Year 3
COUNTING, PROPERTIES OF NUMBERS AND
NUMBER SEQUENCES
number
zero, one, two, three… to twenty and beyond
zero, ten, twenty… one hundred
zero, one hundred, two hundred… one thousand
none
how many…?
count, count (up) to
count on (from, to)
count back (from, to)
count in ones, twos, threes, fours, fives…
count in tens, hundreds
more, less, many, few
tally
odd, even
every other
how many times?
multiple of
sequence
continue
predict
pattern, pair, rule
relationship
PLACE VALUE AND ORDERING
units, ones, tens, hundreds
digit
one-, two- or three-digit number
‘teens’ number
place, place value
stands for, represents
exchange
the same number as, as many as
equal to
Of two objects/amounts:
greater, more, larger, bigger
less, fewer, smaller
Of three or more objects/amounts:
greatest, most, biggest, largest
least, fewest, smallest
one more, ten more, one hundred more
one less, ten less, one hundred less
compare, order, size
first, second, third… tenth… twentieth
twenty-first, twenty-second…
last, last but one
before, after, next
between, half-way between
above, below
ESTIMATING
guess how many, estimate
nearly, roughly, close to
approximate, approximately
about the same as
just over, just under
exact, exactly
too many, too few, enough, not enough
round (up or down)
nearest, round to the nearest ten
MAKING DECISIONS AND REASONING
pattern, puzzle
calculate, calculation
mental calculation
method
jotting
answer
right, correct, wrong
what could we try next?
how did you work it out?
number sentence
sign, operation, symbol, equation
ADDITION AND SUBTRACTION
, add, addition, more, plus
make, sum, total
altogether
score
double, near double
one more, two more... ten more... one hundred more
how many more to make…?
how many more is… than…?
how much more is…?
subtract, subtraction, take (away), minus
leave, how many are left/left over?
one less, two less… ten less… one hundred less
how many fewer is… than…?
how much less is…?
difference between
half, halve
equals, sign, is the same as
tens boundary, hundreds boundary
MULTIPLICATION AND DIVISION
lots of, groups of
, times, multiply, multiplication, multiplied by
multiple of, product
once, twice, three times… ten times…
times as (big, long, wide… and so on)
repeated addition
array
row, column
double, halve
share, share equally
one each, two each, three each... group in pairs, threes…
tens
equal groups of
, divide, division, divided by, divided into
left, left over, remainder
General
same, different
missing number/s
number facts, number pairs, number bonds
greatest value, least value
number line, number track
number square, hundred square
number cards
number grid
abacus
counters, cubes, blocks, rods
die, dice
dominoes
pegs, peg board
geo-strips
same way, different way
best way, another way
in order, in a different order
not
all, every, each
Year 3 Programme of Study
Number - number and place value
• identify, represent and estimate numbers using different
Pupils should be taught to:
representations
• count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more
• read and write numbers up to 1000 in numerals and in words
or less than a given number
• solve number problems and practical problems involving these
• recognise the place value of each digit in a three-digit number
ideas.
(hundreds, tens, ones)
• compare and order numbers up to 1000
Number - addition and subtraction
• estimate the answer to a calculation and use inverse operations
Pupils should be taught to:
to check answers
• add and subtract numbers mentally, including:
• solve problems, including missing number problems, using
• a three-digit number and ones
number facts, place value, and more complex addition and
• a three-digit number and tens
subtraction.
• a three-digit number and hundreds
• add and subtract numbers with up to three digits, using formal
written methods of columnar addition and subtraction
Number - multiplication and division
• solve problems, including missing number problems, involving
Pupils should be taught to:
multiplication and division, including positive integer scaling
• recall and use multiplication and division facts for the 3, 4 and 8
problems and correspondence problems in which n objects are
multiplication tables
connected to m objects.
• write and calculate mathematical statements for multiplication
and division using the multiplication tables that they know,
including for two-digit numbers times one-digit numbers, using
mental and progressing to formal written methods
Number - fractions
• recognise and show, using diagrams, equivalent fractions with
Pupils should be taught to:
small denominators
• count up and down in tenths; recognise that tenths arise from
• add and subtract fractions with the same denominator within
dividing an object into 10 equal parts and in dividing one-digit
one whole [for example, 5/7 + 1/7 = 6/7]
numbers or quantities by 10
• recognise, find and write fractions of a discrete set of objects:
• compare and order unit fractions, and fractions with the same
unit fractions and non-unit fractions with small denominators
denominators
• recognise and use fractions as numbers: unit fractions and non• solve problems that involve all of the above.
unit fractions with small denominators
Measurement
Pupils should be taught to:
• measure, compare, add and subtract: lengths (m/cm/mm); mass
(kg/g); volume/capacity (l/ml)
• measure the perimeter of simple 2-D shapes
• add and subtract amounts of money to give change, using both
£ and p in practical contexts
• tell and write the time from an analogue clock, including using
Roman numerals from I to XII, and 12-hour and 24-hour clocks
• estimate and read time with increasing accuracy to the nearest
minute; record and compare time in terms of seconds, minutes
and hours; use vocabulary such as o’clock, a.m./p.m., morning,
afternoon, noon and midnight
• know the number of seconds in a minute and the number of
days in each month, year and leap year
• compare durations of events [for example to calculate the time
taken by particular events or tasks].
Geometry - properties of shapes
• identify right angles, recognise that two right angles make a halfPupils should be taught to:
turn, three make three quarters of a turn and four a complete
• draw 2-D shapes and make 3-D shapes using modelling
turn; identify whether angles are greater than or less than a right
materials; recognise 3-D shapes in different orientations and
angle
describe them
• recognise angles as a property of shape or a description of a turn • identify horizontal and vertical lines and pairs of perpendicular
and parallel lines.
Pupils should be taught to:
• interpret and present data using bar charts, pictograms and tables
• solve one-step and two-step questions [for example, ‘How many
Statistics
more?’ and ‘How many fewer?’] using information presented in scaled
bar charts and pictograms and tables.
In order to encourage children to work mentally, calculations should always be presented horizontally so children can make decisions about how to tackle them.
Encourage children to choose to use the most efficient method for the numbers and the context. Teach operations together to emphasise the importance of inverse.
Addition
Subtraction
to be taught alongside each other
Multiplication
Children will continue to use: Repeated addition
Children will continue to use empty number lines with increasingly
larger numbers and will begin to use informal methods (jottings)
to support, record and explain partial mental methods, building on
existing mental strategies.
Children will continue to use empty number lines with increasingly
large numbers and will begin to use informal methods (jottings) to
support, record and explain partial mental methods, building on
existing mental strategies.
6 multiplied by 4 = 6 x 4 = 6 ‘four times’
Counting on
Counting back
Count on from the largest number irrespective of the order of
the calculation. Bridge through tens and begin to bridge
through 100’s.
Subtracting the tens in one jump and the units in one jump
(focus on efficiency… e.g. challenge children to solve
subtraction calculations in two steps)
147 -23 = 147 – 20 = 127 127 – 3 = 124
Children should use number lines or bead bars to support.
6
6
6
6
38 + 86 = 124
+30
+4
e.g. 147 – 63
86
116
120
124
84 87
-3
Compensation
147
-10
-10
-10
-10
-10
-10
107
122 123
Use Finding the difference ITP between two numbers by
counting on. Relate to every day contexts such as age, height,
length etc.
(Introduce practically. Encourage children to use when the
calculation can’t be done mentally. Model first with simpler
numbers which they can solve mentally).
91 = 80 + 11
+ 24
80
11
11
80
91
91
Where the numbers involved in the calculation are close together
or near to multiples of 10, 100 etc. counting on using a number
line should be used, alongside resources like bead bars.
+10
102 – 89 = 13
+1
+2
89 90
0
243 = 200 + 40 + 3
+435
Leading to
compact vertical
method.
400 + 30 + 5
678 = 600 + 70 + 8
243
625
+324
+324
900
9
40
40
9
900
949
949
5
53
55
4 x 9 = 36
36÷ 9 = 4
67 = 60 + 7
- 24 - 20 + 4
43 = 40 + 3
67 -
= 43
43 = 67 -
Develop into 3 digit – 2 digit numbers modelling with Base 10.
Partition 3 digit numbers into ways that are helpful for the
subtraction. E.g. 325 – 58 = 325 – 25 - 25 – 5 – 3 = 267
Or 325 – 58 = 267 so 325 becomes 200 + 110 + 15
- 50 - 8
200 + 60 + 7
5
10
5x2
15
20 23
5x2
3
0
10
20 23
Moving towards 2 digit x 1 digit using place value.
90 x 4 = 40 x 9 = 360
360 ÷ 9 = 40
23 ÷ 5 = 4 r3
360 ÷ 4 = 90
5x4
3
0
5
10
25
30
45
50
Also Partition an array to show how to derive an unknown fact
from a known fact e.g. use knowledge of 2 and 5 times tables to
work out multiples of 7, e.g. 7 x 3 = 5 x 3 + 2 x 3
0
20 23
Using symbols to stand for unknown numbers to complete
equations using inverse operations (2 digit ÷ 1 digit numbers)
26 ÷ 2 =
24 ÷
= 12
÷ 10 = 8
Find unit fractions of numbers and quantities
15 + 6 = 21
Start to relate fractions to division in context:
E.g. A cake recipe for 8 people uses 500g of flour.
How much flour would I need to make a cake for 4 people?
What is 1/2 1/3 1/4 1/6 of 12 litres? What is 1/4 or 3/4 of 20kg?
Scaling
67 - 24 = 43
5
3
36 ÷ 4 = 9
63
Expanded informal method using place value
5
23 ÷ 5 = 4 r3
+2
63 - 8
5
Moving towards more efficient approaches, using known facts.
100 102
-10
625
23 ÷ 5 = 4 r3
Children should model a multiplication calculation using an array.
This knowledge will support the development of the grid method.
Compensation (for near multiples of 10) 63 – 8 = 55
+ 435
678
Arrays Increasingly use arrays to make links between x and ÷.
Use number line to show known multiplication facts and then
derive unknown facts. E.g. if you know 5 x 10 = 50.
Count back 5 to derive 5 x 9 etc. 5 x 5 will be half of 5 x 10 etc...
Relate to other ‘tables’.
67
+24
6
Derive facts from unknown facts
Model expanded horizontal partitioning with Base 10.
+24 = 20 + 4
6
Move into chunking (grouping) using these steps. Encourage
children to be as efficient as possible.
24
Important for teachers to be consistent. Either seen as a row of
9, 4 times (9 x 4)... or a column of 4, 9 times (4 x 9).
Both are correct.
-60
Counting on
67
6
147
-3
Expanded informal method using place value
67 = 60 + 7
6
18
Use number lines and known multiplications to solve divisions incl.
with remainders.
-40
84 87
-1
12
Number lines and known multiplication facts to solve division
following on from repeated addition.
147
-20
-3
+50
73
Children will continue to use:
0
84 87
(for near multiples of 10)
49 + 73 = 122
6
Bridging through ten can help children become more efficient.
+4
Ensure that the emphasis in Y3 is on grouping rather than
sharing, except when using fractions as this is sharing.
4 times 6 is 6 + 6 + 6 + 6 = 24 or 4 lots of 6
0
Division
to be taught alongside each other
Use Base 10 equipment to show 10 times bigger / smaller. Model
the enlargement. E.g to show why 6 x 3 helps in solving 60 x3.
Find a ribbon that is 4 times as long as the blue ribbon r = b x 4
5cm
20cm
Using symbols to stand for unknown numbers to complete
equations using inverse operations.
x 5 = 20
3x
= 18
x
Partitioning (2 digit x 1 digit numbers)
38 x 5 = (30 x 5) + (8 x 5) = 150 + 40 = 190
= 32