Expected level of development
Australian Curriculum Mathematics V9: AC9M8M05
Numeracy Progression: Proportional thinking: P5
At this level, students recognise and use rates to solve problems including constant rates, rate of pay, cost per kilogram, recipes, simple interest and average rates. Students will also be required to make comparisons between two related quantities of different units of measurement. They will write rates in their simplest form, giving the amount for one unit of the second quantity, for example, 50km/1 hour as 50km/h.
Students are to apply their knowledge of rates to solve real-world questions determining rates in different contexts, for example, to compare running rates of athletes in sport; to compare the petrol consumption price of different vehicles; to determine the best value for money between two specials; and to determine annual income.
Students will recall on prior knowledge converting between different units of measurement. They will apply rates to solve problems, for example, converting distance from miles to kilometres. They convert between area units (mm2, cm2, m2, hectares and km2) and volume units (mm3, cm3 and m3).
Teaching and learning summary:
- Demonstrate and show the conversion between different units of measurement before solving problems.
- Expand knowledge of rates to then use them in various contexts.
- Apply rates to calculate and solve problems between two quantities, recognising the relationship between them.
- Record rates in their simplest form using correct unit notation.
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Teaching strategies
A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.
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Concrete, Representational, Abstract (CRA)
The CRA model is a three-phased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.
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Explicit teaching
Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.
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Culturally responsive pedagogies
Mathematics is not an exclusive western construct. Therefore, it is important to acknowledge and demonstrate the mathematics to be found in all cultures.
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