Unit Plan 4 (Grade 7 Math): Writing and Using y = kx
7th graders represent proportional relationships using y = kx, interpret key points (0,0) and (1,k) as the origin and unit rate, and solve for missing values with correct units. They connect equations, tables, and graphs to model real-world proportional situations precisely.
Focus: Represent proportional situations with equations; interpret points on the graph (0,0) and (1,k); solve for missing values.
Grade Level: 7
Subject Area: Mathematics (Ratios & Proportional Relationships)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
After identifying proportional relationships and the constant of proportionality k, students now write and use equations of the form y = kx to model real situations, interpret what key points on the graph mean (especially (0,0) and (1,k)), and solve for missing values in context. Emphasis: units on k, consistent variables, and reasonableness checks.
Essential Questions
- How does y = kx capture a proportional relationship in a single rule?
- What do the points (0,0), (1,k), and any (x,y) mean in a real situation?
- How do I solve for unknowns (x or y) and explain my answer with correct units?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Represent proportional situations by writing y = kx, naming variables and units clearly.
- Interpret (0,0) as “zero of one gives zero of the other” and (1,k) as the unit rate; explain any point (x,y) in words.
- Use y = kx to solve for missing values (unknown x or y) and check reasonableness with estimation and units.
- Move among verbal description → equation → table → graph and keep k consistent across representations.
- Diagnose and correct common errors (reversing x and y, dropping units, using a non-origin line).
Standards Alignment — CCSS Grade 7
- 7.RP.2c: Represent proportional relationships by equations (y = kx).
- 7.RP.2d: Explain what a point (x, y) on the graph of a proportional relationship means, especially (1, k) as the unit rate.
- Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.6 (precision).
Success Criteria — Student Language
- I can write y = kx with clear variables and units.
- I can explain (0,0) and (1,k) in words for my situation.
- I can use the equation to find a missing x or y and include units.
- I can show the same k in a table, a graph, and an equation.
- I can spot and fix mistakes like switching x and y or forgetting units.