Unit Plan 29 (Grade 7 Math): Constant of Proportionality—Graphs to Decisions
7th graders interpret and compare constants of proportionality (k) across tables, graphs, and equations. They identify proportional relationships, analyze unit rates, and use k to model real situations and justify data-driven recommendations.
Focus: Interpret k from graphs, tables, and equations; compare competing proportional models to make a recommendation.
Grade Level: 7
Subject Area: Mathematics (Ratios & Proportional Reasoning • Modeling)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students deepen fluency with proportional relationships by detecting when a relationship is proportional, identifying the constant of proportionality (k), and interpreting k as a unit rate with units. They move flexibly among tables, graphs, and equations (y = kx) and use k to compare models (for example, cost per mile, pages per minute, cups per batch). The week culminates in a data-informed recommendation backed by representations and clear reasoning.
Essential Questions
- How can I tell if a situation is proportional and find the constant of proportionality (k)?
- What does k mean in context (units), and how do I see it in a table, graph, or equation?
- How do I use k to choose between competing proportional models and justify my decision?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Decide if a relationship is proportional (passes through the origin; constant y/x across pairs).
- Determine k from tables (k = y/x), graphs (slope from origin), and equations (y = kx).
- Interpret k as a unit rate with correct units and explain its meaning in context.
- Convert among table ↔ graph ↔ equation and keep k consistent across forms.
- Compare two (or more) proportional models using k and make a recommendation supported by math and context.
Standards Alignment — CCSS Grade 7
- 7.RP.2a: Decide whether two quantities are in a proportional relationship (table/graph tests).
- 7.RP.2b: Identify the constant of proportionality (k) in tables, graphs, and equations.
- 7.RP.2c: Represent proportional relationships by equations (y = kx).
- 7.RP.2d: Explain what a point (x, y) on the graph means in context; interpret (1, k) and other points.
- Mathematical Practice MP.4: Model with mathematics (use k and representations to make and justify decisions).
Success Criteria — Student Language
- I can check if data are proportional and explain why.
- I can find k from a table, graph, or equation and state the units.
- I can write y = kx and show how the graph goes through the origin with slope k.
- I can compare k values and choose the better option for the situation.
- I can justify my choice with numbers, units, and a clear sentence.