Overviews of the levels

Home
Aspects of the Continuum
Aspect 1Counting sequences and numeral identification
Aspect 2Counting as a problem solving process - Early Arithmetical Strategies
Aspect 3Pattern and number structure
Aspect 4Multi-unit place value
Aspect 5Multiplication and division
Aspect 6Fraction units
Aspect 7Measurement
The Continuum chart
Interactive Presentations

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Overviews of the levels

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Introducing the decimal point

Before joining the framework

The Continuum

Aspect 1

Introduction
Challenges in the teens
Forward number word sequences
Backward number word sequences
Zero and the counting numbers
Counting by 10 and 100 in the service of calculating
Numeral identification
References & Acknowledgements

Aspect 2

Introduction
Using counting as a problem solving process
Naïve and sophisticated counting strategies
Emergent counters
Perceptual counters
Figurative stage
Counting-on-and-back stage
Flexible (or facile) stage
References & Acknowledgements

Aspect 3

Introduction
Identifying quantity
From spatial structure to numerical units
Five as a base number
Number models that support the use of five as a base
Array structures
Separating and combining
Using friends of ten with subtraction within 20
Overview of pattern and number structure
References & Acknowledgements

Aspect 4

What does multi-unit place value mean?
Developing understanding of place value
Calculating mentally
Using abstract units of ten
How should these approaches be introduced: Jump, split or both?
Introducing the decimal point
Overviews of the levels
Before joining the framework
Pre-place value (Level 0)
Ten as a unit (Level 1)
Tens and ones (Level 2)
Hundreds, tens and ones (Level 3)
Decimal place value (Level 4)
System place value (Level 5)
Pathological splitting
References & Acknowledgements

Aspect 5

Introduction
Level 1: Forming equal groups
Level 2: Perceptual multiples
Level 3 : Figurative units
Level 4: Repeated abstract composite units
Level 5: Multiplication and division as operations
References & Acknowledgements

Aspect 6

Introduction
Understanding fractions as representing multiplicative relationships
Interpreting notation
Avoiding common pitfalls
Introducing the fraction notation
Comparing different types of units
The idea of the fixed unit whole
Fraction models
The concentration model
Coordinating units at different levels
The ‘fraction units’ framework
Looking back
References & Acknowledgements

Aspect 7

Introduction
The measurement framework
Why bother with informal units?
Area Multiplication
Developing the structure of units in length, area and volume
Level 1: Direct alignment (2 objects)
Level 2: Transitive comparison (3 or more objects)
Level 3: Multiple units of the same size
Level 4: Indirect comparison
Level 5: Iterates the unit
Level 6: Structure of composite units of area
Level 7: Structure of repeated layers
References & Acknowledgements

The Numeracy Continuum Chart Aspect 4

Click the image above to view the Aspect 4 chart.

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The Numeracy Continuum Introduction Video

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