PROGRESSION
IN SUBTRACTION
As with addition, each stage shows
progression from informal methods leading to a compact method. As
children move to new stages the focus, in the first instance, should be
on new method and layout, not on harder numbers.
For the majority of children,
decomposition will be the compact method taught. For some children, who
find this difficult, an alternative method is suggested. Children will
have already encountered this method (complementary addition) as a
strategy for mental calculation and will have recorded through informal
jottings. It is also taught as part of the Springboard 5 programme.
DECOMPOSITION
Stage
1
58 – 32
50 – 30 = 20
Starting with what child can do mentally
8
– 2 = 6
Start by dealing with the tens
20 + 6 =26
Child can use known subtraction facts
Stage
2
58
- 32
152 - 41
This stage introduces:
Expanded layout based on partitioning
50 + 8
100 + 50 + 2
Lining up vertically
- 30 + 2
- 40 + 1
Specific position of operation symbol
20
+ 6
= 26
100 + 10 + 1
= 111 Lines to delineate answer
This stage involves calculations that do
not require decomposition in order that children can focus on layout.
Initially start on with digits on right
hand side to reflect mental strategies but then move to working with the
least significant digit first in readiness for decomposition.
Stage
3
Children will need to become familiar
with partitioning such as 84 = 70 + 14 in readiness for decomposition.
84 – 38
362 – 48
80 + 4
70 + 14
300 + 60 + 2
300 + 50 + 12
- 30 + 8
- 30 + 8
-
40 + 8 -
40 + 8
40 + 6
= 46
300 + 10 +
4 = 314
Stage 3a
(for HTU )
362 – 48
50
12
300 + 60
+ 2
This stage introduces:
-
40 + 8
A more compact stage
300
+ 10 + 4
= 314
Stage 4
84 – 38
362 – 48
7
8 14
3 5612
This stage introduces:
-
3 8
- 4
8
Compact method
4 6
3
1 4
Language still reflects
place value
Stages of
partitioning should be introduced progressively when dealing with HTU
·
Partitioning tens into ones
·
Partitioning hundreds into tens
·
Partitioning hundreds and tens into tens
and ones
An example of
the latter would look like this at the various stages:
Stage 3
567 – 378
500 + 60 + 7
500 + 50 + 17
400 + 150 + 17
- 300 + 70 + 8
- 300 + 70 + 8
- 300 + 70 + 8
100
+ 80
+ 9 = 189
Stage 3a
567 – 378
400
150
17
500 + 60 + 7
- 300 +
70 + 8
100 + 80
+ 9
= 189
Stage 4
567 – 378
45 156 17
-
3 7
8
1 8
9
The same stages
can be applied as children are introduced to subtraction with larger
number or decimals.
ALTERNATIVE TO DECOMPOSITION -
COMPLEMENTARY ADDITION
