Gr 7–8 · 30 min
Euler's formula
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.
Count faces, edges and vertices of five solids and discover faces − edges + vertices = 2.
Ontario Gr 7–8 · Spatial Sense E1 (enrichment)
Learning goals
- Collect data from several solids
- Spot and test a pattern
Plan
- 1
Collect10 minStudents
For a cube, triangular prism, square pyramid, hexagonal pyramid and octahedron, count faces, edges and vertices. All five open from this lesson's page.
- 2
Look for a pattern5 minYou lead
Try adding and subtracting the columns. What stays the same?
- 3
Test it10 minYou lead
On the board, open a Free-form shape in FoldNets and drag one corner. Count the corners, edges and flat faces again (a bent face shows as two triangles). Does it still come to 2?
- 4
Explain5 minYou lead
Leonhard Euler wrote this down in 1750. It holds for every solid with flat faces and no holes.
To talk about
- What would a solid with a hole through it (like a picture frame) give?
- Can you have a solid with 7 edges?