A fraction of a set

A fraction of a set describes part of a collection of objects. Your child first identifies the complete set, then uses the denominator to divide that set into equal groups. The numerator tells how many of those groups are wanted. This directly develops the MOE Primary 4 outcome on fraction as part of a set and connects a fraction to an actual number of objects.

• Identify the whole collection named after the word 'of', rather than choosing a total from elsewhere in the question.
• Divide the number in the collection by the denominator to find the number of objects in one equal group.
• Multiply the size of one group by the numerator to find the number represented by the required fraction.
• Distinguish a question asking for a fraction from one asking for a number of objects, and give the corresponding answer form.
• Find the objects outside a stated part by subtracting that part's count from the complete collection, when the categories cover the whole set.

When a non-empty part is a proper fraction of a set, its count must be smaller than the whole set's count. For separate selected and unselected groups that cover the collection, your child can add their counts to recover the original total.

The More questions row contains the apple and bun questions, each asking for a fraction of a known collection. The Intermediate question finds the difference between two groups of chairs after one group's fraction is given. Choose an apple or bun task when your child needs to practise dividing a whole collection into equal parts before finding several of those parts. For the chair comparison, ask for both group counts and check that they add back to the total before finding how many more there are. These questions do not form a Basic or Challenge group. If your child needs a demonstration, members can open the solution film after trying the question. The free chair card includes written working for finding both colour groups and their difference, allowing you to review how each count relates to the whole collection.

What is the difference between a fraction of a shape and a fraction of a set? A shape is treated as one whole split into equal parts of its area. A set is a collection whose objects are grouped or counted. In both cases, your child must identify the whole, but a set question may ask how many objects belong to the stated fraction.

Why does my child divide before multiplying to find the part? Dividing by the denominator finds one equal group; multiplying by the numerator counts the required groups. This order gives each line a meaning your child can explain. For a collection divided into equal groups of whole objects, the first division should produce a whole-number group size.

How can I tell whether my child understands the word 'of'? Ask your child to finish the phrase with the actual collection: a fraction of all the counters, for example, or of one named group. Then ask which number counts that collection. This short explanation shows whether the chosen total matches the fraction before any arithmetic begins.