The Year 4 Learner
Working mathematically
By the end of year 4, children will apply their understanding of maths to solve a wide variety of problems
with more than one step and be expected to prove their thinking through pictures, jottings and conversations.
They will continue to make connections between different areas of maths and ask their own questions, working
in an organised way to find solutions which help them identify common patterns or any errors more easily.
Number
•
Counting and understanding numbers
Children will be very familiar with numbers that have up to 4 digits and will be able to order and compare
by showing them in different ways such as on a tape measure or using hands-on resources.
Using their
understanding of place value (how the value of each digit changes depending on its position in the number),
children will be able to partition (break and make) numbers in different ways e.g. 2345 = 2000 and 300 and
40 and 5 but could also represent this as 1000 and 1000 and 200 and 100 and 40 and 5 or 2000 and
200 and 145.
They will work with numbers securely up to 10,000 and may begin to count beyond in 1s,
10s, 100s and 1000s.
number.
They will use this to help them find 10, 100 or 1000 more or less than any given
They will multiply and divide whole numbers by 10 and 100 and understand that this changes the
value of each digit rather than ‘just adding a 0’.
They will develop their understanding to decimal
hundredths, comparing and ordering these using contexts such as money.
Children will also learn about the
pattern to find any Roman numeral to 100.
Children will develop their expertise when counting forwards and backwards from 0 to include multiples of 6,
7, 9 and 25; decimals with up to 2 places and fractions. They will be able to fluently count in tenths,
hundredths and simple fractions. They will develop their understanding of negative numbers through counting
backwards through 0.
Children will be able to recognise and describe number patterns and relationships
including multiples (e.g. 3, 6, 9, 12 are multiples of 3) and factor pairs (e.g. 1 and 12, 2 and 6, 3 and 4 are
all factor pairs for 12) for known times tables.
•
Calculating
Children will develop various strategies for solving +, -, x, ÷ calculations mentally, using jottings when
appropriate and for checking that their answers are sensible.
Children will be encouraged to share their
methods with others to help them see which work best, are quickest and most accurate. Over the course of the
year, children will become fluent in all multiplication and division facts up to 12 x 12 and apply these facts to
other problems e.g. 232 x 7 = (200 x 7) + (30 x 7) + (2 x 7). Children will use the = sign to demonstrate
equal value e.g. 3 x 8 = 48 ÷ 2 and solve missing number problems e.g. 3 x ? = 48÷2. They will explore
patterns and rules for the times tables they learn and use pictures and objects to support their understanding.
Children will be required to solve problems accurately using the column addition and subtraction methods for
numbers with up to 4-digits and explain how the methods work. They will use apparatus to secure their
understanding of these. This will include addition and subtraction calculations with different numbers of digits
(such as 1286 + 357); and numbers containing 0s (such as 8009 – 3231).
They will use formal written
methods of short multiplication and short division for two and three digit numbers by a single digit.
Children
who become very adept at these types of calculations will be stretched through problems such as those
containing missing numbers so that they know when, if and why they need to use the methods.
•
Fractions including decimals
Children will develop their understanding of fractions by comparing to, or finding a part of, the whole.
Through hands-on resources, pictures or jottings, such as a number line, children will add and subtract two
fractions with the same denominator (e.g. 2/3 + 2/3). Children will solve problems involving fractions such
as ‘find ¾ of 20 litres’ using their knowledge of multiplication and division and through practical equipment.
Children secure their understanding that fractions and decimals are different ways of expressing numbers and
proportions.
Measurement
Children secure their understanding of place value and decimals to record measurements accurately. They use
their understanding of multiplying and dividing by 10, 100 and 1000 to convert between different units of
measure of length (km, m, cm, mm), weight (kg, g) and money (£ and p). Children will link their
understanding of area to multiplication and describe how to find the perimeter of a rectangle quickly. Children
will read and write the time accurately using analogue and digital clocks, including clocks with Roman
numerals.
They will convert between units of time (hours, minutes and seconds). Children estimate, compare,
calculate and solve a variety of problems involving all units of measurement.
Geometry
Children will extend their knowledge of shape to include more unusual quadrilaterals (four-sided shapes) and
triangles. They will use increasingly more specific vocabulary such as parallelogram, rhombus and trapezium;
scalene and isosceles. They refine their understanding of symmetry and solve problems where the shape is not
displayed in its usual way (e.g. it might be on its side). Children find and name different angles and use this
information to decide if a shape is regular or irregular. Children describe position and movement on a grid as
co-ordinates and will plot points to draw 2-D shapes.
Statistics
Children will complete, read and interpret information on bar charts; they will solve problems that involve
finding information in charts, tables and graphs; including time graphs.
Year 4 Programme of Study
Maths – Number
Understanding the number system
Calculating
Arithmetical laws and relationships
Year 4 focus:
 u n d e r s t a n d s a n d a p p lie 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
I can identify, represent and estimate numbers using different
- that 7 x 8 = (5 x 8) + (2 x 8) (distributive) = 7 x 2 x 4
representations
I can count fluently forwards and backwards in multiples of 6, 7, 9, 25
‘rules’ when solving calculations e.g.
(associative)
- ‘balancing expressions’ including those using division, such as 20 + ?
= 100 ÷ 4
I can recognise the place value of each digit in a 4 digit number
 understands the relationship between non-unit fractions and
multiplication and division, to include equivalence and fractions as
operators
I can round any number to the nearest 10, 100 or 1000 and decimals
Mental fluency
and 1000, including negative numbers and hundredths
with one decimal place to the nearest whole number
 u s e s a r a n g e o f m en t a l s t r a t e g ie s f o r a ll four operations appropriate to
context and within the fluency focus
I can recognise that hundredths arise when dividing an object by a
 c o n s id er s t h e r e a s o n a b l en es s o f r e s u l t s b y r e f e r e n c e t o t h e c o n t e x t o r t o
hundred and dividing tenths by ten
the size of the numbers using the skills of estimation and checks accuracy
I can recognise and show equivalent fractions
I can read Roman numerals to 100
I can solve number problems and practical problems within different
contexts
e.g. use of the inverse
 u s e s m ental recall of multiplication facts including all tables up to 12 x
12 and quickly derives corresponding division facts, e.g. uses their
knowledge of tables and place value in calculations with multiples of 100,
such as 600 ÷ 3 = 200 can be derived from 2 x 3 = 6
 u s e s p l a c e v a l u e, kn o w n a n d d er iv ed f a c t s t o m u l t ip ly a n d d iv id e ,
including: multiplying by 0 and 1; dividing by 1; multiplying together three
numbers
 r e c o g n is e s a n d u s es f a c t o r p a ir s a n d c o m m u t a t iv it y in m e n t a l
calculations
Written fluency
 c o m b in e s kn o w le d g e o f n u m b er f a c t s a n d r u l es o f a r it h m e t ic t o s o lv e
written calculations within the fluency focus
 a d d s a n d s u b t r a c t s n u m b e r s w it h u p t o 4
d ig it s u s in g t h e f o r m a l
written methods of columnar addition and subtraction where appropriate
 e s t im a t es a n d u s e s in v e r s e o p e r a t io n s t o c h e c k a n s w er s t o a c a l c u la t io n
 m u l t ip l ie s t w o-digit and three-digit numbers by a one-digit number using
formal written layout
Fractions, decimals and percentages
 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 it h t h e s a m e denominator
 r e c o g n is e s a n d w r it e s d e c im a l e q u iv a le n t s t o ¼ , ½, ¾ 4 F6 a a n d o f a n y
number of tenths or hundredths
 c a l c u l a t es f r a c t io n s o f q u a n t it ies , in c l u d in g n o n-unit fractions where the
answer is a whole number e.g. find ¾ of 20 litres
 f in d s t h e 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
Solving numerical problems (using a range of mental and written methods
across routine and non-routine problems)
 s o l v e s a d d it io n a n d s u b t r a c t io n t w o-step problems in contexts, deciding
which operations and methods to use and why
 s o l v e s p r o b l em s in v o lv in g m u l t ip ly in g a n d a d d in g , in c l u d in g u s in g t h e
distributive law to multiply two-digit numbers by one digit, integer scaling
problems and harder correspondence problems such as n objects are
connected to m objects
 s o l v e s p r o b l em s in v o lv in g in c r ea s in g ly h a r d er f r a c t io n s t o c a l c u l a t e
quantities and fractions to divide quantities, including non-unit fractions
where the answer is a whole number and measure and money problems
involving fractions and decimals to two decimal places
Algebra (in preparation for Year 6 statements)
 b e g in s t o u s e s im p l e f o r m u l a e e x p r e s s ed in w o r d s e . g . r u l es f o r f in d in g
the perimeter of rectilinear shapes
 u s e s a n d in t e r p r e t s c o o r d in a t es in t h e f ir s t q u a d r a n t
Measurement
Properties of Shape
 c o m p a r e s a n d c la s s if ies g e o m e t r ic s h a p es b a s ed o n t h eir p r o p e r t ie s a n d
Money
 is f l u en t in t h e u s e o f a ll d en o m in a t io n s
sizes e.g. quadrilaterals and triangles extending to parallelogram, rhombus
and trapezium; isosceles and scalene
 id e n t if ies a c u t e a n d o b t u s e a n g le s ; c o m p a r es a n d o r d e r s a n g l es u p t o t w o
Metric / imperial measures
right angles (180°) by size
 c o n v er t s d if f e r e n t u n it s o f m e a s u r e e. g . km t o m
 d e c id e s if a p o l y g o n is r e g u l a r o r ir r eg u la r
- builds on their understanding of place value and decimal notation to
 id e n t if ies l in es o f s y m m e t r y in 2-D shapes presented in different
- uses multiplication to convert from larger to smaller units
 r e c o g n is e s line symmetry in a variety of diagrams including where the line
record metric measures accurately, including money
- uses division to convert from smaller to larger units
Perimeter, area, volume
 m easures and calculates the perimeter of a rectilinear figure including
squares in centimetres and metres
- expresses perimeter algebraically in the same units
 f in d s t h e a r ea o f r e c t ilin e a r s h a p e s u s in g c o u n t in g s q u a r e s
- understands area as a measure of surface
- relates area to arrays and multiplication
orientations
of symmetry does not dissect the original shape e.g. the original shape may
be placed at a distance from and parallel to the axis
 c o m p le t e s a s im p le s y m m e t r ic f ig u r e w it h r es p ec t t o a s p e c ific line of
symmetry
 b e c o m es f a m il ia r w it h d if f er en t o r ien t a t io n s o f lin e s o f s y m m e t r y e.g.
vertical, horizontal and diagonal axes
 u s e s a v a r ie t y o f m ed ia e.g. peg boards, geo-strips and ICT representation
Position and Direction
 d es c r ib es p o s it ions on a 2-D grid as co-ordinates in the first quadrant
Chronology
 r ea d s , w r it e s a n d c o n v e r t s b e t w een a n a lo g u e ( in c l u d in g c l o c k f a c es u s in g
Roman numerals) and digital 12 and 24 hour clocks using am and pm
where necessary
 c o n v er t s b e t w e en d if f e r e n t units of measure e.g. hours to minutes
- draws and describes a pair of axes in one quadrant, with equal scales
and integer labels
- reads, writes and uses pairs of co-ordinates e.g.(2,5)
 d es c r ib es m o v em en t s b e t w ee n p o s it io n s a s t r a n s lations of a given unit to
the left/right and up/down
 p lo t s s p e c if ied p o in t s a n d d r a w s s id e s t o c o m p le t e a g iv en p o l y g o n
Solves problems
 e s t im a t es c o m p a r es a n d c a l c u l a t e s d if f e r en t m ea s u r e s , in c l u d in g m o n e y in
pounds and pence
 c o n v er t s b e t w e en h o u r s a n d m in u t e s ; m in u t e s t o s e c o n d s ; y e a r s t o m o n t h s
and weeks to days
- calculates time durations that pass through the hour
Statistics
Processing, representing and interpreting data
 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 p r es e n t ed in b a r c h a r t s ( e . g . : f in d s t h e d if f er en c e b e t w e en t w o b a r s s h o w in g t emperatures, where one is 20°C
and the other is 13°C, on a scale labelled in multiples of five)
 in t er p r e t s a n d p r e s e n t s d is c r e t e and continuous data using bar charts, and time graphs using a greater range of scales
 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 p r es e n t ed in b a r c h a r t s , p ic t o g r a m s , t a b le s a n d o t h er g r a phs
 r el a t es t h e g r a p h ic a l r ep r es en t a t io n of data to recording change over time