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Achievement objective NA6-6

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

  • generalise the properties of operations with rational numbers, including the properties of exponents.


  • Uses algebra to describe the properties of operations (addition, subtraction, multiplication, and division) as they apply to rational numbers and exponents, for example, expanding, factorising, and simplifying.
  • Uses the properties of addition, subtraction, multiplication, division, and exponents in solving problems.
  • Uses the operations on rational numbers without technology.
  • Makes links with exponents NA6-2.
  • See key mathematical ideas on NZmaths.


NA6-6 links to M7-6.

Possible context elaborations

  • Sue and Jane were asked to factorise 12 + 4u. Sue’s answer was 2(6+2u); Jane’s answer was 4(3+u). Which is the better answer and why?
  • Generalising properties of operations (see Quick Times and Really Mr. Bond)
  • Difference of two squares
  • Napier’s method
  • Derive other properties of exponents by applying first principles to specific cases, for example, 32 x 42 = 3 x 3 x 4 x 4 = 12 x 12 = 122 leading to anbn = (ab)n

Assessment for qualifications

NCEA achievement standards at level 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the NZQA website.

The following achievement standard(s) could assess learning outcomes from this AO.

Last updated August 16, 2019