Grade 5 · Stack equal layers of unit cubes · 508 of 750
Stack equal layers of unit cubes: length: 6; width: 3; height: 2
A model box for a classroom activity is 6 unit cubes long, 3 wide, and 2 layers high. Find the number of cubes in one layer and in the complete original box, explain the calculation, and check a related question.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
A model box for a classroom activity is 6 unit cubes long, 3 wide, and 2 layers high. First find the number of cubes in one layer and in the complete original box. Then answer: How many cubes are needed for one additional full layer?
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Volume counts the unit cubes that fill a solid without gaps or overlaps. First count one rectangular layer, then multiply by the number of equal layers.
Work through the reasoning
Step 1
Identify the quantities and the task
A model box for a classroom activity is 6 unit cubes long, 3 wide, and 2 layers high. The first task is to find the number of cubes in one layer and in the complete original box. Volume counts the unit cubes that fill a solid without gaps or overlaps. First count one rectangular layer, then multiply by the number of equal layers.
Step 2
Calculate the original result
V = 6 × 3 × 2 = 36 cubic units. Each layer contains 18 cubes, and 2 layers contain 36. Cubic units describe occupied space, not the outside surface area.
Step 3
Complete the follow-up calculation
How many cubes are needed for one additional full layer? 18 additional cubes. The new volume would be 54 cubic units.
The answer
V = 6 × 3 × 2 = 36 cubic units. Each layer contains 18 cubes, and 2 layers contain 36. Cubic units describe occupied space, not the outside surface area. Follow-up: 18 additional cubes. The new volume would be 54 cubic units.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
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The mathematical idea
A model box for a classroom activity is 6 unit cubes long, 3 wide, and 2 layers high. Volume counts the unit cubes that fill a solid without gaps or overlaps. First count one rectangular layer, then multiply by the number of equal layers. Each layer contains 18 cubes, and 2 layers contain 36. Cubic units describe occupied space, not the outside surface area.
V = 6 × 3 × 2 = 36 cubic units
03 · Reflect and transfer
Explain what changes and why.
Place cubes one layer at a time. Some cubes become hidden behind others in the perspective drawing, but they still contribute to the volume. Explain which quantity changes and which relationship stays valid. Use the starting values again before checking your written answer.
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.