Fractions in division
Number Sequence progression, 4th step
The purpose of the activity
In this activity, the learners further develop their understanding of fractions by cutting and sharing strips of paper equally among a given number of people. The activities “Understanding fractions 1 and Understanding fractions 2” should be completed first.
The teaching points

The learners will understand how to use fractions in division problems where the numbers do not divide evenly.

The learners will understand the relationship between division and fractions – that the number to be shared out is represented by the numerator and the number of ways it is shared by the denominator. For example, if 3 strips are to be shared between 2 people, each person will get 3/2 of a strip. (The learners may have already come across 3 ÷ 2 written as 3/2 .)

The learners will study alternative ways of writing fractions (for example, 3/2 is the same as 1 1/2).

Discuss with the learners other ways they have seen fractions written.

Discuss with the learners the contexts in which they use fractions.
Resources

Strips of paper (approx 5 centimetres by 25 centimetres).

Scissors.
The guided teaching and learning sequence
1. Have the learners work in pairs and give each pair three strips of paper and ask them to share the strips equally between the two of them.
2. Record the different strategies the learners use to share the strips. Some may cut each strip in half so each person has 3/2 strips, while others may give one strip to each person and cut the remaining strip in half so each has 1 1/2 strips.
3. Ask the learners:
“Do these numbers both represent the same amount?” Explain why.
“Can you see a relationship between the number of strips to be divided and the number of people they are to be divided between?”
4. Ask the pairs to join with another pair to form groups of 4 and predict how many strips each person would get if they shared 6 strips of paper equally between them. Ask the learners to share the strips out and check their predictions. Record the different strategies that the learners used (6/4, 1 2/4, 1 1/2) – suggest other possibilities if not all strategies are offered.
5. Again ask the learners:
“Do these numbers all represent the same amount?” Explain why.
“Can you see a relationship between the number of strips to be divided and the number of people they are to be divided between?”
6. Ask the class to regroup to form groups of 6 and have the groups predict how many strips each person would get if they shared 4 strips of paper equally between them. Ask the learners to share the strips out and check their predictions. Record the different strategies the learners used (4/6, 2/3) – suggest other possible strategies if not all are offered. Check whether the relationship suggested in sequence 3 and 5 above (“between the number of strips to be divided and the number of people they are to be divided between”) still holds.
Followup activity
Ask the learners to record the fractions for the following problems and discuss their answers with other learners.

7 people sharing 2 strips equally

2 people sharing 7 strips equally

15 people sharing 4 strips equally

12 people sharing 24 strips equally.