Week 04 · Volume
Build Day
Build Day: The family box
// How much the storage bin holds
⏱ about 20 min
Build Day: The Family Box
Saturday at the Blueprint Table, Raven hands out rulers. "Build Day. Everyone picks a box and predicts its volume."
"Then we pack it with cubes and see who was closest," Rocket says, shaking the tray of dice.
"What do you notice when a box has a fraction edge?" Raven asks Rocket's cousin.
"Use half cubes," she says, "or just multiply. Same answer."
Nova hovers over the row of boxes, her light pausing on the tallest. "Predict before you pack," she says.
"And stack two at the end," Rocket says. "For the shelf."
Nova hums. "Count the hidden faces."
- Volume is the space inside a solid, counted in unit cubes.
- V = l × w × h, or V = B × h: one layer, then the number of layers.
- Half-unit cubes pack a box with fraction edges. Eight make a unit cube, and the formula still works.
- Stacked boxes add their volumes. Their surface area loses the two faces that touch.
- Predict with the formula, then pack and count. A short count means a gap.
◇ THE FAMILY BOX WITH A GROWN-UP
Each person picks a small box and measures its edges in cubes. Write a prediction with l × w × h.
Pack each box with dice or cubes and count. Compare the count with the prediction.
Measure the same boxes in centimeters and find each volume in cubic centimeters.
Stack two boxes. Find the stack's volume, then its surface area, taking away the hidden faces.
Pack each box with dice or cubes and count. Compare the count with the prediction.
Measure the same boxes in centimeters and find each volume in cubic centimeters.
Stack two boxes. Find the stack's volume, then its surface area, taking away the hidden faces.
For a grown-up
This week your student learned that volume is l × w × h, even when an edge is a fraction.
Ask them why 72 half cubes make 9 cubic units. The answer should mention eight half cubes in a unit cube.
Cubes and dice stay away from children under three and pets.
Ask them why 72 half cubes make 9 cubic units. The answer should mention eight half cubes in a unit cube.
Cubes and dice stay away from children under three and pets.
Safety first
Cubes stay in the tray. Nothing goes in a mouth.
Keep stacks low and on the table so nothing falls.
Keep stacks low and on the table so nothing falls.
BUILD DAY CHECK
- Read the question.
- Tap your answer.
What is the volume of the box in cubic centimeters?How many cubes with 0.5-unit edges fill a box 2 by 1 by 1.5?
A box has a base of 15 square centimeters and is 4 centimeters tall. What is its volume in cubic centimeters?
The small box sits fully on the big box. What is the surface area of the whole shelf in square centimeters?
A box is 3 by 3 by 3 cubes. How many cubes fill it? Type the number.
Nine in a layer, three layers.
WHY THIS EXERCISE3 × 3 × 3 = 27 cubic units.
Draw your family box with its edges in cubes. Write the prediction and the count beside it.
Great building, crew. Next week the whole garage fits on one sheet of paper.