Students fix three missing-dimension errors — multiplying instead of dividing and applying the wrong number of divisions. Part B has four problems finding missing dimensions by dividing and completing the inverse formula. Part C has two questions finding a fish tank's width and explaining missing-dimension reasoning.
Correcting missing-dimension errors — where students multiply instead of dividing — builds the inverse-formula reasoning students need to work backward from volume to a single unknown side.
Style:
Volume of Rectangular Prisms
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
If a prism has volume 60 cm³, width 3 cm, and height 4 cm, the length is 60 × 3 × 4 = 720 cm.
Rewrite: If a prism has volume 60 cm³, width 3 cm, and height 4 cm, the length is 60 ÷ 3 ÷ 4 = 5 cm.
2. Fix the sentence:
A box with volume 36 in³, length 6 in, and width 3 in has height = 36 ÷ 6 = 6 in.
Rewrite: A box with volume 36 in³, length 6 in, and width 3 in has height = 36 ÷ 6 ÷ 3 = 2 in.
3. Fix the sentence:
To find a missing width, add the volume, length, and height together.
Rewrite: To find a missing width, divide the volume by both the length and the height.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A prism has volume 80 cm³, length 8 cm, and height 2 cm. The width is 5 cm.
2. If V = l × w × h, then h = V ÷ l ÷ w.
3. A box has volume 120 in³, width 5 in, and height 4 in. The length is 6 in.
4. A rectangular prism has volume 90 m³ and base area 15 m². Its height is 6 m.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A fish tank has volume 72 cubic inches, length 6 inches, and height 3 inches. What is the width?
The width is 72 ÷ 6 ÷ 3 = 4 inches.
2. Explain how finding a missing dimension is the opposite of finding volume.
Finding volume multiplies all three dimensions, so finding a missing dimension divides to undo that multiplication.
Volume of Rectangular Prisms
★ Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1) Fix the sentence:
If a prism has volume 60 cm³, width 3 cm, and height 4 cm, the length is 60 × 3 × 4 = 720 cm.
Rewrite: If a prism has volume 60 cm³, width 3 cm, and height 4 cm, the length is 60 ÷ 3 ÷ 4 = 5 cm.
2) Fix the sentence:
A box with volume 36 in³, length 6 in, and width 3 in has height = 36 ÷ 6 = 6 in.
Rewrite: A box with volume 36 in³, length 6 in, and width 3 in has height = 36 ÷ 6 ÷ 3 = 2 in.
3) Fix the sentence:
To find a missing width, add the volume, length, and height together.
Rewrite: To find a missing width, divide the volume by both the length and the height.
★ Part B: Fill in the Blank
Write the missing word or number on each line.
1) A prism has volume 80 cm³, length 8 cm, and height 2 cm. The width is 5 cm.
2) If V = l × w × h, then h = V ÷ l ÷ w.
3) A box has volume 120 in³, width 5 in, and height 4 in. The length is 6 in.
4) A rectangular prism has volume 90 m³ and base area 15 m². Its height is 6 m.
★ Part C: Short Answer
Answer each question in one or two complete sentences.
1) A fish tank has volume 72 cubic inches, length 6 inches, and height 3 inches. What is the width?
The width is 72 ÷ 6 ÷ 3 = 4 inches.
2) Explain how finding a missing dimension is the opposite of finding volume.
Finding volume multiplies all three dimensions, so finding a missing dimension divides to undo that multiplication.
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9 Questions
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