Gr 7–8 · 45 min
A pyramid holds a third
Coming soon. We're checking this lesson against the app, step by step, so it works when you run it with a class. You can read the plan now. The lesson pack, teaching mode and assigning open once it's checked.
Fill a square pyramid with rice and pour it into a box with the same base and height: it takes three.
Ontario Gr 7–8 · Spatial Sense E2 (enrichment)
Learning goals
- Compare the volume of a pyramid with the prism of the same base and height
- Use volume = ⅓ × base area × height
Plan
- 1
Build15 minStudents
Groups build the pyramid and the cube (Shapes → Cube, 6 cm, or open it from this lesson's page), both printed at real size. Cut the base square off the pyramid's net and the top square off the cube's, so both are open.
- 2
Predict5 minStudents
How many pyramids of rice will fill the cube? Write a guess.
- 3
Pour10 minStudents
Fill the pyramid level and pour it into the cube. Repeat. It takes three.
- 4
The formula10 minStudents
The cube holds 6 × 6 × 6 = 216 cm³, so the pyramid holds 72 cm³: ⅓ × 36 × 6. Check it with FoldNets' volume readout.
- 5
Connect5 minYou lead
A cone holds a third of its cylinder too (see the Cylinders and cones lesson).
To talk about
- Does the ⅓ rule work for a triangular pyramid and a triangular prism?
- A pyramid and a prism have the same volume and base. How do their heights compare?