Step 5 Objective

Multiply and divide decimals mentally by 10 or 100, and integers by 1000, and explain the effect.

Examples of what pupils should know and be able to do

Complete statements such as:

4 ÷ 10 = what number             4 ÷ what number = 0.04
0.4 × 10 = what number             0.4 × what number = 400
0.4 ÷ 10 = what number             0.4 ÷ what number = 0.004
what number ÷ 100 = 0.04             what number ÷ 10 = 40
what number × 1000 = 40,000             what number × 10 = 400

Probing questions

Why do 25 ÷ 10 and 250 ÷ 100 give the same answer?

This calculator display shows 0.001. Tell me what will happen when I multiply by 100. What will the display show?

I divide a number by 10, and then divide the result by 10. The answer is 0.3.

What number did I start with? How do you know?

How would you explain to someone how to multiply a decimal by 10 . . . , how to divide a decimal by 100? . . .

What if pupils find this a barrier?

Use units that pupils are confident with, for example conversions between cm and m.

Encourage pupils to use common sense, e.g. 0.67 × 100. Is the answer larger or smaller?

Moving digits ITP - Zip file (457Kb) can be used to show that it is the digits that 'move' and not the decimal point.

Use Teaching mental calculation strategies loop cards set 10 - Acrobat pdf document (25Kb) to practise