Progression in Division
Ø Our curricular target this term relates to division. The ladder below shows the stages that children should work towards. Your child will be able to tell you which target they should be working towards.
Ø The pages that follow are taken from the school’s calculation policy and show how the children will be taught division.
Ø Each level covers a wide range which children will progress through over a year or more. Your child’s teacher will be able to tell you which methods your child is currently working on or needs to practise.
Ø These methods rely on children knowing times tables facts off by heart and being able to use them to work out division facts, e.g. if 6 x 7 = 42 then 42 ÷ 6 = 7 and 42 ÷ 6 = 7. Children need to learn and practise times tables at home so that they have quick recall of these facts.
Ø The most important thing that parents can do at home to help their children in maths is to talk about the maths that occurs in everyday life, for example:
· Shopping – money, special offers, percentages (25% off)
· Cooking – weighing, time, scaling up or down, fractions (How much of the pizza will each person get?)
· Watching television – time (How long is it until __ starts? How long does __ last?)
· DIY – measuring
· Pocket money (How long will it take to save up for __? How much more money do you need to buy ___? How much will you have left if you buy __?)
DIVISION: Level 1-2 (Year 3-4)
Practical experiences / pictorial representations:
Ø Sorting objects into groups, e.g. ‘How many pairs of socks are there in the launderette?’
Ø Sorting objects into groups, e.g. ’12 children get into teams of 4 to play a game. How many teams are there?’
Ø Solve simple problems pictorially using grouping and sharing, e.g.
4 eggs fit in a box. How many boxes would you need to pack 20 eggs?
¯ Grouping (repeated subtraction)
There are 6 sweets, how many people can have 2 sweets each?
Grouping
6 sweets are shared between 2 people, how many do they each get?
Sharing
Ø Bead bar / string: 12 ÷ 3 = 4 “How many 3s make 12?”
Ø Arrays:
8 ÷ 2
or
Grouping Sharing
(Arranging into groups of 2) (Sharing between 2)
Mental skills:
Ø Count in steps of 2, 5 and 10
Ø Count in tens from 0 to 100 and back
Ø Know half of even numbers up to 10
Ø Halve by partitioning:
16 ÷ 2 = 8
10 + 6
¯ ¯
5 + 3
Ø Derive and recall facts for the 2, 5 and 10 multiplication tables
Ø Use knowledge of multiplication tables to divide:
12 ÷ 2 = How many 2s go into 12? Use knowledge of 2x table.
2 / 4 / 6 / 8 / 10 / 12 / 14Written recording:
Ø Use numbered lines to count on or back
12 ÷ 3 = 4
0 1 2 3 4 5 6 7 8 9 10 11 12
Ø Progress to using empty number line:
18 ÷ 3
Ø Progress further to using remainders on a number line:
13 ÷ 3
DIVISION: Level 3 (Year 3-5)
Mental skills:
Ø Know by heart 2, 5 and 10 x tables
Ø Begin to know 3x, 4x and 6x tables
Ø Use multiplication facts to derive division facts
24 ÷ 4 ‘How many 4s go into 24?’ Use knowledge of 4x table
Ø Know by heart 2, 3, 4, 5 and 10x tables and begin to know 6, 7, 8 and 9x – use them to solve division problems
Ø Divide whole numbers by 10
Written recording (TU ÷ U):
Ø Informal partitioning methods using knowledge of multiplication facts:
Including remainders:
Ø Repeated subtraction on an empty number line
24 ÷ 4 = 6
0 4 8 12 16 20 24
Ø Children should also move onto calculations involving remainders.
13 ÷ 4 = 3 r 1
4 4 4
0 1 5 9 13
Ø When confident, children will then develop their use of repeated subtraction to be able to subtract multiples of the number they are dividing by. Initially, these should be multiples of 10s, 5s, 2s and 1s – numbers with which the children are more familiar.
72 ÷ 5 = 14 r.2
-50
r.2 -5 -5 -5 -5
0 2 7 12 17 22 72
Ø Informal jottings to record ‘chunking’ (this can be easily linked to recording on a number line):
48 ÷ 4
Count up ‘chunks’ of 4s to reach 48
10 x 4 = 40 40
2 x 4 = 8 48
Add up total number of 4s found to make 48
10 + 2 = 12
96 ÷ 4
Count up ‘chunks’ of 4s to reach 96
10 x 4 = 40 40
10 x 4 = 40 40
4 x 4 = 16 96
Add up total number of 4s found to make 96
10 + 10 + 4 = 24
Written recording by chunking (TU ÷ U):
Ø Example: If there are 6 eggs in a box, how many boxes can be filled with 84 eggs?
So we need 84 ¸ 6
What this calculation means is ‘How many sixes are there in 84?’
A way to do this is to subtract each individual 6, as you would when packing six eggs into each box, but this would be inefficient. Encourage the children to think about bigger, friendly ‘chunks’ of 6, such as ten boxes of six (6x10=60). This makes the subtraction easier and quicker.
84
- 60 (10 x 6 boxes = 60)
24
-24 (4 x 6 boxes = 24)
0
The answer is: (10 + 4 boxes) = 14 boxes
Ø Round up or down depending on context
e.g. I have 62p. Sweets are 8p each. How many can I buy?
Answer: 7 (the remaining 6p is not enough to buy another sweet)
Apples are packed into boxes of 8. There are 62 apples. How many boxes are needed?
Answer: 8 (the remaining 6 apples still need to be placed into a box)
DIVISION: Level 4-5 (Year 5-6)
Mental skills:
Ø Know by heart all multiplication facts to 10x10
Ø Divide decimals by 10 or 100 and integers by 1000
Ø Derive division facts involving decimals (e.g. 12 ÷ 4 = 3 so 1.2 ÷ 4 = 0.3)
Written recording (HTU ÷ TU / U.t ÷ U):
Ø Chunking
Ø Progress to using larger multiples of the divisor, estimating first:
To find 196÷6, we start by multiplying 6 by 10, 20, 30,… to find that 6×30=180 and 6×40=240. The multiples of 180 and 240 trap the number 196. This tells us that the answer to 196÷6 is between 30 and 40.
196 ÷ 6
32 r 4
6 ) 196
- 180 30x
16
- 12 2x
4
Answer : 32
The answer 32 (with a remainder of 4) lies between 30 and 40, as predicted.
Ø Extend chunking to dividing by two digit numbers
972 ÷ 36
27
36 ) 972
- 720 20x
252
- 252 7x
0
Answer : 27
Ø Extend chunking to decimals
87.5 ÷ 7
12.5
7 ) 87.5
- 70.0 10x
17.5
- 14.0 2x
3.5
- 3.5 0.5x
0
Answer : 12.5
Ø Begin to show remainders as fractions
977 ÷ 36 = 27 r.5 = 27 5/36
Division policy for parents Page 6 of 7 M. Knight Feb 2009