Decomposition, Complementary Additions, Difference Between
There are three aspects of subtraction. The child must know about these, and understand them. He will then have a full and complete concept of subtraction.
- The method of decomposition (the take away aspects).
- How much more must I add to ‘a’ to make a into ‘b’?
- The difference between two separate quantities.
Decomposition
a) Changing one of a category for a ten of the one below it, i.e.changing one hundred for ten tens:
563
385-
178
b) Adding equal quantities. The children discover that as long as the same amount is always added to both quantities, the difference between them will remain the same.
Exercise with bead bars:
- Lay out bar of 5 and bar of 2, with the ‘minus’ and ‘equal’ signs.
- What is the difference between these 2 bars? 3.
- If we add 4 to each bar (to 5 and to 2) our problem is now 9-6= and the difference is still 3.
Complementary Additions
Step (a) What must I put with 8 to make 16? 8.
16
8–
8**
Step (b) Having used one of the tens, I now ask:
‘What must I put with 1 to make it into 2? 1’
e.g. A had 15 books, B had only 7. How many more did B have to get to reach the same number as A?
Encourage the children to record these problems using mathematical symbols:
| 15 | or 7 | or 7 + ? = 15 | |
| 7 – | 8 + | ||
| 8 | 15 | ||
‘The Difference Between’
Introduce this orally or have prepared slips with simple problems, e.g. John has 5 pencils in his pencil box, Peter has 8. Ask: ‘What is the difference between Peter’s number and John’s?’
N.B. It is important that the child does many problems involving the three aspects of subtraction. It is essential that he should have a knowledge of decomposition before he comes to do division.
**PW uses 36-8=8 for this equation instead of 16-8=8.