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Exam Review: What Did the Wrong Answer Measure?
Boon Jin
A student chooses 20 cm for the perimeter of a 6 cm by 4 cm rectangle. Have they understood the boundary, remembered a formula, or guessed? One extra question can help you decide what to ask next.
Use this short misconception-detective task during exam review. Ask students to answer individually before discussing the examples below.
Give the calculation a meaning
Display a rectangle labelled 6 cm and 4 cm. Keep the worked diagram below hidden at first; the student prompt sheet contains the unworked version.
1. What is the perimeter of this rectangle? Choose 10 cm, 20 cm or 24 cm.
2. Someone answered, “The perimeter is 24 cm because 6 × 4 = 24.” Explain what their calculation actually measures. Give its correct units, then explain how to find the perimeter.
3. Why is 10 cm also a tempting wrong answer? Refer to the sides of the rectangle.
The first choice checks the answer. The explanation checks whether students can connect the numbers to something being measured.
Use the tiles to explain 24 cm² and trace all four edges to explain 20 cm. The two calculations measure different parts of the same rectangle.
Answer key: 6 + 4 = 10 cm counts only one long and one short side. The whole boundary is 6 + 4 + 6 + 4 = 20 cm. The interior contains four rows of six 1 cm² squares, so its area is 24 cm². The multiplication is correct; using it as a perimeter, with cm as its unit, is the mistake.
Read the explanation, not just the choice
Compare these three responses.
“24 is wrong because you should add. 6 + 4 = 10 cm, so the perimeter is 10 cm.”
This response rejects multiplication but counts only two sides. Ask: “Point to the two sides you counted. Which edges are still missing?” Have the student trace the entire boundary and revise the sum. Repeating “add for perimeter” would leave the missing-side error unresolved.
“The perimeter is 2 × (6 + 4) = 20 cm. 24 is wrong because perimeter means add.”
The calculation accounts for both pairs of sides. The explanation still does not say what 24 measures. Ask: “Show me what 6 × 4 counts inside the rectangle. Would its unit be cm or cm²?” A correct formula is useful evidence, but it does not answer that question for the student.
“6 × 4 counts 24 squares inside, each 1 cm², so the area is 24 cm². Perimeter is the distance around all four edges: 6 + 4 + 6 + 4 = 20 cm.”
This connects both calculations to the model and uses the right units. Give a new rectangle next. One complete explanation shows understanding on this example; check whether it transfers.
Use a small three-part rubric when reading responses. Mark each row shown, unclear or incorrect/missing; keep the notes separate rather than turning them into a mastery score.
| Look for | Evidence in the response |
|---|---|
| Whole boundary | Accounts for all four sides and obtains 20 cm. |
| Interior coverage | Explains 6 × 4 as four rows of six unit squares, obtaining 24 cm². |
| Units with meaning | Uses cm for edge length and cm² for area, with a reason for the difference. |
In Deck.Toys, put the rectangle and prompts in a Slide Activity and collect the explanation with the established Text response app. You can use an MCQ app for the first choice, but read the written reasoning before choosing the follow-up. A practice-game score or a corrected choice alone does not establish individual understanding.
Change the shape; keep the distinction
A rectangular fabric patch is 8 cm by 3 cm. A strip goes around all four edges without overlap. How much strip is needed? What is the area of the patch? Explain why 24 answers one question but not the other.
Transfer key: the strip length is 8 + 3 + 8 + 3 = 22 cm. The area is 8 × 3 = 24 cm². The number 24 counts square units covering the patch; it does not measure the boundary. Ask students to answer independently so you can see which part needs another example.
