Folding nets II

Folding nets II

Pencil and paper
Overview
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about identifying nets for 3-D shapes.
Rectangular prism Square-based pyramid Triangular prism Triangle-based pyramid

Some of the nets below can be folded to make the different shapes shown above.

 

Part A: Predict the shape each net will make:

  1. In the prediction box write the name of the 3-D that each net folds to.
  2. Write "none" if you don't think it will fold to make any of the shapes above.

Part B: Check

  1. Cut out all the nets on the next page and fold them to work out which shape they make.
  2. If your prediction was correct tick the shape.
  3. If your prediction was not correct write the correct name of the shape or none next to the shape.

 

Cut out the nets below

Level:
3
Curriculum info: 
Maths, Geometry and Measurement, Shape
Keywords: 
nets, 3-dimensional shapes, matching, folding, prisms, self-assessment, peer assessment
Description of task: 
Students predict which 3-dimensional shapes nets will make and then fold nets to identify the shapes.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Geometric thinking, sets 3-4
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

Part A

a) none
b) none
c) rectangular prism
d) none
e) square-based pyramid
f) triangle-based pyramid
g) triangular prism

Part B
Students can cut out and fold nets to make the shapes, and then self correct (see answers above).

NOTE: Student answers involve both identifying the shapes that nets do make and those that do not fold to make a cube.

To correctly identify all the nets, students need to identify the 4 nets that do and the 3 that do not fold to make a cube.

Teaching and learning: 

This task is completed with pencil, paper and scissors.

This resource is about students making a prediction about which nets fold to make given 3-D shapes, and then exploring and reflecting on their prediction. The focus of the assessment at level 3 is on students' ability to identify the nets that fold to make given 3-D shapes. Accordingly, the assessment should be based on both their initial prediction and their reflection after folding.

Prior knowledge
Students should know how nets are constructed, i.e., (1) the parts are non-overlapping, and (2) once the shape has been made all faces should be accounted for – there should be no openings.

Diagnostic and formative information: 

Common errors
Nets that some students incorrectly identified were:

Triangle-based pyramid Triangular prism Rectangular prism

 

Most of the Year 6 trial students identified the correct nets for the shapes. By folding to check their nets some students changed their answers–both correctly and incorrectly. For a number of students this checking created some uncertainty – especially for   which students after folding still thought folded to the rectangular and triangular prisms, respectively. This suggests the importance that students understand how nets are constructed, i.e., (1) they have no overlapping parts and (2) all faces should be accounted for (Prior knowledge).

The results from the trialling indicate two broad errors:

  1. Incorrectly identifying a net for another shape,
  2. Cutting and then folding nets that have overlap or missing faces.
Next steps: 

Students who could not visualise which nets made particular shapes
These students need to develop their ability to visualise how the nets can fold to make given 3-D shapes. Ensure that students understand how to make nets for 3-D shapes (see above). Then have students work in pairs or small groups to discuss the features of nets that fold to make 3-D shapes. Students could start to describe how they know that particular nets will fold, explaining the folds that need to be made without needing to cut and fold the net. They may need to use words such as base, top and sides, and end to explain how the net makes a given shape. Get them to justify how each net can fold, and classify these into the same three classes. For groups who cannot reach a (correct) consensus, get them to talk with a group who has. If this fails, get them to work with concrete materials by cutting out and trying to fold the shapes to make prisms (you may wish to enlarge the nets using a photocopier).

Cannot fold nets to identify the shape
Students that cannot fold nets to identify the shape should first explore the creating and folding of nets to understand the relationship between nets and shapes. They should be aware that nets involve (1) no overlapping parts and that (2) all faces should be accounted for. Students could be asked to develop a net based on a given 3-D shape to work out how to design and construct the net. Have them work with a peer, to explore and describe how the nets they have drawn fold (or do not fold) to make the given 3- D shape. Students could start to describe how they know that particular nets will fold, without touching them. They may need to use words such as base, top and sidesto explain how the net makes a given shape. Marking an X on the base can provide a reference point that can help students describe how the net folds into the shape, and how other faces on the net relate to that base.

Students who correctly identified all the nets without folding
Have students who identified all the nets correctly articulate their findings in a small group and discuss how they can visualise how the net folds. Have students design their own nets for other prisms and ask others to identify whether the nets can or cannot fold into the given shape. Have students describe how the net is folded and then discuss an easy way to identify how they fold (and be able to explain it to a peer). They could also identify which nets are more difficult and what features make them that way. This could lead to them making and then checking a conjecture about features of nets that fold to make shapes. To explore orientation of nets see Cubes and faces and Folded nets. For a similar resource at Level 3, see Net of an open box II.

Peer assessment
This resource presents an excellent opportunity for students to assess each others' responses. Those who have mastery can demonstrate this as they assess other students' responses. Those who can visualise how the nets fold can assess students who are still learning to visualise.