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.
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
S6-3, algebra
NA6-5, and graphing
NA6-7.
Progression
NA 6-1 links to NA6-3, M7-3
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 NA5-3, 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?
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Activity: Measuring with digital pictures
-
Investigating GST
Assessment for qualifications
NCEA achievement standards at level 1 and 2 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.
Aligned level 3 achievement standards will be registered by NZQA for use in 2013.
Full information on the level 3 draft standards and the alignment process can be found on
NCEA on TKI.
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 draft standards matrix.
Last updated September 25, 2012
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