In 3F–1 pupils learnt how fractions act as operators on a whole. Now they must learn to evaluate the outcome of that operation, for unit fractions of quantities, and connect this to what they already know about dividing quantities into equal parts using known division facts.
In year 3, pupils learn the 5, 10, 2, 4 and 8 multiplication tables, so examples in this criterion should be restricted to finding 1/5, 1/10, 1/2, 1/4 or 1/8 of quantities. This allows pupils to focus on the underlying concepts instead of on calculation. Pupils should begin by working with concrete resources or diagrams representing sets. As in 3F–1, they should identify the whole, the number of equal parts, and the size of each part relative to the whole written as a unit fraction. They should then extend their description to quantify the number of items in a part, and connect this to the unit-fraction operator.
“The whole is 12 oranges. The whole is divided into 4 equal parts.”
“Each part is 1/4 of the whole. 1/4 of 12 oranges is 3 oranges.”
Once pupils can confidently and accurately describe situations where the value of a part is visible, they should learn to calculate the value of a part when it cannot be seen. Bar models are a useful representation here. Pupils should calculate the size of the parts using known division facts, initially with no reference to unit fractions. This is partitive division (3MD–1). Then pupils should make the link between partitive division and finding a fraction of a quantity. They should understand that the situations are the same because both involve dividing a whole into a given number of equal parts. Pupils must understand that, therefore, division facts can be used to find a unit fraction of a quantity.
“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.”