Math Learning Steps

Number bonds for 10

The number 10 is often a handy mental arithmetic midway point to use for doing addition and subtraction problems that involve numbers above 10. Your child should have a strong command of the number bonds for 10 to take full advantage of these methods.

Addition sums over 10

Suppose your child is given the addition problem 5 + 7. The number bond for 10 using 7 is 3, so your child can use 3 of the 5 to get to 10. The remaining 2 of the 5 will bring the total to 12. The point was to break up the 5 into two pieces, 3 and 2 – one which got the 7 to 10, and the other gets added onto the 10. This problem could also have been done the other way. The 7 could have been broken up into 5 and 2 – the 5 would be added to the original 5 to get 10, and then the 2 would be added to 10 to get 12.

Notice that this is similar to the thinking for doing addition compensation.

Subtracting from a number bigger than 10

Let’s use 12 – 7 as our example. We can do this as a take away or a difference problem.

As a take away problem, we’ll use 2 of the 7 to get 12 down to 10. We then have 5 of the 7 left to take the 10 down to 5. We broke 7 into 2 and 5 to be able to use 10 as an intermediate stop along the way.

As a difference problem, the total distance between 12 and 7 is the distance between 12 and 10 plus the distance between 10 and 7. The distance between 12 and 10 is 2, and the distance from 10 and 7 is 3, so the total distance is 2 plus 3, which is 5.