If you pull away the part of the bar on the right, you subtract that part from 10. If you push it back again, you add it to the part on the left to make up 10. This implies the following: • If you know the parts, you can put them together (add) to find the whole. • If you know the whole and one of the parts, you take away that part (subtract) to find the other part.
In the latter case, subtract means to figure out how much more you would have to add to get the whole thing. This process is often referred to as ‘add on’.
Learners should realise that each number bond is part of a four-fact family, e.g.: 3 + 7 = 10 ; 7 + 3 = 10 ; 10 – 3 = 7 ; 10 – 7 = 3
If learners know one of the facts in a family, they know them all. Learners should also realise that they can use any one of the facts to check the others, which means that addition can be used to check subtraction, and vice versa.
Number facts for 20 can be taught by using the following diagram: Number bonds for 20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Pick any number at the top, say 13. The number at the bottom (7) tells what to: • add to 13 to get 20: 13 + 7 = 20 • subtract from 20 to get 13: 20 – 7 = 13
By inserting one, two or three noughts at the back of each number, the diagram above can easily be adapted to cover addition and subtraction facts for multiples of 10, 100 and 1 000.
Times tables Times tables up to the 10 × 10 multiplication table can be taught in a structured way by using the following: • Flow diagrams: If the input values are chosen from 1 to 10, the output values will show which multiples of the operator appear in the 10 × 10 multiplication table.
Section 3: Teaching and learning Mathematics
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