Success criteria
- I split a compound solid into prisms that do not overlap.
- I label dimensions and add the partial volumes.
- I test every design constraint and explain a tradeoff.
Learn and explain
Suppose a stepped display is made from a 6 × 4 × 3 prism and a 2 × 4 × 2 prism placed on top without overlap. Their volumes are 72 and 16 cubic units, so the whole solid has volume 88 cubic units.
Draw the solid. Colour each prism differently, then explain why adding works and why counting any overlapping region twice would fail.
Independent practice
A storage shape combines non-overlapping prisms 7 × 3 × 2 and 3 × 3 × 4. Find its total volume.
Add the two prism volumes: 78 cubic units.
Why must the decomposed prisms not overlap?
Each unit cube should be counted exactly once.
Unfamiliar transfer — Box Builder (offline)
Use cardboard, unit cubes, or squared paper. Design a single rectangular package with whole-number dimensions, volume from 90 to 100 cubic units, and height no more than 4 units. Label it and state why it fits.
One valid candidate is shown only as a check:
Its volume is 96 cubic units, so the constraint check is pass. Your design may be different.
Delayed check
One to two weeks later, redraw the stepped display from memory and solve it using a different decomposition. Confirm that both totals match.
Evidence path
Save a photo and labelled plan to jeremy/portfolio/math/unit-4/lesson-13-box-builder/. Include dimensions, calculations, and one sentence about a design tradeoff.
Next step
- Repair: build the solid physically and mark every unit cube once.
- Continue: if both decomposition and constraint checking are secure, complete the Unit 4 mixed check.
- Stretch: minimize surface area for a fixed volume, labelled clearly as extension work.