Progression in Division
Recording in Years 2 - 4
| Until expanded methods are formally
introduced division should be shown using ¸
rather than
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Recording should be done in a variety of
ways to facilitate understanding.
Recording on a number line
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18 ¸ 4
= 4 lots of 4 and 2 left over
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12 ¸
3 as sharing
= 4 each |
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12 ¸
3 as grouping
There are 4
groups of 3
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Division as grouping should be reflected
in work on arrays.
4 groups
of 3
3 groups
of 4
3 x 4
4 x 3 |
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Introducing
expanded methods
The expanded method for division is
repeated subtraction or ‘chunking’. Pre-requisite skills for this
include earlier work on division as grouping and knowledge of
multiplication tables including division facts. It is important that
calculations children are asked to work on reflect the tables with which
they are secure.
Before tackling a written calculation for
division children should always estimate a sensible answer e.g. in the
example below – “The answer will be more than 20 lots of 3 which is
60 but less than 30 lots of 3 which is 90”.
Stage
1
| At this stage this symbol for division -
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should be introduced |
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3 |
84 |
How many three's in 84? |
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Initially children could be shown that
one group of three could be taken away at a time
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3 |
84 |
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-3 |
(3 x 1) |
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81 |
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-3 |
(3 x 1) |
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78 |
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etc. |
I took away 28 lots of
three |
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Discussion
would establish that this is not an efficient way to perform this
calculation and that use of table facts would help.
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3 |
84 |
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-30 |
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(3 x 10) |
I can take away 10 lots of 3 |
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54 |
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(Children should be able to do this mentally) |
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-30 |
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(3 x 10) |
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24 |
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-24 |
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(3 x 8) |
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0 |
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28 |
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| Also applicable here is for children to
be asking “Should I expect a remainder”
based on knowledge of divisibility rules.
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3 |
86 |
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-30 |
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(3 x 10) |
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56 |
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-30 |
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(3 x 10) |
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26 |
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-24 |
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(3 x 8) |
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2 |
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28 |
r2 |
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Stage
2
Children can move to taking away larger
chunks, provided they are comfortable and secure with doing so.
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6 |
457 |
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-360 |
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(6 x 60) |
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97 |
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-90 |
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(6 x 15) |
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7 |
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-6 |
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(6 x 1) |
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1 |
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76 |
r1 |
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6 |
457 |
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-420 |
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(6 x 70) |
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37 |
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-36 |
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(6 x 6) |
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1 |
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76 |
r1 |
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Stage
3
The same methods can be used for larger
numbers and for decimals. Again, the chunking children do should reflect
what they can do mentally.
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24 |
1328 |
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-960 |
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(24 x 40) |
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368 |
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-240 |
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(24 x 10) |
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128 |
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-120 |
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(24 x 5) |
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8 |
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55 |
r8 |
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Stage
4
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8 |
764 |
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-640 |
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(8 x 80) |
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124 |
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-80 |
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(8 x 10) |
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44 |
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-40 |
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(8 x 5) |
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4 |
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-4 |
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(8 x 0.5) |
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0 |
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95.5 |
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6 |
128 |
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-120 |
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(6 x 20) |
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8 |
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-6 |
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(6 x 1) |
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2 |
.0 |
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-1 |
.8 |
(6 x 0.3) |
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0 |
.2 |
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-0 |
.18 |
(6 x 0.03) |
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21.33 |
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