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Packaging studio: the triangular prism

Grade 8 pupils design packaging shaped as a triangular prism. They use a 3D pen to draw five flat net panels: two bases (3–4–5 cm triangles) and three 6 cm side faces. They arrange the triangles into a rectangle, slide a base along a side face, assemble a corner, and calculate surface area and volume. An optional extension joins the panels into an openwork box.

Age
13–15 years
Length
approx. 45 min
Level
Medium
Where you teach
School
Purpose
Educational
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How to run this session

Stages and timing
  1. Two base triangles
  2. First face and first observation
  3. Final two faces and end of pen work
  4. Packaging corner: two heights
  5. Measure and calculate surface area
  6. Kasia's error and a longer box
  7. Optional: weld the bases
  8. Optional: attach the 3 × 6 cm face
  9. Optional: close and check the model

What gets built

After the lesson, the pupil calculates the surface area of a right prism by adding the areas of two bases and its side faces, and its volume by multiplying base area by prism height. The model explains why: the net has two triangles and three rectangles, and the solid is a base moved through the prism height. The pupil distinguishes base height (a segment perpendicular to a triangle side, here the 3 cm leg) from prism height (the distance between bases, a 6 cm lateral edge), and selects the correct height for each formula.

What it practises
  • Calculating the surface area of a right prism from the areas of its net faces.
  • Calculating prism volume as base area multiplied by prism height.
  • Distinguishing base height from prism height.
  • Drawing a frame and cross-strip with a 3D pen along template lines, and joining panels with fresh PLA along supported contacts.

Success criteria
  • Five flat panels lie on their W1 lines, separately and without welding.
  • W2 contains correctly calculated surface area and volume for packaging 6 cm long.
  • The pupil identifies base height and prism height on the panels and explains why Kasia's calculation is wrong.
  • The pupil calculates surface area and volume for packaging 12 cm long and compares how the results change.

What you need
Filament
PLA
Colours
navy blue (example; pupil chooses the colour), navy blue (example; same colour), navy blue (same filament)
Also
1.2 m of PLA filament per pupil (one colour for all panels), 3D pen with stand (one per pupil), transparent mat, W1: full-size 1:1 packaging net on a grid (A4 sheet supplied, print at 100 %), W2: calculation sheet: my packaging (supplied sheet), pencil, ruler, set square (one per pair), named envelope for panels and worksheet

Files

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Version dc618852-8f4e-483f-8010-1679cf2d10c7 Updated 2026-10-15

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