Number Strategies and Knowledge: Level 4

The Ministry is migrating nzmaths content to Tāhurangi.           
Relevant and up-to-date teaching resources are being moved to Tāhūrangi ( 
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024. 
e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available. 

For more information visit

The key idea of number strategies and knowledge at Level 4 is that rational numbers can be represented and operated on in a variety of ways to solve problems.

At level 4 students have developed an understanding of representations for and a variety of strategies for operating on rational numbers. Rational numbers are any number that can be expressed as a fraction with an integer as the numerator and an integer other than zero as the denominator. All decimal fractions are rational numbers.

Rational numbers also include all:

  • Natural numbers: the counting numbers (1, 2, 3, 4...).
  • Whole numbers: the natural numbers and zero (0, 1, 2, 3...).
  • Integers: positive and negative whole numbers (...-2, -1, 0, 1, 2...)

There are a number of ways that rational numbers can be represented including:

  • Graphically, for example numberlines, tens frames, arrays.
  • Using exponents, for example 94 = 9 x 9 x 9 x 9 = 6561.
  • Expanded form, for example 873 = 800 + 70 + 3.
  • Standard form, for example 120 = 1.2 x 102.

Strategies that can be used to solve problems by students at this level include:

  • Reversibility
  • Doubling and halving
  • Compensation
  • Place value partitioning
  • Using the distributive property

Further information on Number strategies can be found in the books supporting the Numeracy Development Projects.

This key idea develops from the key idea of number knowledge at level 3 where students understood a variety of ways to represent numbers and the key idea of number strategies at level 3 where they could apply a range of strategies to solve simple multiplication and division problems.

This key idea is extended in the key idea of number strategies and knowledge at level 5 where students are able to apply multiple operations to solve problems.