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  • 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

title aspect4

Overviews of the levels

aspect 4 overview table1a

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

aspect4 sm

Click the image above to view the Aspect 4 chart.

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