DIVISION
Year
Rec/1
(Working
towards
and within
L1)
Objective
Solve practical problems that involve
sharing into equal groups
Method / Example
To introduce division it should be practical, using equipment to demonstrate.
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Solve problems involving halving and
sharing
Counters
Unifix
Toys
E.g Here are 8 counters. Arrange them into 2 equal rows or groups.
Here are 12 apples. Share them between 3 people.
Find half of a group (share into 2)
Find a quarter of a group (share into 4)
2
(Levels 2c
and above)
Represent sharing and repeated subtraction
(grouping) as division.
Division, including calculations with
remainders
Division as sharing
They use practical equipment to work out answers like 15 ÷ 3 = 5 or 6 ÷ 2 = 3.
They would share out 15 objects fairly into 3 groups/between three people.
They would share out 6 objects fairly into 2 groups/between two people. E.g.
Division as grouping
Introduce arrays
6÷2=3
6÷3=2
6÷2=3
How many groups of 2 are there in 6?
6÷3=2
How many groups of 3 are there in 6?
They use practical equipment or objects to answer questions such as: How many
2s make 12? They relate this to the division 12 ÷ 2.
Division as repeated subtraction
15 ÷ 5 = 3
-5
0
-5
5
-5
10
15
Find half of a number
Find a quarter of a number by halving and halving again
Language to be used
How many 2s make 10?
10 shared between 2 makes?
10 divided by 2
many groups of 2 How are there in 10?
Division with remainders – only introduce to those really confident in all of the
above
Mentally counting up
3
(Levels 2a
and above)
Use practical and informal written methods
to divide two-digit numbers (e.g. 50÷4);
round remainders up or down, depending
on the context
Use times tables knowledge to count up in multiples of the divisor e.g. 13÷3,
count up in 3s using fingers or tally marks for each group of 3 i.e. 3,6,9 etc until
12 ( 4 lots of 3) and then work out remainder (1).
Continue with division as repeated subtraction using a number line, but with
larger numbers – see above.
Division with remainders
Model Practically
25÷3
25 children – get themselves into groups of 3.
How many groups?
How many left over?
Mentally counting up
Use times tables knowledge to count up in multiples of the divisor e.g. 25÷3,
count up in 3s using fingers or tally marks for each group of 3 i.e. 3,6,9 etc until
24 ( 8 lots of 3) and then work out remainder (1).
Use times tables knowledge to answer division questions in context.
Example: How many 5-minute cartoons can I watch in 20 minutes? What
multiplication fact can help you to find the answer? What division calculation
matches this problem?
4
(Levels 3c
and above)
Understand that division is the inverse of
multiplication and vice versa; use this to
derive and record related multiplication and
division number sentences
Using times tables facts and knowledge of inverse operations
Consider problems such as:
26 ÷ 2 =
24 ÷
= 12
÷ 10 = 8
Develop and use written methods to record,
support and explain division of TU ÷ U,
including division with remainders (e.g. 98 ÷
6)
As a prerequisite, it is ideal that children know their times tables facts up to 10 x
10.
Division using chunking
Method 1
Introduce chunking for division of TU by U
e.g. 96 ÷ 6 =
____
6 ) 96
- 60 (10x6)
36
-36 (6x6)
0
answer: 16 (add together 10 and 6)
Method 2
Chunking with scaffolding e.g. 84 ÷ 6
Tricky to divide 84 by 6 in one go….so
Break 84 down into numbers that we can divide by 6 more easily (using multiples
of 10 as the divisor to help)
84
60
24
60 ÷ 6 = 10
24 ÷ 6 = 4
10 lots of 6 plus 4 lots of 6 = 14
5 and
6
(Levels 3b
and above)
Refine and use efficient written methods to
divide HTU ÷ U
As a prerequisite, it is essential that children know their times tables facts up to
10 x 10.
Extend chunking to HTU ÷ U
e.g. 457 ÷ 5 =
_____
5) 457
-400 (80 x 5)
57
-55 (11x5)
2
answer: 91 r2 (add together 80 and 11)
When chunking, it is useful to list the relevant multiples or times tables at the side
(this can be called a Friendly Number Box). Not all the multiples need to be listed;
generally 1x, 2x, 5x and 10x are the most useful – see below
“Bus Stop” method - short division
1 2 1r2 1) how many 6s in 7 = 1 carry 1
e.g. 6 ) 728
6 )7128
2) how many 6s in 12 = 2
3) how many 6s in 8 = 1 r2
When using bus stop method it can be helpful to list multiples of the divisor in
your Friendly Number box at the side e.g. 2x 6=12, 3x6=18.4x6=24 or simply list
multiples of 6.
6
(Levels 4b
and above)
Extend division to HTU ÷ TU
Extend chunking to two digit divisors – multiples for FNB (Friendly Number Box)
derived through doubling
Extend to THTU ÷ TU
e.g. 567 ÷ 23
____
23)567
-230 (10)
337
-230 (10)
107
-92 (4)
15
FNB
23 (1)
46 (2)
92 (4)
115 (5)
184 (8)
230 (10)
Answer:: 24 r 15 OR 24 r15
23
(The numbers in brackets added together; the remainder is what is left at the end
of the calculation expressed as a fraction over the divisor)
Extend “Bus Stop” method to include giving precise answer as a decimal rather
than remainder.
72. 5
e.g. 6)4315.30
1) how many 6 in 4 (0)
2) how many 6s in 43 (7 carry 1)
3) how many 6s in 15 (2, add a decimal point
bbbbbbbbbbbbbbbbbbbband a zero, carry 3)
4) how many 6s in 30 (5)
So the answer is 72.5
Chunking method as above - multiples for FNB derived through doubling and
multiplying by 10
e.g. 6595 ÷ 25
______
25 )6595
5000 (200)
1595
1000 (40)
595
500 (20)
95
75 ( 3)
20
250 (10)
500 (20)
1000 (40)
2000 (80)
2500 (100)
5000 (200)
Answer: 263 r20 OR 263 20 OR 263 4/5
25
6+
(Level 5a
and above)
Continue to develop division of HTU ÷ TU
and THTU ÷ TU
Introduce the standard method of long division.
Division of decimals
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Write out the multiplication facts for 13 as short multiplications in the
friendly number box e.g. 2x13=26, 3x13=39, 4x13=52, 8x13=104 etc
Work from left to right, considering each digit one at a time.
How many 13s in 2 = 0 with 2 left over
Write 0 above the 2 and carry over 2 into neighbouring column
How many 13s in 23? 1 with a remainder of 10
Write the 1 above the 3 then write the 13 under the 23.
Subtract 13 from 23 in a short division .
Write the answer underneath 13 then drop down the 5
Now, how many 13 in 105 etc
Dividing with decimals.
Dividend is a decimal e.g. 78.7 ÷ 3 =
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Lay the calculation out as a short bus stop division.
Place a decimal point in the answer directly above the
decimal point in the dividend.
Proceed as normal, ignoring the decimal point.
Divisor is a decimal e.g. 561÷3.4 =
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Identify how many decimal places in the divisor.
Multiply by 10,100,1000 to make the divisor a whole
number
DO THE SAME TO THE DIVIDEND i.e. if you multiply
the divisor by 10 to make it a whole number then you
must multiply the dividend by 10
Proceed as a normal long division