Stage 3 - 3D Space – constructing prisms and pyramids

Students need to develop their skills of visual imagery, including the ability to perceive and hold an appropriate mental image of an object or arrangement, and to predict the orientation or shape of an object that has been moved or altered.

Strategy

Students can:

  • create skeletal models of prisms and pyramids
  • represent 3D objects through drawing
  • create prisms and pyramids using a variety of materials

Activities to support the strategy

Activity 1 – prism and pyramid skeletons

Using straws and modelling clay students make skeletal models of square and triangular prisms, similar to the ones below.

Students can work in pairs to determine how many blobs of clay will be needed to show the vertices of each prism and how many straws will be needed to show the edges of each prism.

Students can use the examples to extend their understanding by making pyramids, hexagonal prisms, pentagonal prisms, etc. and complete the table to show the number of vertices and edges.

Activity 2 – drawing 3d objects by using their bases

Teacher demonstrates how to draw 3D prisms using isometric grid paper and coloured attribute blocks. Select a block to form the base of your prism.

  • Align the block on the grid paper and trace around it.

  • Then draw in the second base. Place it above or below it, and a little to the side.

  • Then join the matching vertices with straight lines.
  • Draw dotted lines to show that some of the faces, edges and vertices are hidden from view.

Students can then use the same strategy to draw pyramids.

  • Select a block to form the base of your pyramid.
  • Align the block on the grid paper and trace around it.

  • Then make a point above the base and draw in all of the lines that make the triangular faces of the pyramid to meet at that point.

Students individually draw the following objects using the two techniques discussed.

Ask the students to try to include dotted lines to show details which are hidden and use coloured pencils to show the base of each object.

Draw these 3D objects:

  • Cube
  • Rectangular pyramid
  • hexagonal prism
  • triangular prism
  • triangular prism

Activity 3 – interactive isometric drawing tools

A simple to use isometric grid for maths lessons using the interactive whiteboard. Join the dots to create 3D shapes. Use this interactive tool to create dynamic drawings on isometric dot paper. Draw figures using edges, faces, or cubes. You can shift, rotate, colour, decompose, and view in 2‑D or 3‑D. Start by clicking on the cube along the left side; then, place cubes on the grid where you would like them.

Use this teaching resource to demonstrate the representation of 3D shapes using isometric paper. The top half of the screen displays a variety of shapes that can be rotated. The bottom half of the screen contains an interactive isometric grid. Clicking on one dot and then another connects them with a red line. Clicking on the line removes it. The rotating shapes include use of perspective demonstrating that the isometric drawing is only a representation of the 3D shape.

An interactive whiteboard teaching resource for demonstrating isometric shapes. Designed to enable classroom discussion about the number of small cubes in each shape. After discussing the shape it can be exploded to show its components. It can also be toggled to rotate. There are 7 isometric shapes to consider.

Activity 4 – Geoboards

In pairs, students use Geoboards and elastic bands to make 3D objects.

Instruct the students to use the elastic bands to initially make the base figures. Stretch other elastic bands to form the other edges of the 3D object. If they are making a pyramid, then the elastic bands that form the edges will all meet at one point on the geoboard.

References

Australian curriculum

ACMMG140: Construct simple prisms and pyramids.

NSW syllabus

MA3-14MG: Identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views.

Teachers resources

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