Find non-unit fractions of quantities (3)

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Language focus

“To find of 1/5 , we divide 15 into 5 equal parts.”

“15 divided by 5 is equal to 3, so  1/5 of 15 is equal to 3.”

By the end of year 5 pupils must be able to find unit and non-unit fractions of quantities, including for situations that go beyond known multiplication and division facts. Pupils already understand the connection between a unit fraction of a quantity and dividing that quantity by the denominator. Now they should learn to reason about finding a non-unit fraction of a quantity, using division (to find the unit fraction) then multiplication (to find multiples of the unit fraction), and link this to their understanding of parts and wholes. Initially, calculations should depend upon known multiplication and division facts, so that pupils can focus on reasoning.

Language focus

“Three-fifths is equal to 3 one-fifths.”

“To find 3 one-fifths of 40, first find one-fifth of 40 by dividing by 5, and then multiply by 3.”

Once pupils can carry out these calculations fluently, and explain their reasoning, they should extend their understanding to calculate unit and non-unit fractions of quantities for calculations that go beyond known multiplication table facts. For example, they should be able to:

  • apply place-value understanding to known number facts to find 3/7 of 210
  • use short division followed by short multiplication to find 4/9 of 3,411

Pupils should also be able to construct their own bar models to solve more complex problems related to fractions of quantities. For example:

Miss Reeves has some tangerines to give out during break-time. She has given out  5/6 of the tangerines, and has 30 left. How many tangerines did Miss Reeves have to begin with?

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