Proportional Reasoning Quiz

Name:

Date:

📚 Part 1: Multiple Choice

1. If the edge length of a cube is doubled, the volume becomes:

2 times as large

4 times as large

8 times as large

16 times as large

2. A rectangle's linear dimensions are scaled by a factor of 3. Its area will be:

3 times

6 times

9 times

27 times

3. Two similar cones have linear scale factor 1/2. The surface area of the smaller cone is:

1/2 of the larger

1/4 of the larger

1/8 of the larger

1/16 of the larger

4. A cylinder's radius is doubled but the height stays the same. The cylinder's volume becomes:

2 times

4 times

8 times

16 times

✏️ Part 2: Short Answers

5. A model car is made at a 1:24 linear scale. The model's surface area measures 10 in². Estimate the real car's surface area. Show your work:

6. A rectangular fish tank is 30 in long, 12 in wide, and 12 in tall. A larger tank is built with a linear scale factor of 1.5. Find the new volume (in in³) and the percent increase in volume. Show calculations:

7. A sphere's radius is reduced from 6 in to 3 in. How does the surface area change? How does the volume change? Give the scale factor for each and explain briefly:

8. A party punch recipe serves 8 and uses 2 cups of sugar. You need to serve 20 people. How many cups of sugar are needed? Show the proportional reasoning:

📝 Teacher & Accessibility Notes

I can... I can use scale factors to relate linear measurements, surface areas, and volumes for similar shapes (apply proportional reasoning to problems involving surface area and volume).

Success criteria: Students will (1) identify the linear scale factor, (2) apply squared or cubed factors for area and volume, and (3) show clear steps and units in calculations.

Differentiation strategies: Provide worked-example cards, allow students to use calculators for arithmetic, offer simplified numbers for students needing support, and pair students for peer scaffolding.

Extension activities: Ask advanced learners to derive formulas for percent change when scaling, or analyze how density would change if mass scaled differently than volume.

Dyslexia-friendly reading options: Read questions aloud, provide one-question-per-line print layout, offer colored overlays or increased spacing, and allow extra time for reading and writing responses.