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Two paths around the same area

Grade 6 pupils trace six identical 2 × 2 cm square PLA modules (a frame and a cross dividing it into four regions) using one W1 template. On the grid, they arrange a 6 by 1 strip, a 3 by 2 rectangle and their own shape: a constant area of 24 cm², different perimeters (28, 24, 20 cm), and the shared-side rule. Extension: a rectangle with one corner module removed.

Age
11–13 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. First module: frame and cross
  2. Five more identical modules
  3. Shape A: 6 by 1 strip
  4. Shape B: 3 by 2 rectangle
  5. Shape C: your design
  6. Shared sides and Olek's trap
  7. Optional: less area, the same perimeter

What gets built

A set of six 2 × 2 cm PLA modules and sheet W2 comparing three shapes with the same area of 24 cm² and three different perimeters: A: 28 cm, B: 20 cm, C: 24 cm, explained using shared sides.

What it practises
  • Distinguishing area (number of units) from perimeter (length of the outer boundary) using a physical model.
  • Generalisation: each shared module side reduces the shape's perimeter by 4 cm; perimeter = 48 − 4 · (number of shared sides) cm.
  • Recognising the error of adding separate module perimeters instead of counting the shape's outer boundary.
  • Planning a fair comparison: the same six modules, different arrangements, constant area.

Success criteria
  • On the grid, the pupil shows that a strip, a rectangle and their own shape made from the same six modules always have an area of 24 cm² and identifies the arrangement with the smallest perimeter.
  • Sheet W2: three shapes with area 24 cm² and three different perimeters: A: 28 cm, B: 20 cm, C: 24 cm; reasoning using shared sides; the 3 by 2 rectangle identified; 48 cm rejected with an explanation about sides inside the shape; transfer task 16 cm² and 16 cm, and 16 cm² and 20 cm.
  • The six modules are identical and loose, and are never welded together; they lie separately in the set-aside area.

What you need
Filament
PLA
Colours
colour shown in the illustration
Also
3D pen: 1 per pupil, transparent work mat, pen stand, power supply, W1: 1:1 module template and arrangement grid (A4 printout), W2: observation sheet (A4 printout), pencil, ruler

Files

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Version 956b130f-24a2-47a7-99ad-8ff8191e397d Updated 2026-10-17

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