Proportional Reasoning Checkpoint
A free Pre-Algebra lesson from the “Proportional Reasoning” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint mixes the proportional reasoning skills from the unit. It is intentionally cumulative: students identify the topic, choose a method, solve, and check that the answer makes sense before moving on. In Proportional Reasoning, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Review the major skills from Proportional Reasoning
- Choose methods without topic labels
- Explain and check work across a mixed set
Worked example
Problem. Solve 3/5 = x/20.
- The denominator changed from 5 to 20.
- That is a scale factor of 4.
- Multiply 3 by 4, so x = 12.
- Connect the calculation back to Proportions and Scale Factors so the method, not just the arithmetic, is clear.
Answer: 12
Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Proportional Reasoning Checkpoint review from Proportions and Scale Factors: Solve 2/3 = x/12.
Show solution
- The denominator 3 is multiplied by 4 to get 12.
- Multiply 2 by 4 to get 8.
Answer: 8
2. Proportional Reasoning Checkpoint review from Proportions and Scale Factors: A recipe uses 5 cups of rice for 10 servings. How many cups for 2 servings?
Show solution
- 2 servings is 1/5 of 10 servings.
- 5 cups divided by 5 equals 1 cup.
Answer: 1
3. Proportional Reasoning Checkpoint review from Proportions and Scale Factors: Which table is proportional?
Choices: x: 1, 2, 3; y: 4, 8, 12 · x: 1, 2, 3; y: 4, 7, 12 · x: 1, 2, 3; y: 5, 8, 11 · x: 1, 2, 3; y: 2, 4, 7
Show solution
- Each y-value is 4 times the x-value.
- The constant of proportionality is 4.
Answer: x: 1, 2, 3; y: 4, 8, 12
4. Proportional Reasoning Checkpoint review from Proportions and Scale Factors: Solve 4/7 = 20/x.
Show solution
- 4 is multiplied by 5 to get 20.
- Multiply 7 by 5 to get 35.
Answer: 35
5. Proportional Reasoning Checkpoint review from Proportions and Scale Factors: If y = 6x, what is y when x = 9?
Show solution
- Multiply x by 6.
- 6 x 9 = 54.
Answer: 54
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