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Understand the effects of multiplying and dividing by numbers between 0 and 1

Examples of what pupils should know and be able to do

Understand that multiplying a positive number by a number between 0 and 1 makes it smaller and that dividing it by a number between 0 and 1 makes it larger. Use this to check calculations and to estimate the order of magnitude of an answer.

Probing questions

  • Multiplying makes numbers bigger. When is this statement true and when is it false?
  • Division makes numbers smaller. When is this statement true and when is it false?
  • How would you justify that dividing by 12 is the same as multiplying by 2?

What if pupils find this a barrier?

Explore using a calculator.

For example, start with 100 and then multiply or divide by a succession of numbers to get to a target of 3, for example. The numbers used must be between 0 and 1.

Ordering activities can be helpful. Give pupils sets of cards with appropriate calculations on them. Ask pupils in pairs to order the calculations according to the size of the answer. See Teaching mental mathematics: Place value and ordering.

Pupils may need to revisit step 6.