halves
and quarters.
Count in other
fractions with small
denominators using
number lines
Recognise and
show, using
diagrams,
equivalent
fractions with
small
denominators
Calculating
with
fractions
Express counting in
halves and quarter
as equations
Express counting
in unit fractions
as equations
½ + ½ = 2/2
e.g. 1/6 + 1/6
+1/6 + 1/6 = 4/6
¼ + ¼ = 2/4
This will help to
build
understanding of
what non-unit
fractions mean
for 3b
¼+¼+¼=¾
¼ + ¼ + ¼ + ¼= 4/4
Compare and
order unit
fractions, and
fractions with the
same
denominators
Identify and
explain the larger
of 2/5 and 3/5
Create fraction
families through
division by 3 and
5. Work
practically to
identify
equivalence.
Identify the
smaller out of 3/8
and 1/4 with
supporting
diagrams.
Recognise and
show, using
diagrams,
families of
common
equivalent
fractions
e.g. halves,
quarters, thirds,
fifths, tenths,
hundredths
Add and subtract fractions with the
same denominator within one whole [
𝟓
𝟏
𝟔
for example, + = ]
𝟕
𝟕
𝟕
Low
Recognise that
hundredths arise
when dividing
tenths by ten
(The above
objective has
been split over
high 3 and low 4)
Counting to give
rise to improper
fractions e.g. 9/10,
10/10, 11/10,
12/10
Work on when is a
whole reached?
What would two
wholes look like as
an improper
fraction?
Create equivalent
fractions through
multiplication and
division of the
denominator by a
common factor
Identify, name
and write
equivalent
fractions of a
given fraction,
represented
visually, including
tenths and
hundredths
Level 4
High
Low
Level 5
High
Recognise mixed
numbers and
improper fractions
Understand what
digits represent in
diagrams, writing,
materials
Counting in
proper fractions
giving rise to
improper fractions
and mixed
numbers,
represent
pictorially, on
number lines
Compare and
Identify the
order fractions
smaller out of 2/3
whose
and 13/18 and
denominators are
write down a
all multiples of the
fraction that is
same number
between them.
Identify the
smaller out of 2/3
and 13/18.
Mixed numbers and improper fractions
(when counting, recognition and
understanding of values secure - see
above):
write
convert from one
mathematical
form to the other
statements > 1 as
a mixed number
𝟐
𝟒
[for example, +
𝟔
𝟏
𝟓
𝟓
𝟓
Identify and
compare
fractions more
efficiently by
finding the lowest
common
denominator
Use common
factors to simplify
fractions; use
common
multiples to
express fractions
in the same
denomination
Compare and
order fractions,
including
fractions > 1
i.e. improper,
mixed numbers,
range of
denominators
Apply knowledge
to compare and
order range of
fraction types
including
decimals and
percentages as
Level 5 level of
difficulty
Apply knowledge to convert range of
fraction types and find equivalencies,
explaining how they know, and using
these to calculate and solve problems
including decimals and percentages
as Level 5 level of difficulty
𝟓
= =1 ]
Add and subtract
fractions with the
same
denominator
(also part of Year
5 objective)
Calculate 3/9 +
8/9 = 11/9 and
11/9 ‒ 8/9 = 3/9.
They realise that
11/9 is greater
than one Ext:
suggest ways to
Add and subtract
mixed numbers
With the same
denominator e.g.
3 ¼ +9 ¼
where the fraction
is not improper
Add and subtract
fractions with
denominators that
are multiples of
the same number
e.g 2/3 + 5/18 =
17/18
Then where the
answer is
improper
2/3 + 13/18 =
25/18
Then convert into
a mixed number
Add and subtract
fractions with
denominators
that are not
multiples of the
same number
e.g.
3/4 + 5/6
Can be by
creating /24.
If understood
lowest common
Add and subtract
fractions with
denominators
that are multiples
of the same
number where
the solution is
improper and
requires an
additional
conversion
e.g.
4¾+2½
=6 + ¾ + ½
Add and subtract
fractions with
different
denominators
and mixed
numbers, using
the concept of
equivalent
fractions
e.g.
4 4/6 + 17/4 + 2/3
-­‐
Need to
convert all
fractions
record this.
Find 1/2, 1/3, ¼ of a
length, shape, set
of objects or
quantity
NB
½ of 12 = 6
is the same
mathematically as
½ x 12
This would not be
shown to children
in this way at this
stage
Solving
problems
with
fractions
One-step problems
involving
multiplication and
division, using
materials, arrays,
repeated add,
mental methods,
multiplication
division facts,
including problems
in contexts
Find 2/4 and 3/4
of a length,
shape, set of
objects or
quantity
Recognise, find and write fractions of
a discrete set of objects: unit fractions
and non-unit fractions with small
denominators
e.g. 5/6, 3/8, 6/10
NB
3/4 of 24 = 18
is the same
mathematically
as
3/4 x 24
This would not be
shown to children
in this way at this
stage
NB
5/6 of 600 = 500
is the same mathematically as
5/6 x 600
This would not be shown to children in
this way at this stage
Solve problems that involve all of the above
Lower: pupils can solve problems such as 'I have 12
counters. One-third of them are yellow. The rest are blue.
How many blue counters do I have
Higher: pupils can devise problems such as 'I have 24
counters. One-third of them are blue, one-sixth are red and
one-eighth are green. The rest are yellow. How many are
yellow?'
Apply knowledge
6/10 of 120
= 120 ÷10
=12
12 x 6 = 72
25/18 = 1 7/18
Build up by:
½ x (or of) 49
Halving odd
numbers – realise
you can divide
whole ones again
¼x
Unit fractions e.g.
1/3, 1/5, 1/8, 1/16
5=1¼
proper fractions x
by whole
diagrams and
materials
Solve problems involving increasingly harder fractions to
calculate quantities, and fractions to divide quantities,
including non-unit fractions where the answer is a whole
number Lower: 'I have 12 oatcakes. I eat 3/4 of them for
lunch. Do I have enough left to eat two for a snack in the
afternoon?'
Higher: 'I have £12. I spend 2/5 of it on lunch and need to
save 1/3 of it for the bus fare home. Do I have enough to
spend £2.40 on an ice cream?'
I have 20 oatcakes. I eat 2/5 of them for lunch and need to
save 1/4 of them for an afternoon snack. Do I have enough
to give my friend 8 of them for her lunch?
denominator
(above) would
be looking for /12
=6 + 5/4
=6+ 1 ¼
=7 ¼
Multiply proper
fractions and
mixed numbers
by whole
numbers,
supported by
materials and
diagrams
5 x 3/8 = 15/8 or 1
7/8 therefore 5 x 2
3/8 = 10 + 15/8 =
11 7/8, using
appropriate
diagrams.
Divide proper
fractions by
whole numbers
[for example, 1/3
÷ 2= 1/6
-­‐
into /12
Convert this
answer into
mixed
numbers
Explain how to
divide a fraction
by a whole
number and why
it works.
Calculate 1/4 ÷ 5
using a diagram.
Solve problems involving multiplication and division,
including scaling by simple fractions and problems involving
simple rates
A packet of biscuits was xx there was 1/9 off the price they
are now 72p. How much were they?
Half of the children in class 4 go to the high school, of those
that are left, ¾ get to bake a cake. What fraction of the
whole got to bake a cake?
Decimals
Blue – Year 2
Level 2
Reading,
writing and
understandin
g decimals
Red – Year 3 Green – Year 4 Purple – Year 5 Orange – Year 6 Black – Guidance and exemplars
Low
Identifying the
value of the digits
Value of digits
remaining at
tenths
Use of place value
chart and dienes
blocks
Level 3
Recognise and
write decimal
𝟏 𝟏
equivalents to , ,
𝟑
𝟒 𝟐
𝟒
Use of place value
chart and dienes
blocks
High
Find the effect of
dividing a one- or
two-digit number
by 10 and 100,
identifying the
value of the digits
in the answer as
ones, tenths and
hundredths
Low
Recognise and
write decimal
equivalents of any
number of tenths or
hundredths
Level 4
Read, write, order
and compare
numbers with up to
two decimal places
Know that 20
hundredths=
2/10=0.2
High
Low
Read, write, order
and compare
numbers with up to
three decimal
places
Associate a
fraction with
division and
calculate decimal
fraction
equivalents [for
example, 0.375] for
a simple fraction
[for example 3/8]
Recognise and use
thousandths and
relate them to
tenths, hundredths
and decimal
equivalents
Read and write
decimal numbers
as fractions [for
example, 0.71 =
𝟕𝟏
]
𝟏𝟎𝟎
Rounding
decimals
Calculating
decimals
Solving
problems
with decimals
Add and subtract
amounts of money to
give change, using
both £ and p in
practical contexts
20% Using and applying 50% Number 20% Measures 10% Handling Data Count up and
down in tenths;
recognise that
tenths arise from
dividing an object
into 10 equal parts
and in dividing
one-digit numbers
or quantities by 10
Round decimals with one decimal place
to the nearest whole number
Round decimals
with two decimal
places to the
nearest whole
number
Round decimals
with three decimal
places to the
nearest whole
number and to one
decimal place
Add and subtract
decimals to one
decimal place
without crossing
boundaries
Understanding of
division of multiples
of 10, 100, 1000 by
10, 100 or 1000 e.g.
20÷100= 0.2
Multiply and divide
whole numbers and
those involving
decimals by 10, 100
and 1000
Add and subtract
decimals to two
decimal places
without crossing
boundaries
Add and subtract
decimals to one
decimal place
crossing the tenth
boundary
Add and subtract
decimals to two
decimal places
crossing the
hundredths
boundary into the
tenths
Estimate, compare and calculate different measures, including
money in pounds and pence
Low: Solve simple money problems with use of concrete
materials.
High: Solve different problems up to one decimal place with use
of length cm, m, km and mass kg, g, capacity l.
342÷ 100=
0r
34.2÷10=
Solve simple
measure and
money problems
involving fractions
and decimals to
two decimal places
Solve problems
involving number
up to three decimal
places
e.g. race which
person came first
with times given to
3dp.
Solve problems
which require
answers to be
rounded to
specified degrees
of accuracy
When decimal is
recurring to use
correct notation.
Multiply one-digit
numbers with up to
two decimal places
by whole numbers
1.34 x 4
Recall and use
equivalences
between simple
fractions, decimals
and percentages,
including in
different contexts.
Multiply one-digit
numbers with up to
two decimal
places by whole
numbers
1.34 x 37
Use written division
methods in cases
where the answer
has up to one
decimal place
Use all four
operations to solve
problems involving
measure [for
example, length,
mass, volume,
money]
(The above
objective has been
split over high 4
and low 5.)
Use all four
operations to solve
problems involving
measure [for
example, length,
mass, volume,
money] using
decimal notation,
including scalinge.g. ratio
(The above
objective has been
split over high 4
and low 5.)
Level 5
Identify the value
of each digit in
numbers given to
three decimal
places and
multiply and divide
numbers by 10, 100
and 1000 giving
answers up to
three decimal
places
Use written division
methods in cases
where the answer
has up to two
decimal places
High
Recall and use
equivalences
between simple
fractions, decimals
and percentages,
including in
different contexts.
Percentages
Level 2
Blue – Year 2
Low
Red – Year 3
Level 3
Green – Year 4 Purple – Year 5 Orange – Year 6
High
Low
Understand per cent as meaning number of parts per hundred. Relate simple percentages to hundredths and find such percentages of quantities with an understanding of fractions. E.g. know that 50% is equivalent to half, so find 50% of a quantity by halving it.
Level 4
Recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal Black – Guidance and exemplars
20% Using and applying 50% Number 20% Measures 10% Handling Data High
Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts. Low
Apply knowledge of fractions to find any percentage equivalents using these to solve problems. e.g. 2 different percentages of 2 different values, which is better value, which is more etc... Level 5
65% of xx = 200. What was xx? Prices after and before discounts. Use of inverse and mixture of operations to solve amounts
Solve problems which require knowing percentage and decimal Solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison 𝟏
equivalents of , 𝟏 𝟏 𝟐 𝟒
𝟐
, , , and 𝟒 𝟓 𝟓 𝟓
those fractions with a denominator of a multiple of 10 or 25 High
Data Handling
Level 2
Interpret
data
Interpret and
construct simple
pictograms, tally
charts, block
diagrams and
simple tables
Blue – Year 2
Low
Red – Year 3
Level 3
Green – Year 4 Purple – Year 5 Orange – Year 6 Black – Guidance and exemplars
High
Interpret and present data using bar charts, pictograms and
tables
Low:
Read and interpret data where parts of an image or block
are used to represent a single piece of data. E.g. using a
quarter of a symbol to represent a single piece of data when
the key indicates one symbol represents 4 objects.
Scale represented as 2, 5, 10
Middle:
Where symbols represent more than one e.g. a whole symbol
represents 100 and therefore ¼ of the symbol represents 25.
Estimate between the markers when scales of 5, 10, 20, 100
are used. Is it closer to 20, 25 30
Low
Interpret and
present discrete
data using
appropriate
graphical
methods,
including bar
charts
(The above
objective has
been split
between low 4
and mid-4.)
Level 4
Answer questions
using simple
pictograms, tally
charts, block
diagrams.
Where the scale
is 1 or 2. Where
the images
represent 1 or 2.
Where the
numbers are
within level 2.
Solve one-step and two-step questions [for example, ‘How
many more?’ and ‘How many fewer?’] using information
presented in scaled bar charts and pictograms and tables
Low: Solve problems such as 'Which category has the most
objects in it?'
Middle: Solve problems such as 'Order the categories by the
number of objects they contain'.
High: Solve problems about the categories using comparison,
sum and difference and make up some questions of their
own about the situation.
Solve comparison,
sum and
difference
problems using
information
presented in bar
charts,
pictograms,
tables and other
graphs
Low
Level 5
High
Interpret and
present
continuous data
using appropriate
graphical
methods,
including time
graphs
(The above
objective has
been split
between low 4
and mid-4.)
Complete, read and
interpret information in
tables, including
timetables
Read and interpret
more complex
timetables where
information has to be
inferred from the
information displayed.
Solve problems using
timetables such as 'I
need to be in
Plymouth by 10 a.m.
Which is the latest
train from Bodmin I
can catch and be
there in time?' E.g.
Where it an express
train
Extend
understanding f
line graphs to
interpret scatter
graphs and
conversion
graphs. Interpret
and construct
simple pie charts
where fractions
are easily
identifiable. E.g.
segments that
represent halves,
quarters and
eighths
percentages are
linked to the size
of the segments
50%, 25%, 75%,
10%
Interpret and
construct more
complex pie
charts where
more difficult
fractions are
used-e.g. 2/3
or sixths, a
mixture of
denomination
of fractions e.g.
¼, 1/3, 5/12 or
percentages
are linked to
the size of the
segmentsmoving to
12.5%, 23%,
47%
Interpret and
construct pie
charts and line
graphs and use
these to solve
problems
Solve comparison,
sum and
difference
problems using
information
presented in a
line graph
Interpret and use time
graphs to solve
problems where a
time interval has to be
calculated/
converted.
Begin to
understand the
purpose of the
calculation of
the mean and
the process for
the calculation
of the mean
comparing these
to other types of
averagemedian, range,
mode
Calculate and
interpret the
mean as an
average.
Evaluate use of
types of
average. Which
is the most
appropriate
and explain
why.
High:
Begin to convert simple block graphs into bar charts.
Interpret and refine construction of bar charts to be
appropriate for discrete data, e.g. bars separated and
continuous grouped data e.g. bars adjacent to one another.
Identify which graph is more appropriate for the data they
are presenting.
Solve
problems
involving
data
High
20% Using and applying 50% Number 20% Measures 10% Handling Data