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7.32 Choosing representations for proportional problems Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 7 Math worksheet provides structured practice on 7.32 Choosing representations for proportional problems. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

7.32 Choosing representations for proportional problems - In multiple-choice items, students choose the representation that best matches a proportional situation and select the justification that makes it correct. (CCSS 7.RP.A.2d; CA 7.RP.2d; MA 7.RP.2d; NY 7.RP.2d; FL MA.7.AR.4.4; TX 7.4(A); VA 7.PFA.1)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 7

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 7.32 Choosing representations for proportional problems skill assessments:

Problem 1Difficulty: Mastery

A proportional relationship connects yards and dollars. When yards = 2, dollars = 12.8. Let y represent yards and let d represent dollars. Which choice correctly represents the relationship and supports it with proportional reasoning?

ADouble number line: y: 0 --- 25.6 --- 51.2 --- 76.8 d: 0 --- 4 --- 8 --- 12. Justification: Because the labels are switched, the unit rate is still 6.4 d per y.

BTable: y: 0, 1, 2, 4 d: 0, 6.4, 12.8, 12.8. Justification: The ratio is constant because one pair matches 6.4.

CEquation: d = 6.4y + 7. Justification: The graph of any equation is a line, so it is proportional.

DGraph points (with y on the x-axis and d on the y-axis): (0, 0), (1, 6.4), (3, 19.2). Justification: For y = 1, the matching value is d = 6.4, so the unit rate is 6.4 d per y.

Solution & Explanation:Find the constant of proportionality by dividing: d/y = 12.8/2 = 6.4. In a proportional relationship, d = 6.4y and the graph goes through (0, 0). Points on the correct graph satisfy d = 6.4y; for example (1, 6.4) shows the unit rate.

Problem 2Difficulty: Mastery

A proportional relationship connects miles and dollars. When miles = 5, dollars = 72. Let m represent miles and let d represent dollars. Which choice correctly represents the relationship and supports it with proportional reasoning?

ADouble number line: m: 0 --- 57.6 --- 115.2 --- 172.8 d: 0 --- 4 --- 8 --- 12. Justification: Because the labels are switched, the unit rate is still 14.4 d per m.

BGraph points (with m on the x-axis and d on the y-axis): (0, 0), (1, 14.4), (3, 43.2). Justification: The unit rate is shown by the point (14.4, 1).

CEquation: d = 14.4m. Justification: The ratio d/m stays 14.4 for nonzero m, so the graph is a straight line through (0, 0).

DTable: m: 0, 1, 2, 4 d: 0, 14.4, 29.8, 57.6. Justification: The ratio is constant because one pair matches 14.4.

Solution & Explanation:Find the constant of proportionality by dividing: d/m = 72/5 = 14.4. In a proportional relationship, d = 14.4m and the graph goes through (0, 0). The correct equation uses that unit rate: d = 14.4m.

Problem 3Difficulty: Mastery

A proportional relationship connects trees and dollars. When trees = 4, dollars = 0.6. Let t represent trees and let d represent dollars. Which choice correctly represents the relationship and supports it with proportional reasoning?

ATable: t: 0, 1, 2, 4 d: 0, 0.15, 0.3, 0.3. Justification: The ratio is constant because one pair matches 0.15.

BGraph points (with t on the x-axis and d on the y-axis): (0, 0), (1, 0.15), (3, 0.45). Justification: For t = 1, the matching value is d = 0.15, so the unit rate is 0.15 d per t.

CDouble number line: t: 0 --- 0.6 --- 1.2 --- 1.8 d: 0 --- 4 --- 8 --- 12. Justification: Because the labels are switched, the unit rate is still 0.15 d per t.

DEquation: d = 0.15t - 3. Justification: The graph of any equation is a line, so it is proportional.

Solution & Explanation:Find the constant of proportionality by dividing: d/t = 0.6/4 = 0.15. In a proportional relationship, d = 0.15t and the graph goes through (0, 0). Points on the correct graph satisfy d = 0.15t; for example (1, 0.15) shows the unit rate.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 7 Math students. It aligns with educational standard 7.32 (Practice and review Grade 7 math skill 7.32: Choosing Representations for Proportional Problems.).