AC9M10M03 – Year 10 Mathematics: Measurement
Content Descriptor
This content descriptor sits within Year 10 Mathematics. Use it to identify the learning students need, connect it with the achievement standard and plan suitable evidence of learning.
What this means for planning
AC9M10M03 asks students to solve practical problems with Pythagoras’ theorem and right angled triangle trigonometry. The descriptor extends beyond routine calculation to directions, angles of elevation and depression, so students need to represent the situation before selecting and applying a method.
A practical planning sequence
- Secure the representation: Use diagrams, labels, bearings and angles to translate each practical situation into one or more right angled triangles.
- Choose and justify a method: Ask students to decide whether Pythagoras’ theorem or a trigonometric ratio is appropriate and explain the choice.
- Interpret and check: Return the calculated value to the original context, include suitable units and test whether the result is reasonable.
Evidence to look for
- An accurate diagram or model clearly showing the known and unknown quantities in context.
- A justified method with correct mathematical working, notation and units.
- An interpretation that checks the result against the practical constraints of the problem.
See the complete curriculum context
Open the achievement standard and all linked content descriptors together in the Year 10 Mathematics curriculum map.
Related item: Explore AC9M10ST03: scatterplots and association.
A TeaCheese planning example
Use AC9M10M03 in a TeaCheese planning brief to generate a progression from diagram interpretation to bearings or elevation problems with explicit reasonableness checks.
Planning guides: How content descriptions work in the Australian Curriculum · Turn a content description into learning intentions and success criteria
Elaborations
- • Elaboration applying right-angled trigonometry to solve navigation problems involving bearings; for example, determining the bearing and estimating the distance of the final leg of an orienteering course
- • Elaboration applying Pythagoras’ theorem and trigonometry to problems in surveying and design, where three-dimensional problems are decomposed into two-dimensional problems; for example, investigating the dimensions of the smallest box needed to package an object of a particular length
- • Elaboration using a clinometer to measure angles of inclination, and applying trigonometry, and proportional reasoning to determine the height of buildings in practical contexts
- • Elaboration applying Pythagoras’ theorem and trigonometry, and using dynamic geometric software, to design three-dimensional models of practical situations involving angles of elevation and depression; for example, modelling a crime scene
- • Elaboration investigating how autonomous vehicles use algorithms that use Pythagoras' theorem and trigonometry to calculate distance and navigate spaces; for example, if an autonomous vehicle knows its current position (x, y) and the coordinates of a target location (x', y'), it can determine the straight-line distance between them using the formula distance =\sqrt{(x'-x)^2 + (y'-y)^2}
- • Elaboration exploring navigation, design of technologies or surveying by First Nations Australians, investigating geometric and spatial reasoning, and how these connect to trigonometry
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