Unit Plan 34 (Grade 7 Math): Proportional Modeling Project—From Data to Decision
7th graders design and analyze proportional situations like recipes, speed, or cost. They collect data, compute unit rates, write equations, and graph y = kx to make predictions, compare options, and justify conclusions with clear assumptions and limits.
Focus: Design and analyze a proportional situation (for example, recipes, scaling, speed/cost); present findings with equations and graphs.
Grade Level: 7
Subject Area: Mathematics (Ratios & Proportional Reasoning • Expressions & Equations • Modeling)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students become mathematical modelers. They choose a real situation that is (or is intended to be) proportional, collect or curate data, and use unit rates, equations (y = kx), and graphs to make and defend a recommendation. They check assumptions (through origin, constant ratio), compare options, solve planning questions with equations, and communicate limits.
Essential Questions
- When is a situation truly proportional, and how do I verify it with data?
- How does the constant of proportionality (k) support prediction and comparison?
- How do I make a clear decision from my model and explain assumptions and limitations?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Plan a proportional investigation: define variables, units, and a guiding question; design or curate data.
- Test proportionality from tables and graphs (origin check, constant ratio) and determine k (unit rate).
- Represent the relationship by equation y = kx, interpret (1, k) and other points in context, and use the model to solve planning questions.
- Compare competing proportional options by k and justify a recommendation with evidence.
- Communicate results with units, a clear conclusion, and explicit limitations/assumptions.
Standards Alignment — CCSS Grade 7
- 7.RP.1: Compute unit rates associated with ratios of fractions and rational quantities.
- 7.RP.2a–d: Decide whether relationships are proportional; identify k; represent by y = kx; interpret points.
- 7.RP.3: Use proportional relationships to solve multistep percent/rate problems and to make predictions.
- 7.EE.4a: Write and solve equations of the form px + q = r and p(x + q) = r arising from real situations; interpret solutions.
- Mathematical Practices emphasized: MP.3 (construct viable arguments, critique reasoning), MP.4 (model with mathematics), plus MP.6 (precision) and MP.7 (structure).
Success Criteria — Student Language
- I can explain why my situation is proportional (origin and constant ratio) or explain why it is not.
- I can find and interpret k with units and write y = kx.
- I can predict and solve a planning question using my model and check reasonableness.
- I can compare options by unit rate and make a recommendation.
- I can name at least one assumption and one limitation of my model.