5. Fractions

5.1 Introduction

The idea of dividing whole things into smaller pieces, fractions, is integral to our culture. It is embedded into our language in many ways: in the way we tell the time as ‘quarter to’ or ‘half past’ the hour; the way we write recipes with ‘½ a teaspoon’ or ‘a quarter of a cup’ and how we buy our food using ‘half or quarter kilos’. Understanding and using these terms in the everyday sense is an essential aspect of numeracy.

Unfortunately, fractions have often been dealt with in such an abstract way in secondary schools that many students fear the very word. By focussing on commonly used, everyday fractions such as ½, ¼, ¾, this sections revisits fractions in everyday use to build students’ confidence in relation to fractions.

The section also outlines methods for using hands-on materials to clarify the meaning of fractions with a focus on how they are written in symbols and in words and how they are said. It also outlines activities to briefly explore how fractions relate to one another and what it means to combine or double quantities such as ½ or 1½ as they occur in practical situations, such as recipes.

5.2 The Meaning of Fractions

This activity:

  • Uses hands on materials to explore the meaning of fraction words and symbols

  • Begins with familiar, everyday fractions such as ½, ¼ and ¾

  • Extends the concept and notation to make sense of other fractions

  • Uses circle shapes because it is the easiest to see when you have the whole

5.3 Matching Common Fractions

This activity is designed to be used with small groups or pairs:

  • To revisit the fraction concepts and symbols introduced in The Meaning of Fractions activity.

  • As an alternative introduction to the concepts and language of fractions for students with some prior knowledge.

5.4 Comparing Fractions

This is a two part activity which follows from previous activity The Meaning of Fractions.

This activity:

  • Uses fraction kits and folded paper

  • Explores the relative sizes of fractions

  • Introduces simple ideas of equivalence

  • Provides further practice at naming fractions

  • Builds understanding of fraction concepts and symbols.

5.5 Sorting Fractions of …

This sorting activity forms a bridge between the concept of fractions of single shapes and fractions of a number. It uses familiar quantities such as ‘half an hour = 30 minutes’ to link the process of dividing numbers and finding a fraction of them.

5.6 Exploring Mixed Numbers

This activity presents a brief explanation of fractions, such as 3/2 and 9/4 and their more familiar meanings as 1½ and 2¼.

It introduces the idea that you can have fractions great than 1.

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