# Fraction circles

Purpose

These exercises and activities are for students to use independently of the teacher to practice number properties.

Achievement Objectives
NA3-5: Know fractions and percentages in everyday use.
NA4-4: Apply simple linear proportions, including ordering fractions.
NA3-5: Know fractions and percentages in everyday use.
NA4-4: Apply simple linear proportions, including ordering fractions.
Specific Learning Outcomes

Ordering unit fractions (exercises 1 and 2)
Ordering non-unit fractions (exercises 3 to 5)

Description of Mathematics

Number Sequence and Order, AA (Stage 6)
Number Sequence and Order, AM (Stage 7)

Required Resource Materials
Practice exercises with answers (PDF or Word)

Homework with answers (PDF or Word)

Activity

### Prior knowledge.

Students should have completed the activity ‘fair shares’ Book 7, Fair Shares

### Background

Ordering unit fractions and non-unit fractions, without using equipment involves quite different skills, and are found at different stages of the knowledge framework. A useful introduction to sorting non-unit fractions is to develop students’ strategies for identifying when a fraction is close to one (eg is close to one as there is only 1 little piece missing from a whole) or zero. Likewise for fractions below or above one half (for example 2/5 is less than one half as in one half, the denominator is double the numerator. In two fifths, doubling 2 gives a number smaller than the denominator).

### Comment on the Exercises

Exercise 1
Asks students to identify the bigger fractions in a pair.

Exercise 2
Asks students to order 3 unit fractions from smallest to biggest.

Exercise 3
Asks students to identify the bigger fraction in a pair.  Fractions are halves, quarters, thirds, and fifths.

Exercise 4
Asks students to order 3 fractiosn from biggest to smallest.  The fractions are halves, quarters, thirds, and fifths.

Exercise 5
Asks students to solve word problems that involve identifying the largest fraction.