Ordering unit fractions
Number Sequence progression, 4th step
The purpose of the activity
In this activity, the learners order unit fractions using strips of paper. The learners need to be familiar with the concepts addressed in the “Understanding fractions 1” activity (ordering fractions with the same denominator) before they start this activity.
The teaching points
For unit fractions, as the value of the denominator gets larger, the size of the fraction gets smaller. (Note: This is a difficult concept for learners because of the previous knowledge that, for whole numbers, the sequence 1, 2, 3, 4, 5, … relates to an increase).
Unit fractions are placed between 0 and 1 on the number line.
Discuss with the learners what they already know and how they use what they know when solving a fraction problem.
A set of fraction strips as for the “Understanding fractions 1” activity (ordering fractions with the same denominator).
Cards: one with 0, one with 1 and the rest with one unit fraction (each learner needs one unit fraction card).
The guided teaching and learning sequence
1. Ask the learners to place the fraction strips for 1/2, 1/3 and 1/4 in order from smallest to largest.
2. Ask the learners to identify which is bigger 1/2 or 1/3 and to describe how they know this. Encourage them to use their fraction strips if they are unable to answer this question. Listen for the idea that if a whole is divided into two equal parts, each part is bigger than if it is divided into three equal parts.
3. Repeat this question comparing 1/3 and 1/4.
4. Write 1/2, 1/3, 1/4 on the board and ask the learners to look for a pattern between the denominator and the size of the fraction. Listen for the idea that as the denominator gets bigger, the fraction gets smaller.
5. Ask the learners to consider whether 1/5 or 1/6, 1/7 or 1/9, 1/99 or 1/100 is bigger and to describe how they know this.
6. Once the learners are familiar with the concept:
place the card labelled “0” at one end of the room
place the card labelled “1” at the other end of the room
give each learner a card with a different unit fraction on it and ask the learners to stand in the ‘correct’ place between 0 and 1.
The learners can place sets of unit fractions in order from smallest to largest.