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Achievement objective NA6-1

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:

  • apply direct and inverse relationships with linear proportions.


  • Uses a variety of methods, for example, number strategies, equations, tables and graphs, in solving rates, ratios, and percentages problems.
  • Uses rates in solving problems, for example, speed, blood/alcohol levels, heart rate, pay rates, comparing rates, density.
  • Uses ratios in solving problems, for example, scale factor, recipes, unit costs, comparing quantities.
  • Uses percentages in solving problems, for example, percentage of a quantity, expressing a ratio as a percentage.
  • Uses rates, ratios, and percentages in both directions, for example, inverse percentages (finding the original amount).
  • Investigates situations involving relationships of the form y = kx and y=k/x.
  • Makes links with probability S6-3, algebra NA6-5, and graphing NA6-7.
  • See key mathematical ideas on NZmaths.


NA 6-1 links to NA6-3, M7-3

Possible context elaborations

  • Exploring the golden ratio.
  • Conversion between rates, ratios, and percentages.
  • Solving ratio problems using methods such as partitioning, replicating, and ratio tables.
  • Exploring distance, time, and speed.
    • A car travels from A to B in 25 minutes at 100 kilometres per hour. How long will the trip take at 80 kilometres per hour? This can be represented as 25 x 100 = 80x.
  • Examples such as:
    • find 65% of 43, this can be represented as 65/100 = x/43 or 0.65 x 43 =
    • which is the stronger concentration of syrup to water, 2:7 or 3:11? This can be represented as 2/9 > 3/14 (the fractions represent the part to whole relationships)
    • for what positive integer values of x is the following inequality true, 2/5 > 6/x?
  • Activity: Measuring with digital pictures
  • Investigating GST

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