Singapore Math 5A · Independent learning

Finding the Length of an Edge

Learning target: Recover an unknown cuboid edge from volume and two dimensions using inverse operations.

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

Opening task

Explore · missing cuboid edge

A rectangular box has volume 320 cm³. Its length is 4 cm and width 8 cm. Find its height.

Show answer and worked explanation

Answer: 10 cm

How it works: Base area = 4×8=32 cm²; height = 320 ÷ 32 = 10 cm. Check 4×8×10=320 cm³.

Lesson-specific prerequisite checkpoint

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

What number multiplied by 12 equals 84?

Show answer and worked explanation

Answer: 7

How it works: A missing dimension uses inverse multiplication.

Understand the idea

Recover an unknown cuboid edge from volume and two dimensions using inverse operations.

The volume formula can be reversed. If the volume and two perpendicular edges are known, divide volume by the product of those edges to find the missing length. Check by multiplying the three lengths back to the volume.

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: Dividing by only one known dimension.

Model to study: Dimensioned cuboid and missing-edge label.

Worked examples

Worked examples 1 · missing cuboid edge

A rectangular box has volume 240 cm³. Its length is 8 cm and width 3 cm. Find its height.

Solution: 10 cm

Why: Base area = 8×3=24 cm²; height = 240 ÷ 24 = 10 cm. Check 8×3×10=240 cm³.

Worked examples 2 · missing cuboid edge

A rectangular box has volume 168 cm³. Its length is 7 cm and width 2 cm. Find its height.

Solution: 12 cm

Why: Base area = 7×2=14 cm²; height = 168 ÷ 14 = 12 cm. Check 7×2×12=168 cm³.

Worked examples 3 · missing cuboid edge

A rectangular box has volume 30 cm³. Its length is 3 cm and width 2 cm. Find its height.

Solution: 5 cm

Why: Base area = 3×2=6 cm²; height = 30 ÷ 6 = 5 cm. Check 3×2×5=30 cm³.

Check understanding

Check understanding 1 · missing cuboid edge

A rectangular box has volume 60 cm³. Its length is 4 cm and width 5 cm. Find its height.

Show answer and worked explanation

Answer: 3 cm

How it works: Base area = 4×5=20 cm²; height = 60 ÷ 20 = 3 cm. Check 4×5×3=60 cm³.

Check understanding 2 · missing cuboid edge

A rectangular box has volume 924 cm³. Its length is 11 cm and width 7 cm. Find its height.

Show answer and worked explanation

Answer: 12 cm

How it works: Base area = 11×7=77 cm²; height = 924 ÷ 77 = 12 cm. Check 11×7×12=924 cm³.

Guided practice

Guided practice 1 · missing cuboid edge

A rectangular box has volume 135 cm³. Its length is 9 cm and width 3 cm. Find its height.

Show answer and worked explanation

Answer: 5 cm

How it works: Base area = 9×3=27 cm²; height = 135 ÷ 27 = 5 cm. Check 9×3×5=135 cm³.

Guided practice 2 · missing cuboid edge

A rectangular box has volume 220 cm³. Its length is 10 cm and width 2 cm. Find its height.

Show answer and worked explanation

Answer: 11 cm

How it works: Base area = 10×2=20 cm²; height = 220 ÷ 20 = 11 cm. Check 10×2×11=220 cm³.

Guided practice 3 · missing cuboid edge

A rectangular box has volume 315 cm³. Its length is 9 cm and width 5 cm. Find its height.

Show answer and worked explanation

Answer: 7 cm

How it works: Base area = 9×5=45 cm²; height = 315 ÷ 45 = 7 cm. Check 9×5×7=315 cm³.

Independent practice

Independent practice 1 · missing cuboid edge

A rectangular box has volume 224 cm³. Its length is 7 cm and width 8 cm. Find its height.

Show answer and worked explanation

Answer: 4 cm

How it works: Base area = 7×8=56 cm²; height = 224 ÷ 56 = 4 cm. Check 7×8×4=224 cm³.

Independent practice 2 · missing cuboid edge

A rectangular box has volume 288 cm³. Its length is 8 cm and width 4 cm. Find its height.

Show answer and worked explanation

Answer: 9 cm

How it works: Base area = 8×4=32 cm²; height = 288 ÷ 32 = 9 cm. Check 8×4×9=288 cm³.

Independent practice 3 · missing cuboid edge

A rectangular box has volume 385 cm³. Its length is 11 cm and width 7 cm. Find its height.

Show answer and worked explanation

Answer: 5 cm

How it works: Base area = 11×7=77 cm²; height = 385 ÷ 77 = 5 cm. Check 11×7×5=385 cm³.

Independent practice 4 · missing cuboid edge

A rectangular box has volume 96 cm³. Its length is 3 cm and width 4 cm. Find its height.

Show answer and worked explanation

Answer: 8 cm

How it works: Base area = 3×4=12 cm²; height = 96 ÷ 12 = 8 cm. Check 3×4×8=96 cm³.

Independent practice 5 · missing cuboid edge

A rectangular box has volume 108 cm³. Its length is 9 cm and width 3 cm. Find its height.

Show answer and worked explanation

Answer: 4 cm

How it works: Base area = 9×3=27 cm²; height = 108 ÷ 27 = 4 cm. Check 9×3×4=108 cm³.

Challenge and error analysis

Challenge and error analysis 1 · worked-error diagnosis

Error-analysis notebook: Learner notebook (LESSON): “Missing height=144÷6=24 cm. I ignored width 3 cm.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: A rectangular box has volume 144 cm³. Its length is 6 cm and width 3 cm. Find its height.

Show answer and worked explanation

Answer: 8 cm

How it works: Wrong step/assumption: Learner notebook (LESSON): “Missing height=144÷6=24 cm. I ignored width 3 cm.” Diagnosis: Count full three-dimensional layers, use three perpendicular dimensions and cubic units; use cm³=mL only for capacity conversion. Correct computation: Base area = 6×3=18 cm²; height = 144 ÷ 18 = 8 cm. Check 6×3×8=144 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). A rectangular box has volume 420 cm³. Its length is 6 cm and width 7 cm. Find its height.

Show answer and worked explanation

Answer: 10 cm

How it works: Base area = 6×7=42 cm²; height = 420 ÷ 42 = 10 cm. Check 6×7×10=420 cm³. Verification: show why the answer has a reasonable magnitude and matches the operation, referent and unit.

Exit check

Exit check 1 · missing cuboid edge

A rectangular box has volume 96 cm³. Its length is 4 cm and width 3 cm. Find its height.

Show answer and worked explanation

Answer: 8 cm

How it works: Base area = 4×3=12 cm²; height = 96 ÷ 12 = 8 cm. Check 4×3×8=96 cm³.

Exit check 2 · missing cuboid edge

A rectangular box has volume 275 cm³. Its length is 11 cm and width 5 cm. Find its height.

Show answer and worked explanation

Answer: 5 cm

How it works: Base area = 11×5=55 cm²; height = 275 ÷ 55 = 5 cm. Check 11×5×5=275 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.