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Achievement objective NA6-4

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:

  • find optimal solutions, using numerical approaches.


  • Solves problems that can be modelled by a systematic approach, such as:
    • making lists of possibilities and comparing
    • constructing a table of values (trial and improvement).
  • Finds optimal solutions, which are solutions that maximise or minimise a quantity while meeting the constraints of the situation.
  • See key mathematical ideas on NZmaths.


NA 6-4 links to M7-10, M8-4

Possible context elaborations

  • Find the dimensions of a paddock that has maximum area given a fixed perimeter (for example, set amount of fencing material).
  • Design a car park that fits the most cars and meets certain conditions, for example, each car has a fixed amount of space.
  • Find the maximum volume of an open-topped box created from a sheet of A4 paper.
  • Design a container of minimum surface area that holds items (for example, muesli bars, tennis balls, 330 ml liquid).
  • Maximise profit from selling concert tickets where the price of the ticket depends on the number of seats sold.
  • Find the shortest route (time or distance) from Hamilton to Palmerston North.
  • Find the prism that has minimum surface area, given that the cross-section is square and the volume is 700cm3.

  possible context elaboration table.

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 September 17, 2018