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Number Trail Grade 5 / Week 11 / Wednesday
3/6
Week 11 · Build with cubes

Wednesday

Use the formula
// Volume: unit cubes, layers and length × width × height
⏱ about 15 min

Wednesday: Use the formula

Hazel the Hedgehog wants to build a planter box for her herb garden.

"It will be 4 feet long, 2 feet wide and 3 feet tall," she says.

"How much soil will fill it?"

Bennie the Bear writes on a slate: V = l × w × h.

"We do not need to draw every cube," he says. "The formula counts them for us."

Hazel multiplies. "4 × 2 = 8 for the base. 8 × 3 = 24."

"So the planter holds 24 cubic feet of soil!" says Bennie.

Learn it: two volume formulas

V = l × w × h: length times width times height.

V = B × h: the area of the base times the height.

Both formulas say the same thing, because B = l × w.

Hazel's planter has a base of 4 × 2 = 8 square feet.

So V = 8 × 3 = 24 cubic feet.

A box of unit cubes: 4 long, 2 deep and 3 tall
USE V = L × W × H
  • Read the question.
  • Tap your answer.
A box is 6 by 4 by 5 centimeters. What is its volume in cubic centimeters?
A box is 10 by 3 by 2 inches. What is its volume in cubic inches?
A box is 8 by 5 by 4 feet. What is its volume in cubic feet?
A box is 7 by 6 by 3 centimeters. What is its volume in cubic centimeters?
USE V = B × H
  • Read the question.
  • Tap your answer.
The base of a box is 20 square centimeters. It is 4 centimeters tall. What is its volume in cubic centimeters?
The base of a box is 36 square inches. It is 5 inches tall. What is its volume in cubic inches?
The base of a box is 15 square feet. It is 6 feet tall. What is its volume in cubic feet?

Find a missing side

Sometimes we know the volume and two sides.

Multiply the two sides you know, then ask what times that makes the volume.

FIND THE MISSING SIDE
  • Read the question.
  • Tap your answer.
4 × 5 × ? = 60
6 × 2 × ? = 60
3 × 3 × ? = 72
10 × 4 × ? = 80
SOLVE THE STORY
  • Read the question.
  • Tap your answer.
Hazel's planter is 4 feet by 2 feet by 3 feet. How many cubic feet of soil fill it?
A shoebox is 12 inches by 8 inches by 5 inches. What is its volume in cubic inches?
A storage bin holds 60 cubic feet. Its base is 12 square feet. How tall is it in feet?
Try it
Find a box at home, like a cereal box or a shoebox.
Measure its length, width and height in inches.
Round each one to the nearest inch.
Multiply to estimate its volume in cubic inches.
On paper, draw Hazel's planter and label its length, width and height.

Formula experts! Tomorrow Chris tells a story about two boxes stuck together.

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