Expected level of development
Australian Curriculum Mathematics V9: AC9M10M01
Numeracy Progression: Understanding geometric properties: P7
At this level, students will extend their application of volume and surface area to solve problems on composite solids. Students will need to be able to visualise the individual elements of the composite solids and identify the areas where these elements touch.
This topic has connection with ratio and proportion, circles and cylinders, and Pythagoras and trigonometry.
Students are required to identify and use the correct units appropriate to a particular problem.
Teaching and learning summary:
- Build on students’ understanding of area and volume.
- Introduce surface area.
- Introduce the formula for the volume of a prism – cross-sectional area × height.
- Make connections to composite area.
- Make connections to circles, cylinders and cones.
- Use appropriate units pertaining to surface area and volume.
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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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Teaching resources
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.
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A piece of cake
In this lesson, students build on their skills in finding volumes and surface areas of prisms and cylinders to design a multi-level celebration cake for a party.
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Solid geometry
In this unit, students practise spatial visualisation in three dimensions, and study the effect of dilation on area and volume.
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Volume of a pyramid and a cone
A proof of the formula for the volume of a pyramid and a cone using the ancient Chinese yangma.
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