Nets for a cube

Nets for a cube

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about finding nets that fold to make a cube.
Nets are like maps that can be folded to make 3-D shapes. Some of the nets below can be folded to make a cube with all 6 faces.
  1. Circle all the nets that you predict will fold to make a cube.
  2. Cut out and fold all 6 of the nets on the next page to work out which make a cube.
  3. Tick all the nets that you correctly circled.
Task administration: 
This task is completed with pencil, paper and scissors.
 
[Equipment: scissors; page of nets for cutting out]

  • This resource is designed to be used with a small group of students.
  • Students will need some time to cut out the shapes.
  • The nets could be photocopied onto A3 paper to make them easier to cut out and handle.
  • The folding of the nets supports the students to self-assess their predictions.
  • Students can also show their nets to peers or work on their nets in pairs
Levels:
2, 3
Curriculum info: 
Maths, Geometry and Measurement, Shape
Keywords: 
nets, cubes, prediction, self-assessment, peer assessment
Description of task: 
Students predict nets that fold to make a cube, then cut out and fold the nets to check their prediction.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Geometric thinking, set 3
Geometric thinking, sets 3-4
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

a) Students initially identify the nets for a cube below.*
b) Students fold and show the nets for a cube below.*

*Student answers involve both circling the nets for a cube and not circling nets that do not fold to make a cube.

To correctly identify all the nets, students need to circle the 4 correct nets, and not circle the 2 nets that do not fold to make a cube.

Teaching and learning: 
This resource is about students making a prediction about which nets fold to make a cube, and then exploring and reflecting on their prediction. The focus of the assessment at level 2 is on students' ability towork with netsto identify which fold to make a cube, and at level 3 to identify nets without folding. Accordingly the assessment should be based on both their initial prediction and their reflection after folding.
Diagnostic and formative information: 
Most students visually identified 1-2 and then folded to identify 3-4 correct shapes. Some students initially indicated Net A, but after folding identified that it was not a net for a cube – indicating that the students had self corrected using the nets. No students guessed Net E as a possible shape. The results from the trialling indicate three broad errors:

  1. Not folding nets to correctly identify the shape,
  2. Cannot identify correct nets without folding, but can fold
  3. Could identify correct nets without needing to fold.
Next steps: 

Students who could not fold to correctly identify correct nets
These students could explore making their own nets for a cube and describing how they fold to make the cube. They could then draw their net, cut it out and use to talk through (with a peer) how each other's net folds to make a cube. The nets can be printed on A3 paper to ensure that they can be easily handled.
Students could then look to identify obvious nets that don't fold, e.g., Net A

Get students to describe why it does not fold to make a cube, e.g., "because there is only one square at the top of the net, there is no square that will cover the bottom of the net".
Similarly for Net E

Students who could not visualise to identify – but could fold to identify correct nets
These students need to develop their ability to visualise the nets, to work out those that fold to make 3- D shapes. However, they should first explore the folding and making of nets to understand the relationship between nets and shapes. Students could be asked to develop a net based on a given 3-D shape to work out how the net can be set up. Have them work with a peer, 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.

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 check whether 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 harder and what features make them harder.

To explore orientation of nets see Cubes and faces and Folded nets and 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.