Developing Fractions Knowledge

Supporting and understanding your students’ fractional knowledge is crucial to their overall grasp of numbers and mathematics. By centralising around three key stages of development, this effective guide will help you to assess your students’ understanding of fractions and modify your teaching accordingly.

These key stages are identified as:

• Stage 1a: Fair Sharing
• Stage 1b: Part-Whole
• Stage 2a: Disembedding and Iterating
• Stage 2b: Measuring with Unit Fractions
• Stage 2c: Reversing Fractions
• Stage 3a: Fractions as Numbers
• Stage 3b: Operating with Fractions

As the newest addition to the bestselling Maths Recovery Series, this book will be a useful guide for all primary classroom teachers and assistants, including experienced Mathematics Recovery instructors.

Table of Contents

Introduction

Professional Learning and Three Grand Organizers for Arithmetic Instruction

From Whole Numbers to Fractions

Assessing Stages of Units Coordination

Teaching Students at Stage 1: Fragmenting

Transitioning to Stage 2: Part-Whole Reasoning

Teaching Students at Stage 2: Measuring with Unit Fractions

Teaching Students at Stage 2: Reversible Reasoning

Teaching Students at Stage 3: Fractions as Numbers

Teaching Students at Stages 2 and 3: Equal Sharing of Multiple Items

Teaching Students at Stages 2 and 3: Multiplying Fractions

Teaching Students at Stages 2 and 3: Adding and Subtracting Fractions

Teaching Students at Stages 2 and 3: Dividing Fractions

From Fractions to Algebra

"With its beginnings in whole-number arithmetic understanding, Developing Fractions Knowledge is the most comprehensive look at fractions learning to date. It journeys with the practitioner and learner to view fractions as part-whole concepts, measures, and ultimately as numbers with meaning. The assessment and instructional tasks and practical connections to research and Math Recovery principles make it a must-have resource for educators to use again and again!"
- Carolyn Olijnek, US Math Recovery® Council

"Developing Fractions Knowledge skilfully combines cutting-edge research with practical knowledge of the classroom to provide an essential resource for everyone interested in developing students’ understanding of fractions. I can’t wait to try some of the tasks and activities with students!"
- Dr Janette Bobis, Professor in Mathematics Education, University of Sydney

"The book includes many example assessment tasks and instructional activities to use with pupils who are learning about fractions for the first time, as well as pupils who are struggling and working to relearn concepts. This book provides a comprehensive look at fraction knowledge and understanding. It is a great book for anyone teaching primary maths at any age, but would also be appropriate for a longer-term, on-going departmental professional development."
- Matthew Reames, SATIPS - Support and Training in Prep, Primary and Senior Schools