Progression in
Division
(including Written
Calculations)
PROGRESSION TOWARDS STANDARD WRITTEN METHODS
Introduction
At Park we follow the structure provided by the National Numeracy Strategy ensuring a systematic
approach to teaching number. There is a considerable emphasis on teaching mental calculation
strategies. Up to Level 4 pupils choose an informal written method to recording how they work out their
answers. More formal written methods are only introduced when the child has a secure understanding of
place value.
Reasons for using written methods
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To aid mental calculation by writing down some of the numbers and answers involved
To make clear a mental procedure for the pupil
To help communicate methods and solutions
To provide a record of work to be done
To aid calculation when the problem is too difficult to be done mentally
To develop and refine a set of rules for calculation
Working Towards Level 1
1.
Share objects into equal groups and count how many in each group.
2.
Use apparatus and drawings to help share into equal groups.
6 cakes to share
6 cakes shared onto 2 plates
6 cakes shared into groups of 2
3.
Use symbols to represent a question
6 cakes shared onto 2 plates, 3 cakes on each plate:
6 cakes shared onto 3 plates, 2 cakes on each plate:
Level 1
5.
Solve practical problems that involve sharing into equal groups (use objects to physically complete
task).
How many apples in each bowl if I share 12
apples into 3 bowls?
+6
Level 2
1. Know by heart halves to 10.
5+5
5 + 5 = 10
2.
Count back in 2s, 5s & 10s from 20.
3.
Use symbols on a numberline to represent a question.
How many bowls will I need if I share 6
apples into groups of 2?
Level 3
1. Use pictures and symbols to solve problems
Four eggs fit in a box. How many boxes will be needed for 20 eggs?
2.
Able to divide two digit numbers by 2, 5 and 10 including remainders.
15 shared by 5
3.
Know by heart division facts for 2, 3, 4, 5 and 10 times tables (fact families).
If
4 x 5 = 20
If
7 x 3 = 21
Then
20 ÷ 4 = 5
Then
21 ÷ 7 = 3
And
20 ÷ 5 = 4
And
21 ÷ 3 = 7
4.
Divide two digit numbers by a single digit with remainders (TU ÷ U) using number lines
33 ÷ 5 = 6 r3
5.
Round remainders up or down depending on context.
Four eggs fit in a box. How many boxes will be needed for 22 eggs?
22 ÷ 4 = 5 r2
5 remainder 2 means you need to round up to 6
boxes
6.
Refine and use efficient methods to divide two digit numbers by single digit numbers (TU ÷ U) and
three digit numbers by single digit numbers (HTU ÷ U) with no remainders.
Short division (bus stop method) with no remainders
291 ÷ 3 =
Estimate 3 x 90 = 270
use times tables
3, 6, 9, 12, 15, 18, 21, 24, 27, 30
3 291
How many times does 3 go into 2?
Check times tables, 0 (zero)
Carry over 2,
How many times does 3 go into 29?
Check times tables, 9 rem 2
How many times does 3 go into 21?
Check times tables, 7.
0
3 291
09
3 29 921
097
3 29 921
Level 4
1.
Record, support and explain answers using times tables to solve problems involving 2 digit divided by
single digit numbers. (TU ÷ U).
96 ÷ 6 = 16
2.
Partition (multiples of the divisor)
64 ÷ 4 = 16
40 = 10 x 4
24 = 6 x 4
64 16
3.
Refine and use efficient methods to divide three digit numbers by single digit numbers (HTU ÷ U) and
two digit numbers less than 30 (HTU ÷ TU)
a. Short division (bus stop method) with remainders
292 ÷ 6 =
Estimate 6 x 50 = 300
6, 12, 18, 24, 30,
6 292
How many times does 6 go into 2?
Check times tables, 0 (zero)
Carry over 2,
How many times does 6 go into 29?
Check times tables, 4 rem 5
use times tables
0
6 292
04
6 2 9552
How many times does 6 go into 52?
Check times tables, 8 rem 4
Check if the question needs the
answer to be rounded up or not.
048r4
6 2 952
Example
OR
If eggs are packed 6 in a box how
many egg boxes are needed for 292
eggs?
If Mary has 292 crayons to share
with her 6 friends how many
crayons does each friend get?
The answer is 49 as the extra 4 eggs
would go into another egg box.
The answer is 48 and Mary has 4
left for herself.
b. Long division
195 ÷ 15
Write down multiples of 15
15
195
15
0
195
15, 30, 45, 60
How many times does 15 go into 1?
Check multiples, 0 (zero)
Carry over 1,
How many times does 15 go into 19?
19 - 15 = 4
Bring down next digit, 5
How many times does 15 go into 45?
45 - 45 = 0
01
15 1 9 5
-1 5
04
013
15 1 9 5
-1 5
045
45
00
Level 5
1.
Use efficient methods divide a whole number by a single digit number (HTU ÷ U), a whole number by
two digit numbers (HTU ÷ TU) and decimals by a single digit number (TU.t ÷ U).
a.
Long division with remainders
b. Short division involving decimals