FoldNets
3D shape → paper net
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Gr 6–8 · 50 min

Design a package

Every box must hold 48 cm³: which shape uses the least card?

Ontario Gr 6–8 · Spatial Sense E2 · Common Core 6.G.A.4, 7.G.B.6

Learning goals

  • Find boxes with the same volume and different dimensions
  • Compare their surface areas from their nets
  • Explain why the most cube-like box uses the least card

Plan

  1. 1

    The brief5 minYou lead

    A company wants a box that holds exactly 48 cm³, using as little card as possible.

  2. 2

    Find boxes10 minStudents

    List whole-number boxes with volume 48: 6 × 4 × 2, 4 × 4 × 3, 8 × 3 × 2, 12 × 2 × 2 and more.

  3. 3

    Design15 minStudents

    Each group sets one box's sizes in FoldNets and reads its surface area: 88, 80, 92 and 104 cm² for the four above.

  4. 4

    Build15 minStudents

    Print the nets at real size and build them. Line them up from least card to most.

  5. 5

    Conclude5 minYou lead

    4 × 4 × 3 wins: the closer to a cube, the less card for the same volume.

To talk about

  • Why might a company choose a box that uses more card?
  • What size cube would hold 48 cm³? Why can't we print it with whole centimetres?