Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M7M02
Numeracy Progression: Understanding units of measurement: P9
At this level, students become familiar with the concepts of volume and surface area. They understand that volume is the amount of space occupied by a threedimensional (3D) object and is measured in cubic units.
Students should understand the difference between volume and capacity (how much an item can hold), and the units of capacity – litres (L) and millilitres (mL).
Students will apply the formula for the volume of rectangular prisms Volume (V) = Length (L) × Width (W) × Height (H). They should understand that the formula is the same as calculating the area of the base and multiplying this by the height. This understanding will be important when they move to finding the volume of a right triangular prism and solve problems involving right prisms.
Using concrete materials such as unit cubes, students can build and calculate the volume of models. Students may also experiment with dynamic geometric software and note how volume changes with change in variables.
Teaching and learning summary:
 Build on students’ understanding of area.
 Develop the concept of volume.
 Discuss what is a prism – constant crosssection.
 Discuss the units used in volume – why they are cubic.
 Introduce and derive the formula for the volume of right rectangular and triangular prisms.
 Discuss the relationship between volume and capacity and their units.
Students will:
 identify a rectangular and triangular prism
 use the formula to find the volume of rectangular and triangular prisms
 use the correct units for volume and capacity.
Some students may:
 confuse area and volume
 give the solution with incorrect units
 find the product of all measurements given, not just those that they need
 believe that for all prisms you multiply three dimensions, not appreciating it is the crosssectional area × length
 get confused with the terminology 'length', 'height' and 'width' when shown the same object in different orientations
 be unable to visualise the unobserved sides of a solid object
 believe if nothing can be put inside the object, then it doesn’t have a volume
 confuse volume with capacity.
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
Learning intention
 I am learning to understand the concept of volume being the space inside a threedimensional object.
 I will apply the formula to calculate the volume of various shapes.
Why are we learning about this?
If you can understand how to use the formula to find the volume of a rectangular prism and understand the difference between volume and capacity, then you can design, plan, experiment and navigate the 3D world you live in.
What to do
 Using square and rectangular building blocks, design, draw or create a model of an object with a volume no greater than 50 cm^{3}.
 Explain how you calculated the volume.
Success criteria
 I can understand the difference between volume and capacity.
 I can understand the units of capacity: litres (L) and millilitres (mL).
 I can discuss the concept of volume and what a prism is
 I can discuss the relationship between volume and capacity.
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Teaching strategies
A collection of evidencebased 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.

Concrete, Representational, Abstract (CRA)
The CRA model is a threephased 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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Collaborative Learning
For group work to be effective students need to be taught explicitly how to work together in different settings, such as pairs or larger groups, and they need to practise these skills.
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Differentiated teaching
Differentiation involves teachers creating lessons that are accessible and challenging for all students.
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Feedback
It has been shown that good feedback can make a significant difference to a student’s future performance.
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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.

Volume and modelling: Video and teaching guide
Use this video as a springboard to explore volume of composite shapes, adjusting numbers to make calculations friendlier, and drawing on reasoning and mathematical modelling.
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Unit cubes and volume
This lesson uses unit cubes and hollow objects to demonstrate the concept of volume and the units used.
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Measurement and geometry
This resource gives detailed explanations of the curriculum content, worked examples and assessment questions focusing on the volume of a rectangular prism and how the units of volume and capacity are related.
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