Prime shape rules
The compact shape for any N follows simple rules.
We always build 3D, six-sided rectangular blocks made of unit cubes. These rules make efficiency visual—students see the cost of stretching a dimension or flattening a layer.
- •Dimensions multiply to N (volume stays fixed).
- •Surface area is minimized (fewest exposed faces).
- •Ties pick the shape closest to a cube (smallest max side).
- •Axes ordered for clarity: Height ≥ Width ≥ Depth.
How it works
From number to shape
Every step keeps students anchored in a single number N while they flex spatial reasoning.
1. Choose N
Pick a cube count or let the app randomize. N becomes the fixed volume to explore.
2. Test dimensions
Students try factor triples. They see how tall or flat shapes change surface area.
3. Reveal the prime shape
With one tap they compare their build to the optimal shape that minimizes exposed faces.
Classroom moves
- • Predict which factor triple wins before building.
- • Rank shapes by surface area and discuss efficiency.
- • Connect to packing, shipping, and sustainability.
Ready to build?