FoldNets
3D shape → paper net
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Gr 7–8 · 50 min

Scale and real size

Print at real size and at a scale, measure, and see what doubling does to area and volume.

Ontario Gr 7–8 · Spatial Sense E1 · Common Core 7.G.A.1

Learning goals

  • Use a scale factor to find lengths
  • See that areas scale by k² and volumes by k³

Plan

  1. 1

    Check the printer5 minStudents

    Print at real size and measure the ruler in the footer. It should read 50 mm. If it's off, set the print dialog's scale to 100% (Actual size), not 'fit to page'.

  2. 2

    Measure10 minStudents

    Measure edges on the real-size net. They match the model.

  3. 3

    Scale it15 minStudents

    Print the same net at Fit page. FoldNets prints the percentage on the sheet. Predict an edge's length, then measure.

  4. 4

    Double it20 minStudents

    Double every length in FoldNets and build both boxes. How many small boxes fit in the big one (8)? How much more paper did it take (4 times)?

To talk about

  • A map's scale is 1:50 000. How far is 3 cm on the map?
  • Why does doubling lengths multiply volume by 8?