Gr 7–8 · 50 min
Volume and surface area of a house
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.
A box with a prism roof: add the volumes, and find which faces still count once the parts are glued.
Ontario Gr 7–8 · Spatial Sense E2 · Common Core 7.G.B.6
Learning goals
- Find the volume of a solid made of a rectangular prism and a triangular prism
- Find the surface area of a composite solid, leaving out the faces glued together
Plan
- 1
Build15 minStudents
Build the walls (an 8 × 5 × 6 cm box) and the roof (a triangular prism with 6 cm sides, 8 cm long), but don't glue them together yet.
- 2
Volume10 minStudents
Find each part's volume and add them: 240 cm³ for the walls, about 125 cm³ for the roof (the triangle's area is about 15.6 cm², from its height, the dotted line: about 5.2 cm), about 365 cm³ in all. Click each part in FoldNets to check its volume.
- 3
Surface area15 minStudents
Glue the roof on. Which two faces disappear? The box's top and the roof's bottom (48 cm² each) are now inside. Add up only the outside: about 315 cm².
- 4
Extend10 minYou lead
On the board, make the roof taller or the box longer in FoldNets (Builds → Custom build). Students predict the new volume, then check.
To talk about
- Why does gluing the roof on change the surface area but not the volume?
- If the house were twice as long, what would happen to its volume?