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