Achievement objective NA61
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.
Indicators
 Uses a variety of methods, for example, 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.
 Makes links with probability
S63, algebra
NA65, and graphing
NA67.
 See
key mathematical ideas on NZmaths.
Progression
NA 61 links to NA63, M73
What is new/changed?
 Using a range of different methods in solving rate, ratio, and percentage problems, not just the algorithmic numerical method.
 Basic operations on fractions is covered in NA53, understanding operations on fractions, decimals, percentages, and integers.
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:
 AS 91026 Mathematics and statistics 1.1 Apply numeric reasoning in solving problems
Refer to the
mathematics and statistics matrix.
Last updated September 26, 2013
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