Singapore Math 5A · Independent learning

Volume of Cuboids

Learning target: Compute volume as length × width × height and explain layer multiplication.

Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.

Opening task

Explore · cuboid volume

Find the volume of a cuboid that is 8 cm long, 4 cm wide, and 7 cm high.

Show answer and worked explanation

Answer: 224 cm³

How it works: Each layer has 8×4=32 cubes; 7 layers yield 32×7=224 cm³.

Lesson-specific prerequisite checkpoint

Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.

How many cubes are in two layers of 3 by 4 cubes?

Show answer and worked explanation

Answer: 24 unit cubes

How it works: Each layer has 12 cubes; 2 × 12 = 24.

Understand the idea

Compute volume as length × width × height and explain layer multiplication.

A cuboid is an array of identical square-grid layers. One layer has length×width cubic units, and height tells the number of layers. Multiply all three perpendicular dimensions; volume is in cubic units.

Vocabulary focus: unit cube, cuboid, cubic units, capacity. Make a small labeled model, work through the arithmetic, and explain the result in words.

Watch for: Computing perimeter or surface area instead.

Model to study: Array-of-unit-cubes layer model.

Worked examples

Worked examples 1 · cuboid volume

Find the volume of a cuboid that is 9 cm long, 8 cm wide, and 4 cm high.

Solution: 288 cm³

Why: Each layer has 9×8=72 cubes; 4 layers yield 72×4=288 cm³.

Worked examples 2 · cuboid volume

Find the volume of a cuboid that is 3 cm long, 5 cm wide, and 9 cm high.

Solution: 135 cm³

Why: Each layer has 3×5=15 cubes; 9 layers yield 15×9=135 cm³.

Worked examples 3 · cuboid volume

Find the volume of a cuboid that is 5 cm long, 4 cm wide, and 3 cm high.

Solution: 60 cm³

Why: Each layer has 5×4=20 cubes; 3 layers yield 20×3=60 cm³.

Check understanding

Check understanding 1 · cuboid volume

Find the volume of a cuboid that is 12 cm long, 6 cm wide, and 2 cm high.

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Answer: 144 cm³

How it works: Each layer has 12×6=72 cubes; 2 layers yield 72×2=144 cm³.

Check understanding 2 · cuboid volume

Find the volume of a cuboid that is 10 cm long, 5 cm wide, and 5 cm high.

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Answer: 250 cm³

How it works: Each layer has 10×5=50 cubes; 5 layers yield 50×5=250 cm³.

Guided practice

Guided practice 1 · cuboid volume

Find the volume of a cuboid that is 8 cm long, 5 cm wide, and 3 cm high.

Show answer and worked explanation

Answer: 120 cm³

How it works: Each layer has 8×5=40 cubes; 3 layers yield 40×3=120 cm³.

Guided practice 2 · cuboid volume

Find the volume of a cuboid that is 6 cm long, 4 cm wide, and 2 cm high.

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Answer: 48 cm³

How it works: Each layer has 6×4=24 cubes; 2 layers yield 24×2=48 cm³.

Guided practice 3 · cuboid volume

Find the volume of a cuboid that is 9 cm long, 2 cm wide, and 2 cm high.

Show answer and worked explanation

Answer: 36 cm³

How it works: Each layer has 9×2=18 cubes; 2 layers yield 18×2=36 cm³.

Independent practice

Independent practice 1 · cuboid volume

Find the volume of a cuboid that is 11 cm long, 8 cm wide, and 5 cm high.

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Answer: 440 cm³

How it works: Each layer has 11×8=88 cubes; 5 layers yield 88×5=440 cm³.

Independent practice 2 · cuboid volume

Find the volume of a cuboid that is 7 cm long, 3 cm wide, and 2 cm high.

Show answer and worked explanation

Answer: 42 cm³

How it works: Each layer has 7×3=21 cubes; 2 layers yield 21×2=42 cm³.

Independent practice 3 · cuboid volume

Find the volume of a cuboid that is 6 cm long, 3 cm wide, and 3 cm high.

Show answer and worked explanation

Answer: 54 cm³

How it works: Each layer has 6×3=18 cubes; 3 layers yield 18×3=54 cm³.

Independent practice 4 · cuboid volume

Find the volume of a cuboid that is 6 cm long, 2 cm wide, and 5 cm high.

Show answer and worked explanation

Answer: 60 cm³

How it works: Each layer has 6×2=12 cubes; 5 layers yield 12×5=60 cm³.

Independent practice 5 · cuboid volume

Find the volume of a cuboid that is 4 cm long, 6 cm wide, and 3 cm high.

Show answer and worked explanation

Answer: 72 cm³

How it works: Each layer has 4×6=24 cubes; 3 layers yield 24×3=72 cm³.

Challenge and error analysis

Challenge and error analysis 1 · worked-error diagnosis

Error-analysis notebook: Learner notebook (LESSON): “Volume = length×width=22 cm²; I omitted the 4 cm height.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Find the volume of a cuboid that is 11 cm long, 2 cm wide, and 4 cm high.

Show answer and worked explanation

Answer: 88 cm³

How it works: Wrong step/assumption: Learner notebook (LESSON): “Volume = length×width=22 cm²; I omitted the 4 cm height.” Diagnosis: Count full three-dimensional layers, use three perpendicular dimensions and cubic units; use cm³=mL only for capacity conversion. Correct computation: Each layer has 11×2=22 cubes; 4 layers yield 22×4=88 cm³.

Challenge and error analysis 2 · reasoning transfer

Reasoning and transfer: Solve, then explain a different way to check your answer (inverse operation, estimate, model, or units as appropriate). Find the volume of a cuboid that is 10 cm long, 5 cm wide, and 3 cm high.

Show answer and worked explanation

Answer: 150 cm³

How it works: Each layer has 10×5=50 cubes; 3 layers yield 50×3=150 cm³. Verification: show why the answer has a reasonable magnitude and matches the operation, referent and unit.

Exit check

Exit check 1 · cuboid volume

Find the volume of a cuboid that is 4 cm long, 6 cm wide, and 6 cm high.

Show answer and worked explanation

Answer: 144 cm³

How it works: Each layer has 4×6=24 cubes; 6 layers yield 24×6=144 cm³.

Exit check 2 · cuboid volume

Find the volume of a cuboid that is 9 cm long, 8 cm wide, and 2 cm high.

Show answer and worked explanation

Answer: 144 cm³

How it works: Each layer has 9×8=72 cubes; 2 layers yield 72×2=144 cm³.

Target for independent mastery: all exit-check problems correct plus a justified explanation. A tutor may reteach the concept if calculations are correct without meaningful reasoning.