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Geometry and Measurement 6-8 / Week 04 / Friday
5/6
Week 04 · Volume

Friday

Volume all around
// How much the storage bin holds
⏱ about 20 min

Friday: Volume All Around

Rocket walks through the kitchen with a ruler. "That drawer. That cereal box. That shoebox. Everything is a box!"

"Not everything," Raven says, holding up a round can. "What do you notice about this one?"

"No corners," Rocket admits. "Cubes would not pack it."

Nova hovers between them, her light tracing the can's round top. "Save that one for later," she says. "Boxes first."

"Next week we draw the whole garage to scale," Raven says. "Every wall on one sheet of paper."

Rocket looks at the tape measure, then at the garage door. "That is a lot of centimeters."

Nova hums. "That is why we scale."

Boxes at home

ThingEdges (cm)Volume (cubic cm)
Shoebox30 by 18 by 126,480
Cereal box20 by 6 by 303,600
Drawer40 by 35 by 1014,000
Small gift box7 1/2 by 6 by 4180

These are the crew's measurements of things at the Blueprint Table, not standard sizes. Yours will differ.

Any box-shaped space works the same way: three edges, one product. Fraction edges are no harder than whole ones.

A round can is not a box. Its volume waits for the circle week and the round solids week.

How to find any box's volume

  1. Measure the three edges in the same unit.
  2. Multiply the three edges, or multiply the base area by the height.
  3. Write the answer in cubic units: cubic centimeters for centimeter edges.
  4. For stacked boxes, add the volumes. For their surface area, take away the hidden faces.
BOXES AT HOME
  • Read the question.
  • Tap your answer.
A box 30 cm long, 18 cm wide and 12 cm tallThe shoebox is 30 by 18 by 12 cm. What is its volume in cubic centimeters?
A box 7.5 cm long, 6 cm wide and 4 cm tallThe gift box is 7 1/2 by 6 by 4 cm. What is its volume in cubic centimeters?
A box has a base of 60 square centimeters and is 8 centimeters tall. What is its volume in cubic centimeters?
A flat tray is 2 by 2 by 1/2 units. How many half-unit cubes fill it?
WEEK REVIEW
  • Read the question.
  • Tap your answer.
A box 6 cm long, 5 cm wide and 4 cm tallWhat is the volume of the box in cubic centimeters?
16 half-unit cubes fill a box exactly. Each one is 1/8 of a cubic unit. What is the volume in cubic units?
The shelf is an 8 by 4 by 3 cm box with a 4 by 4 by 3 cm box on top. What is the total volume in cubic centimeters?
A box 2 cm long, 3 cm wide and 1.5 cm tallWhat is the volume of the box in cubic centimeters?
Week reviewTrue or false?
4 × 3 × 2 = 24?
2 × 2 × 2 = 8?
72 ÷ 8 = 9?
A box with a fraction edge cannot use V = l × w × h.?
Two stacked boxes have the sum of their volumes.?
WHY THIS EXERCISEPacking half cubes gave the same number as l × w × h, so the formula holds for fraction edges.
OUR WEEK, IN ORDER
  • ?We packed half cubes into a box with a fraction edge and got the same volume.
  • ?We packed a bin with unit cubes and found V = l × w × h and V = B × h.
  • ?We sized four bins and stacked two boxes into an L-shaped shelf.
  • ?We ran Build Lab, predicting and counting three boxes.
WHY THIS EXERCISEEach day grew the formula: whole edges, fraction edges, then two boxes at once.
Try it
Find three box-shaped things at home. Measure each in centimeters and find the volume.
Write them in your Blueprint Book from smallest to largest.
Safety first
Measure things you can reach from the floor. Ask a grown-up before moving anything heavy.
Draw your biggest box at home with its three edges labeled. Write its volume underneath.

A week of cubes and layers. Tomorrow is Build Day: pack a family box and size the clubhouse bins.

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