IB Math AI - Square-cubed Law Model Buildings

IB Math AI Unit 3 — Scaled Buildings (Square–Cube Law) Need a fun, topical, memorable activity for your IB math class? Look no further.

Students build a scaled model of a familiar structure to test how surface area and volume/mass change with scale, then compare predictions to measurements.

Key relationships

• Surface area
• Volume & (same-density) mass
• Scaled linear dimensions ~ real dimensions

What students do

1. Choose & approximate a building; decompose into standard solids (prisms, cylinders, cones) and note assumptions/sources.
2. Select a scale (1:N); compute scaled lengths/areas/volumes and predicted mass (adjust for density differences or hollow parts).
3. Build the model using nets/templates; plan materials, assemble from base upward, and check scale accuracy (≈±2–3 mm).
4. Measure & compare mass/dimensions; calculate % error and explain discrepancies.

Student calculation sheet

Tables scaffold: component formulas and scaled dimensions, totals for area/volume, density-based mass, and comparison/%-error.

Assessment (high level)

Rubric emphasizes: applying the square–cube law with justification, calculation accuracy/units, data collection, model quality & scale fidelity, visuals, reflection, and communication (100 pts).

Materials

Rulers/scale, modeling materials (foam board/cardboard/clay) or digital tools, calculators/spreadsheets, research resources, and the printed calculation sheet.

Why it matters: Turns abstract scaling laws into testable predictions and connects math to real engineering choices.