Fractions, Decimals and Percentages
Year 1
Year 2
Pupils should count in
fractions up to 10,
starting from any
number and using
the1/2 and 2/4
equivalence on the
number line (Non
Statutory Guidance)
Year 3
count up and dow n in
tenths
recognise, find and name
a half as one of tw o equal
parts of an object, shape
or quantity
recognise, find, name
recognise, find and
w rite fractions of a
discrete set of objects:
unit fractions and nonunit fractions with
small denominators
recognise that tenths
arise from dividing an
object into 10 equal
parts and in dividing
one – digit numbers or
quantities by 10.
recognise and use
fractions as numbers:
unit fractions and nonunit fractions with
small denominators
1
and w rite fractions / ,
1
2
4
recognise, find and name
a quarter as one of four
equal parts of an object,
shape or quantity
3
3
/ , / and / of a length,
4
4
shape, set of objects or
quantity
COUNTING IN FRACTIONAL STEPS
Year 4
count up and dow n in hundredths
RECOGNISING FRACTIONS
recognise that hundredths arise w hen
dividing an object by one hundred and
dividing tenths by ten
Year 5
Year 6
recognise and use thousandths and
relate them to tenths, hundredths and
decimal equivalents
(appears also in Equivalence)
COMPARING FRCTIONS
compare and order
unit fractions, and
fractions with the
same denominators
compare and order fractions whose
denominators are all multiples of the
same number
DECIMALS
compare numbers w ith the same number
of decimal places up to tw o decimal places
read, w rite, order and compare
numbers w ith up to three decimal
places
round decimals w ith one decimal place to
round decimals w ith tw o decimal
the nearest w hole number
places to the nearest w hole number
and to one decimal place
EQUIVALENCE (INCLUDING FRACTIONS, DECIMALS AND PERCENTAGES)
compare and order fractions, including
fractions >1
identify the value of each digit in numbers
given to three decimal places
solve problems w hich require answers to be
rounded to specified degrees of accuracy
Fractions, Decimals and Percentages
w rite simple fractions
1
e.g. / of 6 = 3 and
2
recognise the
2
equivalence of / and
recognise and show ,
using diagrams,
equivalent fractions
w ith small
denominators
recognise and show , using diagrams,
families of common equivalent fractions
identify, name and w rite equivalent
fractions of a given fraction,
represented visually, including tenths
and hundredths
use common factors to simplify fractions;
use common multiples to express fractions
in the same denomination
recognise and w rite decimal equivalents of
any number of tenths or hundredths
read and w rite decimal numbers as
associate a fraction w ith division and
calculate decimal fraction equivalents (e.g.
4
1
/.
2
71
fractions (e.g. 0.71 = /
100
add and subtract
fractions with the
same denominator
w ithin one w hole (e.g.
5
1
6
7
3
0.375) for a simple fraction (e.g. / )
8
recall and use equivalences betw een simple
fractions, decimals and percentages,
including in different contexts.
add and subtract fractions with different
denominators and mixed numbers, using the
concept of equivalent fractions
recognise mixed numbers and
improper fractions and convert from
one form to the other and w rite
mathematical statements > 1 as a
/ + / = /)
7
)
recognise and use thousandths and
relate them to tenths, hundredths and
decimal equivalents
recognise and w rite decimal equivalents to recognise the per cent symbol (%) and
1
1
3
understand that per cent relates to
/ /
/
4
2
4
“number of parts per hundred”, and
w rite percentages as a fraction with
denominator 100 as a decimal fraction
ADDITION AND SUBTRACTION OF FRACTIONS
add and subtract fractions with the same
add and subtract fractions with the
denominator
same denominator and multiples of the
same number
7
2
4
6
1
mixed number (e.g. / + / = / = 1 / )
5
5
5
5
MULTIPLICATION AND DIVISION OF FRACTIONS
multiply proper fractions and mixed
numbers by w hole numbers,
supported by materials and diagrams
multiply simple pairs of proper fractions,
w riting the answ er in its simplest form (e.g.
1
1
1
/ × / = /)
4
2
8
multiply one-digit numbers w ith up to tw o
decimal places by w hole numbers
divide proper fractions by whole numbers
1
1
(e.g. / ÷ 2 = / )
3
6
MULTIPLICATION AND DIVISION OF DECIMALS
find the effect of dividing a one- or tw odigit number by 10 and 100, identifying the
value of the digits in the answ er as ones,
tenths and hundredths
multiply one-digit numbers w ith up to tw o
decimal places by w hole numbers
multiply and divide numbers by 10, 100 and
1000 w here the answers are up to three
decimal places
identify the value of each digit to three
decimal places and multiply and divide
Fractions, Decimals and Percentages
numbers by 10, 100
and 1000 w here the answers are up to three
decimal places
associate a fraction w ith division and
calculate decimal fraction equivalents (e.g.
0.375) for a simple fraction
(e.g. 3/8)
use w ritten division methods in cases w here
the answ er has up to tw o decimal places
PROBLEM SOLVING
solve problems that involve all of the
above
solve problems involving increasingly
harder fractions to calculate quantities,
and fractions to divide quantities,
including non-unit fractions where the
answ er is a w hole number
solve simple measure and money
problems involving fractions and
decimals to tw o decimal places.
solve problems involving numbers up to
three decimal places
solve problems w hich require knowing
1
percentage and decimal equivalents of / ,
1
1
2
2
4
/ , / , / , / and those w ith a denominator
4
5
5
5
of a multiple of 10 or 25.