3. Using group work to explain equivalent fractions

How can pupils compare fractions that have different denominators (e.g. 3/5 + 1/4)?

They could make fraction strips to compare the different fractions, but although this supports comparison, it doesn’t help them add or subtract such fractions. To do this, they must understand common denominators. Resource 5: Comparing fractions explains how these work.

Case Study 3: Using the part-whole model

Mrs Dokono decided to use the part-whole model to introduce equivalent fractions to her class and to develop her skills of using group work and practical work.

She knew that using everyday objects helps pupils’ understanding, and took to her class some biscuits to help her explain equivalent fractions. First, she divided the class into groups of eight and told them they were going to explain how 20 biscuits could be shared equally among a number of children.

Next, she assigned each group a different number of biscuits. She gave one group 2 biscuits and asked them to share these biscuits among 4 pupils. They saw that 2 divided by 4 gave each pupil 1/2 a biscuit. She wrote on the board 2 divided by 4 = 2/4 = 1/2.

She repeated this problem with other groups and 3 biscuits among 6 of the pupils.

Then she gave 4 biscuits among 8 pupils, each getting half a biscuit.

Each time she wrote the fractions on the board 2/4, 3/6, 4/8 with each equal to 1/2.

She told the pupils that these are called equivalent fractions.

Mrs Dokono was pleased with the class response to her mathematics lesson using the biscuits to explain equivalent fractions.

Key Activity: Equivalent fractions

Using halves, thirds and quarters, write down five additions, e.g.

  • (1/2 + 1/4)
  • (1/3 + 1/2),
  • (3/4 + 2/3),
  • (2/4 + 1/3),
  • (2/3 + 1/4).

Show how to work out the common denominator of the first sum. Ask pairs of pupils to calculate the remaining common denominators.

Show pupils how to convert the numerator for the first two sums; ask pupils to complete the next three sums.

Show how to find the answer to the first two sums; ask pupils to complete the last three sums.

Ask each pair of pupils to make up and solve as many similar problems as they can in ten minutes.

After the lesson, look at Resource 6: Questions for self-evaluation and ask yourself questions on your use of practical activities and resources.

2. Adding and subtraction with fraction strips

Resource 1: Fractions