• Suppose you wanted to do: 76 + 9. One way to do the addition is to think: 76 + 9 is 76 + 10 - 1 (9 is 10 - 1). 76 + 10 is 86, then subtract 1 gives the answer 85. This kind of thinking is also called 'making 10'. By 'making 10' the adding is easier to do. The mathematical principle involved is do/undo (or compensation).

• Suppose you wanted to do: 76 + 8. One way to do the addition is to think: 76 + 8 is 76 + 10 - 2 (8 is 10 - 2). 76 + 10 is 86, then subtract 2 gives us the answer of 84. Notice again, that 'making 10' is involved.

• Suppose you wanted to do: 76 - 9. One way to do the subtraction is to think: 76 - 9 is 76 - 10 add 1 (- 9 is - 10 + 1). 76 - 10 is 66, then add 1 gives the result of 67. Again, 'making 10' is involved.

• Suppose you wanted to do: 47 - 18. One way is to think: 47 - 20 + 2 (-18 is - 20 + 2). 47 - 20 is 27, then add 2 gives the result of 29. 'Making a multiple of 10' is involved.

• Suppose you wanted to do: 9 x 8. One way to do the multiplication is to think: "9 x 8 is 10 x 8 less 1 x 8". 10 x 8 is 80, less 8 gives the result of 72. Notice that 'making 10' is involved because 10 x something is easier to figure out .

• Suppose you wanted to do 9 x 82. One way to do the multiplication is to think: "9 x 82 is 10 x 82 less 1 x 82". 10 x 82 is 820, less 82 gives the result of 738. Notice, again that 'making 10' is involved.

Subtraction can be done by adding. This is sometimes known as "store keeper" thinking. Suppose you wanted to do 123 - 81. You can think of this as 81 + ? = 123. To obtain the answer you would do:

• Add 19 to 81 to reach 100.
• Add 23 to 100 to reach 123

The answer to the subtraction is 19 + 23 = 42

Try these using "store keeper" thinking:

Known doubles can be used to add (or subtract).

For example, 6 + 7 can be thought of as 6 + 6 + 1. [This assumes comfortablility with the double, 6 + 6.]

For example, 5 + 7 can be thought of as 5 + 5 + 2. [This assumes comfortablility with the double, 5 + 5.]