Interpret the Units of a Drawing Scale

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: An original plan uses 1 cm for 4 m. A corridor is 2 cm on the plan. What actual length does the plan represent? Candidate answers: (A) 16 m (B) 7 m (C) 8 m (D) 9 m.
• Independent check inputs: An original plan uses 1 cm for 4 m. A corridor is 3 cm on the plan. What actual length does the plan represent? Candidate answers: (A) 11 m (B) 12 m (C) 13 m (D) 24 m.

Learn the idea

A scale drawing links represented and actual lengths through a fixed factor. Geometric relationships connect angles through straight lines and triangles, so a justified equation can replace guessing from a sketch. A scale ratio says how much actual length corresponds to each drawing unit. Multiplication by the labeled rate converts a measurement while making the drawing units cancel.

Here is the method on the supplied teaching case. Multiply 2 cm by 4 m/cm: 8 m. The centimeters cancel. This is a representation, not an on-site measurement.

The drawing is a model rather than proof of an actual measured corridor. Use the stated scale consistently; centimeters of drawing and meters of represented length must not be added together.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

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Take it further

Changed-input task: An original plan uses 1 cm for 4 m. A corridor is 9 cm on the plan. What actual length does the plan represent? Candidate answers: (A) 35 m (B) 36 m (C) 37 m (D) 72 m. Show the mathematical reason, not only the selected answer. Expected result: 36 m. Multiply 9 cm by 4 m/cm: 36 m. The centimeters cancel. This is a representation, not an on-site measurement.

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