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Leicestershire Numeracy Team 2003 3division
What is division?
How would you illustrate this division to a child? What would you draw and what
language would you use?
12 3 = 4
Leicestershire Numeracy Team 2003 4division
12 3 = 4
Sharing
There are three children and 12 cakes. How many can they each have, if I share them out equally?
(Sharing 12 things equally into 3 piles. How many in each)
Skills in Early Division
Leicestershire Numeracy Team 2003 5division
12 3 = 4Grouping
There are 12 cakes. How many children can have three each?
(How many threes are there is 12?)
Skills in Early Division
Leicestershire Numeracy Team 2003 6division
Language and division
Since the sign represents both the sharing and grouping aspects of division, encourage the children to read this as ‘divided by’ rather than ‘shared by’.
Leicestershire Numeracy Team 2003 7division
6000 1000 =
Would you group or share for this calculation?
Leicestershire Numeracy Team 2003 8division
Introducing division
In Year 2 children are encouraged to understand the operation of division as:
• sharing equally
• grouping or repeated subtraction e.g. How many tens are in 60?
Leicestershire Numeracy Team 2003 10division
Sharing
• Supports an understanding of halving and the 1 to 1 correspondence between objects.
• Requires little knowledge or skill beyond counting.
• Becomes more difficult to visualise as the divisor increases.
• Is inefficient.
Leicestershire Numeracy Team 2003 17division
Key Stage 1 - Calculations• Encourage children to use jottings, as well, to check answers to
calculations that have been reached by mental methods
Q29
1 2c 2b 2a 3 All
4% 4% 12% 27% 61% 31%
Leicestershire Numeracy Team 2003 18division
Grouping
• Links to counting in equal steps on a number line.
• Requires knowledge of subtraction facts (repeated subtraction) and addition facts (counting up).
• Is more efficient than sharing as the divisor increases.
• Provides a firmer basis on which to build children’s understanding of division.
Leicestershire Numeracy Team 2003 19division
Introducing divisionIn Year 3 and 4 children also need to know that:
• dividing a whole number by 1 leaves the number unchanged: e.g. 12 1 =12
• 16 2 does not equal 2 16
• division reverses multiplication (the inverse) – this allows them to solve division calculations by using multiplication strategies (18 3 by counting the hops of 3 to 18)
•there will be remainders for some division calculations (to be expressed as whole-number remainders).
Leicestershire Numeracy Team 2003 21division
Continuing division
In Year 4 children need to begin to :
• relate division and fractions
• use a written method for division (chunking).
Leicestershire Numeracy Team 2003 25division
Teaching chunking - partitioning72 5
Partition 72 in to a convenient multiple of 5 + the rest
72 = 50 + 22
Divide each part
50 ÷ 5 = 1022 ÷ 5 = 4 rem 2
Recombine the parts
Answer: 14 remainder 2
Leicestershire Numeracy Team 2003 26division
72 ÷ 5 =
Grouping - How many 5’s are there in 72?
Adding groups of 5
Teaching chunking - number line
40 45 50 55 60 65 70 72 0 5 10 15 20 25 30 35
5 x 10 or
10 groups of 55 x 4 or
4 groups of 5
Leicestershire Numeracy Team 2003 27division
Teaching chunking - vertical
72 5 = 72
50 (5 x 10)
22
20 (5 x 4)
2
Answer: 14 remainder 2
5 x 1 = 5
5 x 2 = 10
5 x 5 = 25
5 x 10 = 50
Leicestershire Numeracy Team 2003 28division
Using calculators for repeated subtraction
The constant function
To calculate 72 5 using repeated subtraction
Press 5 - - = then press 72
Leicestershire Numeracy Team 2003 29division
Teaching chunking - larger numbers
7 x 1 = 7
7 x 2 = 14
7 x 5 = 35
7 x 10 = 70
256 7 = 256 210 (7 x 30) 46 42 (7 x 6) 4
256 7256 = 210 + 46
210 ÷ 7 = 30 46 ÷ 7 = 6 remainder 4
or
Answer: 36 remainder 4
Leicestershire Numeracy Team 2003 30division
Continuing division
In Year 5 and 6 children also need to understand:
• that a number cannot be divided by zero
• how a quotient can be expressed as a fraction and as a decimal fraction
• how to interpret the display when dividing with a calculator.
Leicestershire Numeracy Team 2003 31division
185 people go to the school concert.
They pay £1.35 each.
How much ticket money is collected?
Programmes cost 15p each.
Selling programmes raises £12.30
How many programmes are sold?
Show your method you may get a
mark.
£
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