Year 5 Maths
Age-related expectations of what your child should know
by the end of Year 5
Explanations and ideas of how to help your child
Place Value
Read, write, order and compare numbers to at least
1 000 000 and determine the value of each digit.
Count forwards or backwards in steps of powers of 10 for
any given number up to 1 000 000.
Interpret negative numbers in context, count forwards and
backwards with positive and negative whole numbers,
including through zero.
Round any number up to 1 000 000 to the nearest 10, 100,
1000, 10 000 and 100 000.
Solve number problems and practical problems that involve
all of the above.
Read Roman numerals to 1000 (M) and recognise years
written in Roman numerals.
Can your child form a number with up to six digit cards
and write it in words?
Ask your child to write the number of megabytes on a
memory stick in words and numerals.
Ask your child to can count backwards from a certain
number, for example, 962,471 in steps of 100,000,
10,000, 1000, 100 and 10.
Can your child reduce any six-digit number to zero by
subtracting the appropriate number of each of the
appropriate powers of 10?
Can your child answer these questions:
'Which is colder ‒2⁰C or ‒10⁰C?'
‘Which is warmer -1⁰C or -9⁰C?’
You could discuss problems with your child such as how to
identify the biggest change in temperature between day
and night on the planets in the solar system.
Can your child round 306,812 to the nearest 10,000?
Ask your child if they can identify the largest multiple of
9 that rounds to 250,000 to the nearest 100.
Ask your child problems such as:
'What is the term-to-term rule for the sequence 14.5,
13, 11.5? Can you write down the next two terms?’
Can your child interpret the date written using Roman
numerals? Can they identify the year a film was made?
Addition & Subtraction
Add and subtract whole numbers with more than 4 digits.
Please look at our Calculations Policy to see the different
written methods taught.
Add and subtract whole numbers with more than 4 digits,
including using formal written methods (columnar addition
and subtraction).
Add and subtract numbers mentally with increasingly large
numbers (example, 12 462 - 2300 = 10 162)
Please look at our Calculations Policy to see the different
written methods taught.
Use rounding to check answers to calculations and
determine, in the context of a problem, levels of accuracy.
Can your child check the answer to 56,713 ‒ 3156 + 954
by rounding to 60,000 ‒ 3000 + 1000 = 58,000
Solve addition and subtraction multi-step problems in
contexts, deciding which operations and methods to use and
why.
Can your child work out these questions mentally?
23,712 ‒ 1610 = 22,102.
45,762 + ? = 105,761.
Can your child also check the reasonableness of the
answer to a problem such as:
'I buy a book at £6.99 and pay with a £20 note. How
much change should I get?' by noticing that an answer of
£3.01 is too small.
Try giving your child word problems such as:
'It is 560 km from Penzance to Manchester and Ali has
completed 218 km of the journey. How far
must he now travel until he is 100 km from Manchester?',
Your child can make up problems involving several steps
and prompting different calculation strategies such as
'It is 560 km from Penzance to Manchester. Ali drives
315 km and notes that he is 112 km from Birmingham.
How far is it from Birmingham to Manchester?'
Multiplication & Division
Identify multiples and factors, including finding all factor
pairs of a number, and common factors of two numbers.
Give your child a set of number cards up to 50. Ask your
child to pick out a card and identify the the multiples and
factors. For example, the factors of 40 are as 1, 40; 2,
20; 4, 10; 5, 8.
Can your child recognise common factors of two numbers,
e.g. 5 is a common factor of 40 and 35.
Know and use the vocabulary of prime numbers, prime
factors and composite (non-prime) numbers.
Establish whether a number up to 100 is prime and recall
prime numbers up to 19.
Multiply numbers up to 4 digits by a one- or two-digit
number using a formal written method, including long
multiplication for two-digit numbers.
Multiply and divide numbers mentally drawing upon known
facts.
Divide numbers up to 4 digits by a one-digit number using
the formal written method of short division and interpret
remainders appropriately for the context.
Ask your child if they can list the prime numbers up to
19.
Can your child apply their knowledge of the prime
numbers below 20 to quickly test numbers up to 200 to
ascertain whether they are prime?
Please look at our Calculations Policy to see the different
written methods taught.
Try asking your child questions such as:
‘Calculate 25 x 80 x 2.5’
Encourage your child to solve problems such as
'Use the numbers 6, 3, 7, 9, 25 and 50 once each, and use
any of the four operations to make the target number of
573' (similar to Countdown).
Please look at our Calculations Policy to see the different
written methods taught.
Multiply and divide whole numbers and those involving
decimals by 10, 100 and 1000.
Can your child work out:
2.3 x 1000 = 2300
98 ÷ 1000 = 0.098
Discuss with your child how the digits move the left
(when multiplying) and to the right (when dividing).
Recognise and use square numbers and cube numbers, and
the notation for squared (2) and cubed (3).
Help your child identify whether a given number is a
square number or a cube number up to 100. Can they
interpret 6² as 6 x 6 = 36 and 2³ as 2 x 2 x 2 = 8?
Help your child to sort the numbers below 200 into a
Venn diagram with two sets: square numbers and cube
numbers.
Can your child also interpret
3⁴ as 3 x 3 x 3 x 3 = 81 and extend the idea to higher
powers?
Encourage your child to solve problems such as:
'I am thinking of a two-digit number. The difference
between its digits is a cube number and the tens digit is a
square number. It is a multiple of 13. What is the
number?'
Solve problems involving multiplication and division including
using their knowledge of factors and multiples, squares and
cubes.
Solve problems involving addition, subtraction,
multiplication and division and a combination of these,
including understanding the meaning of the equals sign.
Discuss problems with your child such as:
'Sam buys seven bottles of water and gets 20p change
when he pays with a £10 note. How much was each
bottle?'
Solve problems involving multiplication and division,
including scaling by simple fractions and problems involving
simple rates.
Can your child solve problems such as:
'Two rulers cost 60p. How much do five rulers cost?'
Your child could make up problems such as:
'Helen cycles 40 km in two hours. How far would she
cycle in 20 minutes at the same speed?'
Fractions (including Decimals & Percentages)
Compare and order fractions whose denominators are all
multiples of the same number.
Identify, name and write equivalent fractions of a given
fraction, represented visually, including tenths and
hundredths.
Give your child two fractions such as 2/3 and 13/18. Can
they identify the smaller out of the two?
Can they think of a fraction that is between them?
Can your child use a fraction wall to show the relationship
between halves, thirds, quarters, sixths and
Recognise mixed numbers and improper fractions and
convert from one form to the other and write mathematical
statements > 1 as a mixed number [for example, 2/5 + 4/5 =
6/5 = 11/5].
Add and subtract fractions with the same denominator and
denominators that are multiples of the same number.
twelfths, and use it to identify groups of equivalent
fractions? Are they able to explain why some have
several equivalent fractions and others do not have any?
Help your child to recognise that improper fractions have
a numerator that is larger than the denominator and so
can be written as a combination of whole numbers and
proper fractions.
For example, 8/6 can be written as 1 and 2/6.
Can your child calculate 2/6 + 5/6? (same denominator)
Can your child calculate 3/4 + 5/12?
Multiply proper fractions and mixed numbers by whole
numbers, supported by materials and diagrams.
Your child could draw diagrams to help them work out
5 x 3/8 = 15/8 or 1 7/8
and hence deduce that
5 x 2 3/8 = 10 + 15/8 = 11 7/8
Read and write decimal numbers as fractions [for example,
0.71 = 71/100].
Ask your child what decimal numbers would be as
Recognise and use thousandths and relate them to tenths,
hundredths and decimal equivalents.
Ask your child to write 1/1000 as a decimal (0.001).
Help your child to recognise that ten-thousandths equal
one-hundredth and 100- thousandths equal one-tenth.
Can your child round 4.76 to the nearest whole number
(5) and to one decimal place (4.8).
Ask your child if they can identify a number that rounds
to 6.6 to one decimal place and is the smallest number for
which this is true.
Round decimals with two decimal places to the nearest
whole number and to one decimal place.
fractions e.g. 0.51 as 51/100 and 0.126 as 126/1000
Read, write, order and compare numbers with up to three
decimal places.
Write down different decimal numbers on pieces of card,
for example 2.608 and 2.86. Can your child choose the
larger number out of the two? Can they write down a
number between them?
Solve problems involving number up to three decimal places.
Discuss problems such as these with your child:
'I have 2m of ribbon and use lengths of 12.7 cm, 87.5 cm,
23 cm and 47 cm. How much do I have left?'
'I have 12 m of wood split into 1.5 m lengths. I need ten
80 cm lengths, fifteen 15 cm lengths and seven 16 cm
lengths. Can I cut this from my wood?'
Help your child to recognise that 1%,
one-hundredth, 0.01 and 1/100 all represent the same
amount.
Support your child to write percentages as fractions and
decimals e.g. 45% as 45/100 and 0.45. Can they simplify
45/100 to 9/20?
Encourage your child to work out the best deal when
shopping, for example:
‘Which is more 25% off or 1/3 off the full amount?’
'Which is more: 20% off or 0.75 off the full amount?'
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.
Solve problems which require knowing percentage and
decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those
fractions with a denominator of a multiple of 10 or 25.
Measurement
Convert between different units of metric measure (for
example, kilometre and metre; centimetre and metre;
centimetre and millimetre; gram and kilogram; litre and
millilitre).
Understand and use approximate equivalences between
metric units and common imperial units such as inches,
pounds and pints.
Support your child to apply their knowledge of
multiplying and dividing by 10, 100 and
1000 and the relationship between
metric units to convert 3.1 kg to 3100 g
and 250 cm to 2.5 m.
Discuss the equivalences of 2.5 cm = 1 inch, 2(.2) pounds =
1 kg to convert between metric and imperial units. You
could then discuss equivalences around the house,
perhaps a bag of flour or a bottle of milk.
Measure and calculate the perimeter of composite
rectilinear shapes in centimetres and metres.
Draw an ‘L shape’ for your child on a piece of paper. Can
they measure the perimeter? Can they estimate the
perimeter first?
Calculate and compare the area of rectangles (including
squares), and including using standard units, square
centimetres (cm2) and square metres (m2) .
Encourage your child to solve problems such as:
'A rectangle has a perimeter of 20 cm. Its length and
width are whole numbers. What possible areas could it
have? Which is the largest area?'
Draw irregular shapes for your child on squared paper.
Can your child estimate the area of the shape by using
the squares and parts of squares?
Estimate the area of irregular shapes.
Estimate volume [for example, using 1 cm3 blocks to build
cuboids (including cubes)] and capacity [for example, using
water].
Give your child real life scenarios such as:
‘Can you put enough water in the jug to pour drinks for
the family?’
‘Can you fill the kettle so there is enough water to make
three cups of tea?’
Solve problems involving converting between units of time.
Your child could try solving problems like these:
'What date is it when you reach the one thousandth hour
of the year?'
'What date was it when you reached one million minutes
old?'
Try giving your child problems such as:
'I need 0.6 m of ribbon and my friend needs six times as
much. We buy 5 m between us. How much will be left?’
You could then ask your child how much will be left in
inches.
Use all four operations to solve problems involving measure
[for example, length, mass, volume, money] using decimal
notation, including scaling.
Geometry: Properties of Shape
Identify 3-D shapes, including cubes and other cuboids,
from 2-D representations.
You could give your child drawings of 3d shapes and ask
them to identify each one.
Know angles are measured in degrees: estimate and
compare acute, obtuse and reflex angles.
Draw different angles for your child. Can they estimate
the size of the angles to within 5⁰?
.
Draw given angles, and measure them in degrees (0).
Using a protractor, ask your child to draw different
angles, for example 48⁰ or 195⁰.
Could they draw a triangle with angles of 48⁰, 60⁰ and
72⁰?
Identify:
angles at a point and one whole turn (total 360°);
angles at a point on a straight line and 1/2 a turn (total
180°)
Support your child to identify in geometric diagrams
instances where angles meet at a point and sum to 360⁰
and instances where angles lie on a straight line and so
sum to 180⁰.
Use the properties of rectangles to deduce related facts
and find missing lengths and angles.
Can your child solve problems such as:
'The perimeter of a rectangle is 20 cm. One side is 4 cm
long. How long are the other sides?'
Can your child use the given dimensions of a compound
shape to help calculate missing side lengths?
You could cut out different polygons for your child to
sort. Your child could sort them according to whether
they have equal sides and whether they have equal angles.
Support your child to understand that polygons with
equal sides and equal angles are regular polygons.
Distinguish between regular and irregular polygons based on
reasoning about equal sides and angles.
Geometry: Position & Direction
Identify, describe and represent the position of a shape
following a reflection or translation, using the appropriate
language, and know that the shape has not changed.
Discuss with your child the meaning of ‘reflection’ and
‘translation’. Look at different shapes, which have been
reflected or translated. Discuss how the shape has not
changed in any way.
Statistics
Solve comparison, sum and difference problems using
information presented in a line graph.
Complete, read and interpret information in tables,
including timetables.
Your child could measure the temperature in your house
or garden throughout the course of a day and draw a line
graph to show the results. You could ask them questions
such as:
'When is it warmest? What is the lowest temperature?'
You could look at different bus or train timetables with
your child.
Give your child questions such as:
‘I get to the bus stop at 8:35 a.m. and catch the first bus
that arrives. What time do I arrive at the town centre?'
by interpreting an appropriate bus timetable.
Can your child complete timetables and deduce what is
needed from the available information?