The Year 5 Learner
Working mathematically
By the end of year 5, children will apply their mathematical experiences to explore ideas and raise relevant
questions, constructing complex explanations and reasoned arguments. They will be able to solve a wide
variety of complex problems which require sustained concentration and demand efficient written and mental
methods of calculations. These will include problems relating to fractions, scaling (times as many), converting
between units of measure and employ all four operations (+, -, x, ÷).
Number
•
Counting and understanding numbers
Children extend and apply their knowledge of place value for numbers up to one million, rounding, estimating
and comparing them (including decimals and negative numbers) in a variety of situations. They are introduced
to powers of ten and are able to count forwards or backwards from any number (for example, -50, -5… 5,
50, 500, 5000...). Through investigations, they will discover special numbers including factors, primes,
square and cube numbers.
•
Calculating
Children will be fluent in a wide range of mental calculation strategies for all operations and will select the
most appropriate method dependent on the calculation. They apply their knowledge of place value fluently to
multiply and divide numbers (including decimals) by 10, 100 and 1000. When mental methods are not
appropriate, they use formal written methods of addition and subtraction accurately. They continue to develop
their understanding of the formal methods through hands-on resources and use their known facts within long
multiplication (up to 4 digit numbers by 2 digit numbers e.g. 2345 x 68) and short division (up to 4 digit
numbers by 1 digit number e.g. 2345 ÷ 7) which may result in remainders. They solve multi-step problems in
meaningful contexts and decide which operations to use.
•
Fractions including decimals and percentages
Children secure their strong understanding that fractions express a proportion of amounts and quantities (such
as measurements), shapes and other visual representations. Children extend their knowledge and understanding
of the connections between fractions and decimals to also include percentages. They will be able to derive
simple equivalences (e.g.
67% = 67/100 = 0.67) and recall percentage and decimal equivalents for ½, ¼, 1/5,
2/5, 4/5 and fractions with a denominator of a multiple of 10 or 25 (e.g. 25% = 25/100).
They order, add and subtract fractions, including mixed numbers and those whose denominators are multiples
of the same number, for example
3
10
+
1
5
=
3
10
+
2
10
=
5
10
=
1
.
2
Using apparatus, images and models, they multiply
proper fractions and mixed numbers by whole numbers. Children continue to develop their understanding of
fractions as numbers, measures and operators by finding fractions of numbers and quantities in real life
situations.
Measurement
Through a wide variety of practical experiences and hands-on resources, children extend their understanding of
measurement. They convert larger to smaller related units of measure and vice-versa including length, capacity,
weight, time and money.
Children will convert between imperial (such as inches, pints, miles) and metric units
(such as centimetres, litres, kilometres). Children will measure, calculate and solve problems involving perimeter
of straight-sided, right-angled shapes (rectilinear) and learn to express this algebraically such as, 4 + 2b =
20. They find and measure the area of these shapes with increasing accuracy. They begin to estimate volume.
Geometry
Children will measure, identify and draw angles in degrees, developing a strong understanding of acute,
obtuse, reflex and right angles. They use this knowledge to find missing angles and lengths in a variety of
situations, including at a point, on a straight line and within a shape. Children will move (translate), reflect
shapes and describe their new positions.
Language will be used with increasing sophistication to compare
and classify shapes based on their properties and size. They will be able to visualise 3-D shapes from 2-D
diagrams. They will use their understanding or shapes to solve problems.
Statistics
Children will complete, read and solve comparison, sum and difference problems using information presented in
graphs, charts and tables, including timetables. They begin to decide which representations of data are the
most appropriate and are able to justify their reasons.
Year 5 Programme of Study
Maths – Number
Understanding the number system
Calculating
Arithmetical laws and relationships
Year 5 Focus:
 u s e s t h e c o m m u t a t iv e , a s s o c ia t iv e a n d d is t r ib u t iv e ‘
r u l es ’w h en
Number and place value
domains e.g.
I can understand and apply the knowledge of place value e.g. reads, writes,
orders, compares, estimates, multiplies and divides numbers by 10, 100 and
1000 up to 1 000 000 and to 3 decimal places and as fractions
I can round decimals with two decimal places to the nearest whole number
solving calculations in the four operations and other mathematical
- distributivity can be expressed as a(b+c)= ab + ac
- construct equivalence statements (3 x 270 = 3 x 3 x 9 x 10 = 9² x
10)
- finding the volume of a cuboid
and to one decimal place and any whole number up to 1,000,000 to the
 r e c o g n is e s , d es c r ib es u s in g c o r r e c t v o c a b u l a r y , a n d u s e s n u m b er
I can count fluently forwards and backwards to include:
- multiples, all factor pairs for a given number and common factors for
nearest 10, 100, 1000, 10,000, and 100,000
- powers of 10 from any given number up to 1,000,000
- including through zero and interprets negative numbers in context
I can read Roman numerals to 1000 (M) and recognise years written in
Roman numerals
I can recognise and convert mixed numbers, improper fractions and
recognise and use thousandths and relates to tenths, hundredths and
patterns and relationships to establish e.g.
two numbers
- prime factors and composite (non-prime) numbers to 100 (recall primes
to 19)
- square and cube numbers (and uses notation and recall all square
numbers to 144)
decimal equivalents
Mental fluency
I can compare and order fractions whose denominators are all multiples of
 j u s t if ie s s o l u t io n s a n d determines in the context of the problem levels
I can identify equivalent fractions of a given fraction represented visually
 u s e s a r a n g e o f m en t a l m e t h o d s o f a d d it io n a n d s u b t r a c t io n w it h in
the same number
I can recognise and show approximate proportions of a whole and use unit
and non-unit fractions, decimals and percentages to describe these,
I can solve number problems and practical problems within the context of
the fluency focus
of accuracy using estimation, rounding and use of inverse operation
the fluency focus e.g. decimal complements to 1
 m u l t ip l ie s a n d d iv ides numbers mentally using known facts 5C6a and
uses derived facts e.g. 2.3 x 4 = 9.2
 m u l t ip l ie s a n d d iv id es w h o le n u m b e r s a n d t h o s e in v o l v in g d e c im a ls
by 10, 100 and 1000
Written fluency
 u s e s f o r m a l w r it t e n c o l u m n a r m e t h o d s o f a d d it io n a n d s u b t r a c tion
within the fluency focus and reasons why they are appropriate
 m u l t ip l ie s n u m b er s w it h u p t o f o u r d ig it s b y a o n e o r t w o d ig it
number using a formal written method, including long multiplication for
two digit numbers
 d iv id es n u m b e r s w it h u p t o f o ur digits by a one digit number using
the formal written method of short division and interprets remainders
appropriately for the context
Measurement
Metric / imperial measures
Fractions, decimals and percentages
 c o n v er t s b e t w e en d if f e r e n t u n it s o f m e t r ic u n it s o f m ea s u r e f o r le n g t h ,
 a d d s a n d s u b t r a c t s f r a c t io n s w h o s e d en o m in a t o r s a r e m u ltiples of the
capacity and mass, e.g. 1.2 kg = 1200 g; how many 200 ml cups can be
filled from a 2 litre bottle?; write 605cm in metres
 u n d e r s t a n d s a n d u s e a p p r o x im a t e e q u iv a le n c e s b e t w e en m etric units and
common imperial units such as inches, pounds and pints
same number
 m u l t ip l ie s p r o p er f r a c t io n s a n d m ix e d n u m b er s b y w h o le n u m b e r s
supported by materials and diagrams
Solving numerical problems (using a range of mental and written
methods across routine and non-routine problems)
Perimeter, Area, Volume
 m ea s u r e s a n d c a l c u l a t e s t h e p er im e t er o f c o m p o s it e r e c t ilin ea r s h a p es in
centimetres and metres
- calculates the perimeter of rectangles and related composite shapes
including using the relations of perimeter or area to find unknown lengths
- missing measure questions can be expressed algebraically
e.g. 4 + 2b = 20 for a rectangle of sides 2 cm and b cm and perimeter
of 20 cm
 s o l v e s n u m erical problems within the fluency focus and through a
range of contexts including understanding the meaning of the = sign
e.g.
- addition and subtraction multi-step problems in contexts deciding
which operation to use and why
- using knowledge of factors, multiples, squares and cubes
- scaling by simple fractions and problems involving simple rates
- multiplying and dividing by powers of 10 in scale drawings
 c a l c u l a t es a n d c o m p a r e s the area of rectangles (including squares), and
- using all four operations to balance equations (33 = 5 x a)
(m²) and estimate the area of irregular shapes
Algebra
including using standard units, square centimetres (cm²) and square metres
 e s t im a t es v o l u m e , e.g.: using 1cm³ blocks to build cuboids (including
cubes) and capacity (e.g. using water)
Chronology
 c a l c u l a t es t h e d u r a t io n o f a n e v en t u s in g a p p r o p r ia t e u n it s o f t im e , e.g.
‘a film starts at 6:45pm and finishes at 8:05pm. How long did it last?’
- calculates time durations that bridge the hour
 r ea d s a n d in t e r p r e t s t im e t a b l es
Solve problems
 s o l v e s p r o b l em s in v o lv in g c o n v e r ting between units of time
 u s e s a ll f o u r o p e r a t io n s t o s o lv e p r o b le m s in v o l v in g m e a s u r e ( a : m o n e y ;
b: length; c: mass / weight; d: capacity / volume) using decimal notation,
including scaling
 b e g in s t o w r it e e q u ations to express situations
 l o c a t e s p o in t s a n d s o lv e s p r o b le m s in t h e f ir s t q u a d r a n t
Statistics
Geometry
Processing, representing and interpreting data
Properties of shape
 c o m p le t e s , r ea d s a n d in t e r p r e t s in f o r m a t io n in t a b le s , in c l u d in g t im e t a b les ( 5 
S 1) u s e s t h e p r o p e r t ies o f r e c t a n g l es t o d ed u c e r el a t e d f a c t s a n d f in d
 s o l v e s c o m p a r is o n , s u m a n d d if f e r e n c e p r o b l em s u s in g in f o r m a t io n
presented in a line graph
- collects, represents and interprets continuous data
- decides upon an appropriate scale for a graph, e.g. labelled divisions
representing 2, 5, 10, 100
- reads between the labelled divisions, e.g. reads 17 on a scale labelled in
fives
missing lengths and angles
 d is t in g u is h e s b e t w ee n regular and irregular polygons based on
reasoning about equal sides and angles
- uses conventional markings for parallel lines and right angles
 id e n t if ies 3 D s h a p e s in c l u d in g c u b e s a n d o t h e r c u b o id s , f r o m 2 D
representations
 kn o w s a n g l es a r e m e a s u r ed in degrees: estimate and compare acute,
obtuse and reflex angles
 id e n t if ies :
- angles at a point and one whole turn (total 360°)
- angles at a point on a straight line and ½ a turn (total 180°)
- other multiples of 90°
 d r a w s g iv e n a n g l es a n d m easure them in degrees(°)
 u s e s t h e t e r m d ia g o n a l a n d m a ke s c o n je c t u r es a b o u t t h e a n g le s
formed between sides, and between diagonals and parallel sides and
other properties of quadrilaterals
Position and direction
 id e n t if ies , d e s c r ib e s a n d r ep r e s e n t s the position of a shape
following a reflection or translation, using the appropriate language,
and know that the shape has not changed
- translates shapes horizontally or vertically
- uses a grid and co-ordinates in the first quadrant to plot the
reflection in a mirror line presented in lines that are parallel to the
axes
- begins to use the distance of vertices from the mirror line to reflect
shapes more accurately