PROGRESSION IN DIVISION
EYFS
What will division look like?
Cut the sandwich in half. How many pieces are there?
Pupils use concrete objects and practical situations to explore sharing to
answer questions such as:
• Share the biscuits out so that everyone has the same number.
• Cut the sandwich in half. How many pieces are there?
Children will understand equal groups and share items out in play and
problem solving. They will count in 2s and 10s and later in 5s.
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PROGRESSION IN DIVISION
Year 1
What will division look like?
Pupils solve one-step problems involving division, by calculating the answer
using concrete objects, pictorial representations and arrays with the support of
the teacher. Pupils use sharing and grouping to solve division problems.
Sharing
e.g. 6 cakes are shared equally between 2 people. How many cakes does
each person get?
Grouping
How many pairs of socks can we make from this pile of socks? Count the
pairs.
The teaching in Year 1 should introduce the division sign.
2
PROGRESSION IN DIVISION
Year 2
What will division look like?
Pupils calculate mathematical statements for multiplication and division within
the multiplication tables and write them using the multiplication (×), division (÷)
and equals (=) signs
4 x 3 = 12
3 x 4 = 12
12 ÷ 4 = 3
12 ÷ 3 = 4
Pupils solve problems involving multiplication and division, using practical
materials, arrays, repeated addition, mental methods, and multiplication and
division facts, including problems in contexts, e.g.
15 pencils are put into boxes of 5. How many boxes of pencils will there be?
Also use arrays to model division.
15 ÷ 5 = 3 and 15 ÷ 3 = 5
There will be 3 boxes of 5 pencils
Children will also be taught the importance of knowing their tables (see
multiplication section) to solve division questions and identify the link
between division and multiplication.
6÷2=
20 ÷ __ = 2
__ ÷ 3 = 8
3
PROGRESSION IN DIVISION
Year 3
What will division look like?
Pupils write and calculate mathematical statements for division using the
multiplication tables that they know, using mental and progressing to formal
written methods.
Children should be able to relate division facts about numbers which relate to
multiplication:
30 ÷ 5 = 6
therefore
5 x 6 = 30
300 ÷ 5 = 60
therefore
30 ÷ 5 = 6
therefore
30 ÷ 6 = 5
Use knowledge of multiplication facts and repeated addition to answer division
questions, e.g.
How many 3s are there in 39?
Children may also use a number line to solve this problem:
+3
0
+3
3
+3
6
+3 +3
9
12
+3
15
18
+3
21
+3 +3
24
+3
27
+3
30
+3
33
+3
36
39
39 ÷ 3 = 13 (jumps)
The same process can also be introduced to model remainders. Note that
the vertical line at the end of the number line acts as a barrier to stop the
jumps continuing.
43 ÷ 5 = 8 r 3
+5
0
+5
5
+5
10
+5
15
+5
20
+5
25
+5
30
+5
35
r3
40
43
How many jumps were taken? How many left over?
Pupils are introduced to the formal written method of short division with whole
number answers, using the image of the array and place value apparatus
initially.
4
PROGRESSION IN DIVISION
Pupils are introduced to the formal written method of short division with whole
number answers, using the image of the array and place value apparatus
initially.
56 ÷ 8 = 7
By the end of the Summer term, all pupils should have been introduced to the
short method for division.
The process requires the children to work out “How many times does 7 fit into
9?” (once) It has 2 left over which is then placed before the 8, making this 28.
Then ask “How many times does the 7 fit into 23?” The answer is 4. Note that
the answer sit above the line.
5
PROGRESSION IN DIVISION
Year 4
What will division look like?
Pupils continue to use the number line to support mental division.
257 ÷ 7 =
30 x 7
0
6x7
210
r5
252
257
The teacher should also ensure that the children should be able to apply the
key skills of short division to the above, moving away from the number line for
division:
3 6 r5
7
2 5 47
The process above being: “7 into 2 doesn’t go therefore 7 into 25 goes 3
times with 4 left over. The 4 is then placed before the 7, making that 47. 7
goes into 47, 6 times with 5 left over”
It is essential that the teacher also introduces the formal method of
division (chunking) to support this learning process also. This will be in
the Summer Term.
7
2 5 7
2 1 0 (7 x 30)
47
4 2 (7 x 6)
5
6
PROGRESSION IN DIVISION
Year 5
What will division look like?
Pupils 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, e.g.
432 school children go on a camping trip. Each tent sleeps five. How many
tents will they need to take?
Answer: They will need to take 87 tents
As the year progresses and through effective Assessment for Learning,
the teacher will implement the formal method of long division (chunking),
usually in the Summer Term:
432 ÷ 15 =
15 4 3 2
3 0 0
1 3 2
1 2 0
1 2
(15 x 20)
(15 x 8)
7
PROGRESSION IN DIVISION
Year 6
What will division look like?
Pupils divide numbers up to 4 digits by a two-digit whole number using the
formal written method of long division, and interpret remainders as whole
number remainders, fractions, or by rounding, as appropriate for the context,
e.g.
Chocolates are packed in trays of 15. If I have 432 chocolates, how many full
trays will I have and how many chocolates will be left over?
432 ÷ 15 =
15 4 3 2
3 0 0
1 3 2
1 2 0
1 2
(15 x 20)
(15 x 8)
Answer: there will be 28 trays of chocolates and 12 chocolates left.
Pupils progress to expressing their remainders as a fraction,
e.g. 432 litres of water are stored in 15 litre drums. How many full drums of
water will there be and what fraction of the final drum will be filled?
Answer: there will be 28 full drums and the 29th drum will be 4/5 full.
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PROGRESSION IN DIVISION
Progressing to expressing the remainder as a decimal, e.g.
£432 was raised at the school fair and is to be shared equally between 15
classes. How much will each class receive?
Answer: Each class will receive £28.80
Pupils divide numbers up to 4 digits by a two-digit number using the formal
written method of short division where appropriate, interpreting remainders
according to the context, e.g. 496 pupils attend a football tournament. When
they are put into teams of 11, how many full teams will there be? Will
everyone be in a team?
Answer: There will be 45 full teams of 11 players and one pupil will not have
a team.
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