Unit Plan 3 (Grade 7 Math): Proportional Relationships—Tables, Graphs, and k
7th graders learn to identify proportional relationships, compute and interpret the constant of proportionality (k) from tables and graphs, and represent them using y = kx. They connect multiple representations to explain meaning, units, and real-world applications with precision.
Focus: Identify proportional relationships; compute/interpret the constant of proportionality (k) from tables/graphs; connect to y = kx.
Grade Level: 7
Subject Area: Mathematics (Ratios & Proportional Relationships)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students deepen proportional reasoning by deciding when two quantities are proportional and how to represent them. They will test tables for a constant ratio, recognize graphs that pass through the origin, compute k (the constant of proportionality) from tables and graphs, and write matching equations of the form y = kx. Emphasis: consistent units, multiple representations, and interpreting what k means in context.
Essential Questions
- How can I tell if a situation is proportional from a table or a graph?
- What does the constant of proportionality (k) represent in a context?
- How do tables, graphs, and equations (y = kx) tell the same story in different ways?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Decide whether two quantities are in a proportional relationship using tables and graphs (look for constant ratios and a line through the origin).
- Compute and interpret k from tables (y ÷ x) and from graphs (slope as rise/run or reading the point (1, k) when appropriate).
- Represent proportional relationships with the equation y = kx, keeping units and meaning of k explicit.
- Switch among table ↔ graph ↔ equation and explain how each representation confirms proportionality.
- Check reasonableness with estimation, benchmarks, and unit statements.
Standards Alignment — CCSS Grade 7
- 7.RP.2a: Recognize proportional relationships; decide proportionality from tables or by graphing and checking line through origin.
- 7.RP.2b: Identify the constant of proportionality (k) in tables, graphs, equations, diagrams, or verbal descriptions.
- 7.RP.2c: Represent proportional relationships by equations (y = kx).
- Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.6 (precision).
Success Criteria — Student Language
- I can say if a relationship is proportional and explain why.
- I can find k from a table (y ÷ x) and from a graph (rise/run or (1, k)).
- I can write y = kx with units and explain what k means in my problem.
- I can use a table, graph, and equation to show the same relationship.
- I can estimate and check that my answer makes sense.