Numeracy and National Standards

Numeracy stages are used to describe the mental strategies that children use when thinking mathematically. Children progress through these stages as they develop their understanding of a range of strategies for solving number problems. Each of these stages is quite precise and may take longer than a year level to master and there are eight stages altogether. The table below shows the stages that a student making expected levels of progress would be at for each year level. 

Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8
Stage 0/1 Level 1	Stage 2/3 Level 1	Stage 4 Level 1	Stage 4/5 Level 2	Stage 5 Level 2	Stage 5/6 Level 3	Stage 6 Level 3	Stage 6/7 Level 4	Stage 7/8 Level 4
Emergent One-to-One Counting	Counting from One on Materials Counting from One by Imaging	Advanced Counting	Advanced Counting Early Additive Part-Whole	Early Additive Part-Whole	Early Additive Part-Whole Advanced Additive Part-Whole	Advanced Additive Part-Whole	Advanced Additive Part-Whole Advanced Multiplicative Part-Whole	Advanced Proportional Part-Whole

What do these Stages mean?

The following table describes the key features of each strategy stage.

Stage 0	The student is unable to consistently count a given number of objects because they lack knowledge of counting sequences and/or one-to-one correspondence.
Stage 1	The student is able to count a set of objects or form sets of objects but cannot solve problems that involve joining and separating sets.
Stage 2	The student is able to count a set of objects or form sets of objects to solve simple addition and subtraction problems.The student solves problems by counting all the objects.
Stage 3	The student is able to visualise sets of objects to solve simple addition and subtraction problems.The student solves problems by counting all the objects.
Stage 4	The student uses counting on or counting back to solve simple addition or subtraction tasks.
Stage 5	The student uses a limited range of mental strategies to estimate answers and solve addition or subtraction problems. These strategies involve deriving the answer from known basic facts (for example doubles, fives, making tens).
Stage 6	The student can estimate answers and solve addition and subtraction tasks involving whole numbers mentally by choosing appropriately from a broad range of advanced mental strategies (for example place value positioning, rounding and compensating or reversibility). The student uses a combination of known facts and a limited range of mental strategies to derive answers to multiplication and division problems (for example doubling, rounding or reversibility).
Stage 7	The student is able to choose appropriately from a broad range of mental strategies to estimate answers and solve multiplication and division problems. These strategies involve partitioning one or more of the factors (for example place value partitioning, rounding and compensating, reversibility).
Stage 8	The student can estimate answers and solve problems involving the multiplication and division of fractions and decimals using mental strategies. These strategies involve recognising the effect of number size on the answer and converting decimals to fractions where appropriate.  These students have strongly developed number sense and algebraic thinking.

Click on the NZ Curriculum Online picture below for further explanation about what is involved in moving through each of these stages.

Please remember that your child's teacher is the best person to discuss your child's progress in Maths with. They know their learners and can help to explain the National Standards information above.