Expected level of development
Australian Curriculum Mathematics V9: AC9M6SP01
Numeracy Progression: Understanding geometric properties: P5
At this level, students extend their knowledge of simple prisms and pyramids (polyhedra) and their nets. They compare the parallel cross-sections of objects and recognise their relationships to right prisms.
Students explore the properties of 3D objects such as a cube, a square prism, rectangular prism, hexagonal prism and triangular prism and a tetrahedron (triangular pyramid) and square-based pyramids.
Use the context of architecture to investigate real-life examples of commonly used polyhedra – prisms and pyramids.
Build on the terms base, apex, edges, faces, net and corners (vertices). Introduce cross-sections using a variety of objects, including fruit, to demonstrate that cutting at a right angle provides the cross-section. Show a cut at an angle not at a right angle to show the difference in shape compared to the cross-section.
Have students investigate the cross-sections of a range of objects.
Teaching and learning summary:
- Construct models of prisms and pyramids.
- Use the context of architecture to investigate prisms and pyramids.
- Introduce the cross-sections of right prisms.
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
- We are learning how to construct models of prisms and pyramids.
Why are we learning about this?
- Shapes and objects are all around us.
What to do
- Look around your home to see what 3D objects you can find. Can you find objects that look like this?
a cylinder
a rectangular prism
a cube
a triangular prism
- Draw a picture of the objects you found. Label the properties of each shape based on their faces, bases, edges and vertices (corners).
- Choose one object to make using a net.
- Choose a small item to store for safekeeping. It could be a coin, a lolly or a similar-sized object.
- Find an old greeting card and use this to create a box to keep your item in.
- Draw a plan of how you are making your box. Think about how to add a lid.
Success criteria
I can:
- identify 3D objects
- construct a prism from nets
- describe prisms by their properties such as faces, bases, edges and vertices
- create a 3D object using a net.
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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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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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Mathematics investigation
By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.
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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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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.
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Polyhedra
In this lesson, students are introduced to 3D objects (polyhedra), their properties and nets.
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reSolve: Authentic problems – Pyramids in a box
This sequence of four lessons focuses on working with solids and their nets.
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Prisms and pyramids – Years 5 and 6
This resource provides four activities to develop students' familiarity with 3D objects, in particular prisms and pyramids.
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Construction of prisms and pyramids
This resource for both teachers and students focuses on prisms and pyramids, including their properties and their construction from nets.
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Boxes
Students see how many different sized boxes they can make with exactly 24 blocks.
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Net exploration
Students investigate the different ways to create a net for a cube.
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Assessment
By the end of Year 6, students are identifying the parallel cross-section for right prisms.
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Assessment task: The coloured cube
Use this diagnostic task to assess a student’s understanding of objects and their nets.
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Construction of prisms and pyramids
Refer to the Student resources sections Construction of prisms (p 5) and Construction of pyramids (p 4) for assessment tasks where students self-check answers.
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Mathematics: ACARA work sample portfolio summary – Year 6
Refer to ACARA work sample 8, 'Geometry – 3D structure', and the related task for guidance in assessing students’ understanding of perimeter and area.
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Seven Wonders of the Ancient World
Students uncover the probable dimensions of an ancient wonder, using mathematics to convert imperial and metric measurements and create plans of prisms. Refer to page 144.
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