Thursday
Thursday: Counting the Cardboard
Rocket spreads the clubhouse plan on the Blueprint Table. "The walls are a box, 20 by 20 by 15 centimeters."
"And the roof is a pyramid with a 20 centimeter square base and 20 centimeter triangles," Raven adds. "It fits the box top exactly."
"We have sheets of cardboard, each 30 by 20," Rocket says. "How many do we need?"
"What do you notice about which faces we actually cut?" Raven asks.
Rocket thinks. "The floor is the table. No floor. The roof covers the top, so no top either. Four walls and four triangles."
Nova hovers above the plan, her light tracing each wall. "Then add," she says, "and divide by one sheet. Round up. Then check the pieces really fit."
"Walls, 1,200. Triangles, 800." Rocket divides. "More than three sheets. So four." Nova hums. "Four, with scraps left over."
Faces the crew will cut
The clubhouse walls are a box. The floor is the tabletop and the roof covers the top, so the crew cuts only the four walls.
Front and back: 20 × 15 = 300 each. The two ends: 20 × 15 = 300 each. Walls: 2 × 300 + 2 × 300 = 1,200.
The whole box, with top and bottom, would be 2,000 square centimeters. Leaving out two faces saves 800.
Raven's cardboard table
The crew's own clubhouse measurements and the cardboard each part needs, from Raven's Blueprint Book, in centimeters.
| Part | Shape | Edges (cm) | How many | Cardboard (sq cm) |
|---|---|---|---|---|
| Front and back walls | rectangle | 20 by 15 | 2 | 600 |
| End walls | rectangle | 20 by 15 | 2 | 600 |
| Roof triangles | triangle | base 20, height 20 | 4 | 800 |
| Total to cut | 8 | 2,000 |
One roof triangle is ½ × 20 × 20 = 200. Four of them make 800. The roof's base is not cut: the box top is already there.
All the cardboard to cut: 1,200 + 800 = 2,000 square centimeters. One sheet is 30 × 20 = 600, so 2,000 ÷ 600 is between 3 and 4. Round up: 4 sheets.
Dividing tells you the fewest sheets you could use. Pieces cannot be cut in half and taped, so check that they really fit. Two 20 by 15 walls fit side by side on one 30 by 20 sheet, so four walls take two sheets. Two roof triangles fit on one sheet, one of them flipped upside down beside the other, so four triangles take two sheets. That is 4 sheets, so the plan works.
- Read the question.
- Tap your answer.
If the clubhouse box were closed on every side, 20 by 20 by 15 cm, what would its surface area be?- Read the question.
- Tap your answer.
| From the cardboard table | True or false? |
|---|---|
| The crew cuts cardboard for the floor of the clubhouse. | ? |
| 2 × 300 + 2 × 300 = 1,200 | ? |
| A part of a sheet left over means the crew needs one more whole sheet. | ? |
| The roof pyramid's square base is cut from cardboard too. | ? |
List the faces you would cut, find each area, add them, and work out the sheets you need. Then sketch the pieces on the sheets to check they fit.
Eight faces, four sheets. Tomorrow you find nets and surface area all around you and review the week.