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
Practice problems
1. Proportional Reasoning Checkpoint review from Proportions and Scale Factors: Solve 2/3 = x/12.
Show solution
- Warm-up: First identify exactly what the question is asking: Solve 2/3 = x/12.
- For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
- The denominator 3 is multiplied by 4 to get 12.
- Multiply 2 by 4 to get 8.
- Check the result by substituting or estimating: the response should match 8 and make sense in the original problem.
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
- Warm-up: First identify exactly what the question is asking: A recipe uses 5 cups of rice for 10 servings. How many cups for 2 servings?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- 2 servings is 1/5 of 10 servings.
- 5 cups divided by 5 equals 1 cup.
- Check the result by substituting or estimating: the response should match 1 and make sense in the original problem.
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
- Warm-up: First identify exactly what the question is asking: Which table is proportional?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Each y-value is 4 times the x-value.
- The constant of proportionality is 4.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
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
- Core Practice: First identify exactly what the question is asking: Solve 4/7 = 20/x.
- For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
- 4 is multiplied by 5 to get 20.
- Multiply 7 by 5 to get 35.
- Check the result by substituting or estimating: the response should match 35 and make sense in the original problem.
Answer: 35
5. Proportional Reasoning Checkpoint review from Proportions and Scale Factors: If y = 6x, what is y when x = 9?
Show solution
- Core Practice: First identify exactly what the question is asking: If y = 6x, what is y when x = 9?
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Multiply x by 6.
- 6 x 9 = 54.
- Check the result by substituting or estimating: the response should match 54 and make sense in the original problem.
Answer: 54
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