Small Numbers, Big Ideas: Essential Concepts for Teaching Early Maths

US$ 23.99

The publisher has enabled DRM protection, which means that you need to use the BookFusion iOS, Android or Web app to read this eBook. This eBook cannot be used outside of the BookFusion platform.

Description

Contents

Reviews

Language

English

ISBN

9781036003722

Cover

Title Page

Copyright Page

Acknowledgements

Reviews

Contents

Introduction

Manipulatives and models

Chapter 1 – Counting

The counting principles

• The stable order principle

• One-to-one correspondence

• The cardinal principle

• Cardinality

• Conservation of number

• Order irrelevance

• Abstraction

Further counting skills

• Substitution

• Ordinal counting

• Counting larger sets

• Counting backwards

Knowing how many without counting

• Understanding zero

• What is subitising?

• Effective subitising practice

Chapter 2 – Composition

The part-whole concept

• Partitioning numbers

• Part-whole models

• Part-whole bar models

Number bonds

• Bonds to 10

• All bonds within 10

Early place value

• ‘Ten and some more’

• Straws and elastic bands

• Dienes blocks

• Place value grids

• Bead strings

Odd or even?

• Introducing odd or even

• Odd or even beyond 10

• Zero is even

• Common misconceptions of odd or even

• Exploring odd or even more deeply

Chapter 3 – Comparison and equality

Comparing sets of objects

Comparison problems

Progression in comparison

Understanding equality #1

Introducing comparison symbols

Comparing expressions

Understanding equality #2

Finding the difference

Comparison bar models

Bar models summary

Comparing and sorting numbers by properties

Chapter 4 – Number sense

Why represent numbers in many ways?

Matching numbers to collections without counting

Estimation

Ten-frames and rekenreks

Number lines

Chapter 5 – Addition and subtraction

What is addition?

What is subtraction?

Commutativity

Inverse operations

Adding three or more numbers

Subtraction of two or more parts

Fact families

Explicitly teaching all bonds within 10

Typical conceptual progressions

• Progression in addition

• Progression in subtraction

• Other key strategies for addition and subtraction

Missing number problems

Chapter 6 – Multiplication and division

Equal and unequal groups

Adding equal groups (repeated addition)

Exploring equal groups

Commutativity of multiplication

Multiplying by one

Multiplying by zero

What is division?

• Division by sharing

• Division by grouping

Subtracting equal groups (repeated subtraction)

Introducing remainders

Multiplication and division fact families

Missing number problems

Chapter 7 – Shape, space and measures

Shape

• 2D and 3D shapes

• Properties of shapes

• Comparing and sorting shapes

Spatial reasoning

• Positional language

• ‘Perspective-taking’

• Direction and navigation

• Decomposing and recomposing shapes

• Do identical shapes fit together?

• Thinking about size and shape

• Pattern

Measures

• Conservation principles

• Measure misconceptions

Money

• How money works

• Money misconceptions

• Making amounts of money

• Change

Afterword

Taking it further

Bibliography

The book hasn't received reviews yet.