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Numeracy 2003. Presented by JB 2003. “To be numerate is to have the ability and inclination to use mathematics effectively in our lives – at home, at work and in the community.” Curriculum Update 45 Ministry of Education 2001. Ministry Philosophy. Research based Dynamic and evolutionary

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numeracy 2003

Numeracy 2003

Presented by




“To be numerate is to have the ability and inclination to use mathematics effectively in our lives – at home, at work and in the community.”Curriculum Update 45 Ministry of Education 2001

ministry philosophy
Ministry Philosophy
  • Research based
  • Dynamic and evolutionary
  • Teachers are key figures in change
  • Focus is to improve student performance through teacher professional development
  • Ministry Taskforce report 1995
  • Count Me In Too Australia
  • Trialled in New Zealand 2000
  • Australian modeladapted to suit NZ students and framework extended
  • Numeracy projects 2001 ENP ANP NEST
  • 2002/3 ENP ANP INP SNP
learning outcomes
Learning Outcomes
  • Teachers will gain an awareness of the New Zealand Number Framework and Assessment Tool.
  • Teachers will develop an understanding of the progression of student’s number acquisition.

Creates new knowledge through use


Provides foundation for strategies

Strategy is about how children solve number problems, in particular the mental processes they use.

Knowledge considers the key items of knowledge that children need to acquire.

stages of development
Stages of Development

Stage 0 Emergent

Stage 1 1 – 1 counting

Stage 2 Counting from 1 on Materials

Stage 3 Counting from 1 by Imaging

Stage 4 Advanced Counting

Stage 5 Early Additive

Stage 6 Advanced Additive/Early Multiplicative

Stage 7 Advanced Multiplicative/Early Proportional

Stage 8 Advanced Proportional


This child is unable to count a set of objects


Rote count to 5 at least.

one to one counting

Count a set of objects to 10 by one to one matching


Rote count to 10 at least

One To One Counting
counting from one on materials

Solve simple addition and subtraction problems to 20 by counting all the objects.


Rote count to 20 at least

Instant recognition of patterns to 5 including finger patterns

Forward and backward number word sequence 0 – 20

Order numbers to 20

Numbers before and after in the range 1 - 20

Counting from one on Materials
counting from one by imaging

Solve addition and subtraction problems to 20 by counting all the objects and or numbers in my head.


Instant recognition of patterns to 10 including finger patterns

Ordering numbers 0-20

Forward and backward word sequence in the range 0 –20

Say the number before and after a given number in the range 0-20

Counting From One By Imaging
advanced counting

Solve addition and subtraction problems by counting on or back in my head from the largest number using supporting materials then moving to imagery.

Solve addition and subtraction problems by counting on in 10’s and 1’s.

Solve multiplication problems by skip counting in 2s, 5s 10s.


Recognising numbers 0 –100

Ordering numbers 0-100

Forward and backward word sequence 0-100

Numbers before and after a given number from 0-100

Skip count in 2s, 5,s 10s forwards and backwards.

Advanced Counting
early additive part whole

Solve addition and subtraction problems in their head by working out the answer from basic facts they know.

Solve addition and subtraction problems with 2 or 3 numbers using groupings of 10 and 100.

Use addition strategies to solve multiplication strategies


Recall doubles to 20 and corresponding halves

Recall the names for 10

Recall the teen numbers

Skip count in 2s,5s, 10s forwards and backwards

Early Additive Part Whole
advanced additive part whole

Choose from:


Place Value

Compatible numbers


Equal Additions


to solve + and - problems.

Use pencil and paper or calculator to work out answers where the numbers are large or untidy

Carry out column + and – with whole numbers of up to 4 digits.

Solve multiplication and division problems using known strategies eg doubling, rounding.


Identify numbers 0-1000

Forward and backward sequence by 1,10,100 to 1000

Order numbers from 0-1000

Recall + and - facts to 20

Recall multiplication facts for 2, 5, and 10 times tables.

Advanced Additive Part Whole
advanced multiplicative part whole

Solve +, - , x and ÷ problems with whole numbers (and decimals) using a range of strategies.

Solve problems involving fractions, decimals, proportions and ratios using multiplication and division strategies


Identify, order and say forward and backward number sequence from 0 –1000000

Recall multiplication and division facts.

Order fractions, including those greater than 1.

Advanced Multiplicative Part Whole
advanced proportional part whole

Choose appropriately from a broad range of strategies to +, -, x and ÷ fractions and decimals.


Know equivalent proportions for unit fractions with numbers to 100 and 1000

Know fraction, decimal, % conversion for unit fractions.

Order decimals to 3 places.

Advanced Proportional Part Whole
stage and behavioural indicators
Stage and Behavioural Indicators
  • When testing students you will observe their strategies and knowledge within the framework stages of development.
  • This is what they can do now.
  • Strategy teaching begins with consolidation at students highest current stage before moving them into the next stage.
numeracy project assessment numpa
Numeracy Project Assessment -NumPA
  • NumPA is a diagnostic tool.
  • The interview consists of two main parts; knowledge questions and strategy questions.
  • NumPA is an individual interview with children. This is necessary for two reasons:
    • Uncovering mental strategies involves finding out how they solve number problems.
    • The interview process is invaluable for developing the teacher’s knowledge about each child’s mathematical understandings.

Purpose of Strategy Window

  • To assist teachers in being able to:
  • Focus on uncovering student thinking.
  • Determine which interview form to administer through the use of careful questioning.
  • Save time.


  • To uncover thinking after the student responds:
    • How did you get the answer?
    • What numbers came into your head?
    • Where did you start counting?
    • What did you start with?
    • What numbers came next?
    • What did you do with the numbers?
    • Allow maximum of 10 seconds thinking time .
    • What are you trying to do?