Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M8M02
Numeracy Progression: Understanding units of measurement: P9
At this level, students further develop their understanding of volume and capacity of right prisms by developing formulas, taking measurements and investigating, making approximations and solving problems in many contexts.
Time should be taken to review the concept of volume/capacity and the definition of a right prism – a 3D object with plane, rectangular faces and bases that are aligned above each other.
Concrete objects, such as unit cubes and dynamic geometry software, can support students’ understanding. Students solve realworld problems using many examples from everyday life. Provide opportunities for students to investigate volume and capacity in different ways. For example, if a washing machine takes x minutes to fill, what is the capacity of the drum?
When introducing a new prism, students should be shown the object in a variety of orientations. Demonstrating how the crosssection is identical along the length (or height) of the shape can be done by cutting a plasticine model.
Introduce the formula for the volume of prisms as ‘area of the crosssection × length (height)’. Encourage students to identify the shape of the crosssection, calculate the area and then multiply this by the length (or height).
When solving and answering problems, students should choose the appropriate measurement to measure volume and surface area. Give students opportunities to convert the sameshaped objects from the very small (a model of a prism) to to the very large (similarshaped reallife example). This will support and develop student understanding of the selection of an appropriate unit of measurement for area and volume. It also initiates thinking in the idea of scaling.
Teaching and learning summary:
 Build on students’ understanding of volume and capacity.
 Discuss what a right prism is – constant crosssectional area – and use realworld examples.
 Introduce the formula for the volume of a right prism – crosssectional area × height.
 Discuss the meaning of the prefixes – milli, centi, kilo, mega.
 Relate to the decimal system.
 Discuss when to use cubed units and why.
 Discuss how to convert from one unit to another for length/height and for volume.
 Solve problems involving converting units.
Students:
 identify a prism
 use the formula to find the volume of a prism
 use the correct units for volume
 use knowledge to solve problems involving prisms and volume
 identify the correct unit of measurement to use in a given context, for example:
 kilometre, metre, centimetre, millimetre
 cubed
 are able to convert between units of measurement.
Students may:
 confuse area and volume – they need to have an understanding that volume is the amount of space taken up by a 3D object.
 give the solution with incorrect units.
 mistakenly multiply any three given measurements, not calculating 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 ‘hidden’ sides of a solid object.
 get confused when converting units of measurement for area and volume.
 have mastered converting linear units of measurement (centimetres to metres) but may not yet have made the connection between linear (cm), area (cm squared) and volume (cm cubed) units of measurement. Use conversion charts and help students make the connection between square and cubic factors to support their understanding.
 need encouragement to estimate if their answer will be a greater or lesser value once they convert to the new unit.
 not give the correct units for area and volume, forgetting to add the superscript.
 multiply instead of divide (and vice versa) when converting units.
 multiply or divide by the wrong scale factor.
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 apply the formula for the volume of a prism – crosssectional area × height.
 I will interpret problems involving prisms and volume.
 I will build my understanding of area, perimeter and volume.
Why are we learning about this?
You learn this topic to understand that the volume of a solid is the quantity of the space enclosed and that volume is a concept widely used, for example, in the construction industry.
What to do
Activity 1: volume of prisms
 Open the webpage, Volumes of prisms
 View section 1 'Volume of a rectangular prism' and record information that you found useful.
 Work through sections 2, 3, 4 and 5. Read each worded problem carefully, calculate the volume and record your answers in your book. Remember to show all working out.
 Learn about triangular prisms by selecting the next tab. View section 1 and record information that you found useful.
 Work through sections 2, 3, 4 and 5. Calculate the volume of triangular prisms and record your answers.
Activity 2: cuboid challenge
 Open the PDF worksheet and view the Cuboid challenge
 Complete the task and take a photo of your open box. Measure its dimensions and calculate the volume of the box.
Success criteria
 I can identify a prism.
 I use the correct units for volume.
 I use the formula to find the volume of a prism.
 I solve practical problems using prisms and volume.
Please note: This site contains links to websites not controlled by the Australian Government or ESA. More information here.
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.
Go to resource 
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.
Go to resource
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 of prisms
This resource focuses on the volume of rectangular prisms and the units of capacity. It gives detailed explanations of the curriculum content, worked examples and assessment questions.
Go to resource 
Packing a truck
This task asks students to pack a truck with boxes in an efficient way. The resource includes a lesson plan and sample student work.
Go to resource