# Stage 3 -space and geometry – 3D

Identify the net of a 3D object; visualise a 3D object given different views

## Strategy

Students can:

• identify the net of a 3D object
• visualise a 3D object given different views
• determine the number of faces, edges and vertices of a 3D object

## Activities to support the strategy

### Activity 1: visual arts

In visual arts, students are often required to recognise measure, draw and construct three-dimensional objects.

Students need to be familiar with key terms used to describe lines, two-dimensional shapes and three-dimensional objects.

When making artworks, it is important that students are able to recognise, visualise and draw two-dimensional shapes and three-dimensional objects.

### Group sculpture project

Students construct a free-standing sculpture using three-dimensional objects.

1. Ask students to collect or make a variety of three-dimensional objects (cones, cubes, prisms, pyramids and cylinders). They could collect everyday packaging such as cereal boxes or toilet rolls.

2. Have students identify and classify the objects according to their properties. Ask students to compare the objects in terms of the number and shape of the faces, and the number of corners and edges. Ensure that students use correct terminology such as prism, pyramid, cylinder, cone, cube, face, edge, corner, angle, vertex, flat, parallel, circular, square and rectangular.

3. Ask students to visualise and draw the nets of several objects.

To check the accuracy of the students' drawings, demonstrate by cutting along edges of the everyday packaging to show the net, then re-form the objects.

### Drawing

Students make linear (using only line) drawings of several objects from observation.

Students imagine, then draw the 'invisible' edges of these objects.

Students identify 3D objects used by Picasso in his early Cubist period.

### Group sculpture

Groups of 3–5 students each select 4–8 objects and cooperatively plan the construction of a three-dimensional sculpture. The sculpture may represent a theme such as space technology or machinery, or a concept such as power, dynamics or balance. Have each student sketch their proposed sculpture.

Have each group:

• construct their sculpture and paint it using one light colour (e.g. white, yellow or light blue)
• measure and record the dimensions of their sculpture.

Students make three scale drawings of the sculpture on grid paper. The drawings should show a front, side and top view. Demonstrate to students how to select a suitable scale for the drawings by following these steps.

• Measure and record the length, width and height of their sculpture in centimetres.
• Measure and record the length and width of the grid paper.
• Determine how many times the dimensions of the sculpture need to be reduced to fit the paper whilst remaining in proportion. The length, width and height of the sculpture must be reduced by the same amount.
• Use this ratio of sculpture to paper to determine the scale (e.g. 1 cm on the paper = 5 cm on the sculpture, a ratio of 1:5).

In small groups, students then compare their drawings to the actual views of the sculpture.

### Drawing light and dark

Select some sculptures and arrange them in the centre of the room. Use a strong directional light such as an OHP to emphasise the form of the sculptures.

• Have students move around the works, making quick sketches using soft drawing media to record the shadows.
• Repeat the exercise on black paper using white or yellow chalk, crayon or pencil to record the lightened areas.
• Display and compare the two works.

### Further teaching activities

In groups, students decide on a potential location within the school to build a large scale model of their sculpture. The proposed site should be accurately measured and a plan drawn to scale.

Include accurate measurements for someone else to construct the sculpture. Show front, side, rear and top views.

Use the detailed plan and measurements to develop a list of materials needed. For example, from the scale drawings students could calculate the amount of timber required for the framework by converting the scale drawings to the actual lengths of timber.

Have students present their proposed sculpture to the rest of the class, explaining the design, its dimensions and materials.

### Activity 2

Students use the Exploring surface area, volume and nets learning object to explore surface area, volume, 3D objects and nets. Objects include rectangular and triangular prisms; rectangular and triangular pyramids; cylinders and cones. Included are print activities, solutions and learning strategies.

## References

### Australian curriculum

ACMMG111: Connect three-dimensional objects with their nets and other two-dimensional representations.

### 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.

## Teacher resources

• Mathematics K-6 (2003) Stage 3 – Three-dimensional Space, pp 143-146
• Rectangular prisms, Stage 3, from Mathematics K-6 Assessment and Work Samples, NSW Education Standards Authority (NESA), CD Rom

### Lesson plans and activities

Students use a real-world situation to help develop spatial visualization skills and geometric understanding. Students determine how many different nets are possible and then analyse the resulting cubes.

The Dynamic Paper tool can be used to create shapes and objects, number lines, number grids, tessellations, spinners and nets. The image created can be exported as a PDF activity sheet for your students or as a JPEG image for use in other applications or on the web.