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5th Grade

Deeper reading, structured writing, fractions, and multi-step problem solving

Worksheet for 2026-10-08

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📖 The Cube Packing Problem

A fictional model box measured 6 centimeters long, 4 centimeters wide, and 3 centimeters high inside. Students planned to fill it with 1-centimeter cubes without gaps. Each layer held 24 cubes, and three layers held 72. Another box measured 8 by 3 by 3 centimeters and also held 72 cubes. The boxes had equal volume but different shapes. A long model object might fit one and not the other. The students learned that volume tells how much space a box encloses, while the dimensions also matter when deciding whether a particular object can fit.

1. How many cubes fit in one layer of the first box?

 

2. What is each box's volume?

 

3. Why do three layers fit in the first box?

 

4. Why does equal volume not guarantee the same objects fit?

 

✏️ Writing

Explain volume and fit using both boxes.

➕ Math

1. A school collects 7 boxes containing 22 books each. How many books are collected? ______
2. 93 books are donated to another school. How many remain? ______
3. Write an equation representing both steps: __________________
4. Explain how you know your answer is reasonable: __________________

🎨 Color & Create

Draw labeled box diagrams and show one cube layer.

View Answer Key

📖 Reading Answers

  1. 24.
  2. 72 cubic centimeters.
  3. The inside height is 3 cm and cubes are 1 cm tall.
  4. Different dimensions create differently shaped spaces.

➕ Math Answers

  1. 154
  2. 61
  3. 7 × 22 − 93 = 61
  4. An estimate close to the exact answer shows it is reasonable

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