Unit Plan 31 (Grade 6 Math): Relationship Modeling Project—y in Terms of x
6th graders model real-world two-quantity situations by building tables, graphs, and equations of the form y = mx + b. Students interpret rate (m) and starting amount (b) with units, analyze relationships, make predictions, and explain assumptions clearly.
Focus: Plan and analyze a two-quantity situation; make a table/graph; write an equation (y in terms of x); interpret rate and starting amount.
Grade Level: 6
Subject Area: Mathematics (Expressions & Equations — Two-Variable Relationships)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students turn real-world stories into mathematical models. They identify independent (x) and dependent (y) variables, build tables, draw graphs, and write equations of the form y = mx + b to represent the relationship. They interpret rate (m) as “per 1” and starting amount (b) as the value when x = 0, connect features of the graph to the context, and communicate limitations.
Essential Questions
- What is changing with what? Which quantity should be x (independent) and which should be y (dependent)?
- How do tables, graphs, and equations represent the same relationship in different ways?
- What do rate (per 1) and starting amount mean in the context?
- How do my assumptions (units, domain) affect the model and conclusions?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- From a real situation, define x as independent and y as dependent; choose units and a sensible domain.
- Build a table of values, then graph the ordered pairs; describe what a single point (x, y) means.
- Write an equation y = mx + b (or y = kx for proportional cases) and interpret m (rate per 1 x) and b (starting amount).
- Use the model to predict and to explain results with units, noting assumptions/limitations.
- Critique and revise models (MP.3): compare two candidate equations and justify which better fits the situation/data.
Standards Alignment — CCSS Grade 6
- 6.EE.9: Use variables to represent two quantities in a real-world problem that change in relationship; write an equation to express one quantity (y) in terms of the other (x); analyze the relationship using tables, graphs, and equations, and relate these to the situation.
- MP.3: Construct viable arguments and critique the reasoning of others.
- MP.4: Model with mathematics.
Success Criteria — Student Language
- I can name the variables and tell which is independent and which is dependent.
- I can make a table and graph, and explain what a point like (3, 12) means in the story.
- I can write y = mx + b (or y = kx) and explain m as the rate per 1 and b as the starting amount.
- I can predict with my equation and give a unit sentence.
- I can defend my model and revise it if the data or context suggests a better choice.