Proportional Relationships Detective | 7th Grade Math 7.RP.A.2a-d Activity

🔍 PROPORTIONAL RELATIONSHIPS DETECTIVE — GRADE 7 MATH | 34-PAGE CASE-FILE INVESTIGATION

Transform your 7th graders into math detectives with this premium, CCSS-aligned proportional relationships resource! Students investigate four real-world cases—a lemonade stand, a road trip, recipe scaling, and a savings account—while developing all four components of CCSS 7.RP.A.2 in one connected investigation.

Instead of practicing each skill in isolation, students use tables, graphs, equations, and verbal descriptions as evidence throughout the case files, building understanding from one investigation to the next.

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This detective-themed unit connects all four parts of 7.RP.A.2 through a single investigation framework. Students test proportional relationships, identify the constant of proportionality, write equations, and interpret points on graphs using realistic contexts.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 📁 4 DETECTIVE CASE FILES — 16 PROBLEMS TOTAL ━━━━━━━━━━━━━━━━━━━━━━━━━━━━

**CASE 1 — Testing for Proportional Relationships | 7.RP.A.2a**

**The Lemonade Stand Investigation**

• Test equivalent ratios using tables • Graph relationships on coordinate planes • Compare proportional and non-proportional examples • 4 problems with evidence-collection worksheets and coordinate-plane graphs

**CASE 2 — Identifying the Constant of Proportionality | 7.RP.A.2b**

**The Road Trip Investigation**

• Find the constant of proportionality (unit rate) • Work from tables, graphs, equations, diagrams, and verbal descriptions • Emphasis on k = y/x and the unit-rate point (1, r) • 4 problems using multiple representations

**CASE 3 — Representing Proportional Relationships by Equations | 7.RP.A.2c**

**The Recipe Scaling Investigation**

• Write and use equations in the form y = kx • Substitute values and solve for unknowns • Compare correct and incorrect equations • 4 real recipe-scaling problems

**CASE 4 — Explaining Points on a Graph | 7.RP.A.2d**

**The Savings Account Investigation**

• Interpret points (x, y) in context • Focus on (0, 0) and (1, r), where r is the unit rate • Compare proportional and non-proportional graphs • 4 problems with labeled coordinate planes and written explanations

━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 📦 EVERYTHING INCLUDED — 34 PAGES ━━━━━━━━━━━━━━━━━━━━━━━━━━━━

✔ Detective Notebook Cover

✔ 4 Color-Coded Tab Dividers

✔ Case-File Folder Template with Evidence Checklist

✔ CCSS Alignment Anchor Chart mapping each case to 7.RP.A.2a–d

✔ 4 Case Files with 16 problems total

✔ Evidence-Collection Worksheets with data tables and coordinate planes

✔ Detective Tip Boxes with key concept reminders

✔ Complete Answer Key with Worked Exemplars showing multiple representations

✔ Teacher Pacing Guide with a 7-day schedule and differentiation tips for struggling, advanced, and ELL students

✔ Review Request Page

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**7.RP.A.2a** — Decide whether two quantities are in a proportional relationship by testing equivalent ratios in a table or graphing on a coordinate plane.

**7.RP.A.2b** — Identify the constant of proportionality (unit rate) from tables, graphs, equations, diagrams, and verbal descriptions.

**7.RP.A.2c** — Represent proportional relationships by equations in the form y = kx.

**7.RP.A.2d** — Explain what a point (x, y) on the graph means in terms of the situation, with special attention to (0, 0) and (1, r), where r is the unit rate.

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• 7th Grade Math classrooms

• Middle school math intervention and enrichment

• Homeschool math curriculum

• Math centers and small-group instruction

• Test prep and SBAC/PARCC review

• Sub plans with self-contained, no-prep activities

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✓ The detective theme connects the four proportional-relationship skills into one coherent investigation.

✓ Multiple representations are used throughout the answer exemplars so students can see how tables, graphs, equations, and verbal descriptions relate.

✓ Evidence worksheets and coordinate planes provide structured workspace for mathematical reasoning.

✓ A 7-day pacing guide includes differentiation guidance for struggling, advanced, and ELL students.

✓ The resource can be used as a complete unit or for small-group practice and review.

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