Unit Plan 17 (Grade 6 Math): Two-Variable Relationships—Tables, Graphs, Equations
6th graders model two-variable relationships using tables, graphs, and equations. They write y in terms of x, identify rate of change and initial value, and explain real-world patterns with precision, reasoning, and units.
Focus: Represent relationships with tables and graphs; write y in terms of x; analyze patterns and rate.
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 learn to model real situations where two quantities change together. They identify the independent variable (x) and dependent variable (y), build tables (as ordered pairs), sketch graphs on the coordinate plane, and write equations that express y in terms of x. Emphasis: making sense of rate of change, reading initial value, and writing clear interpretations with units.
Essential Questions
- How do I decide which quantity is independent (x) and which is dependent (y)?
- How do tables, graphs, and equations show the same relationship in different ways?
- What are rate of change and initial value, and how can I find them from a table or graph?
- How do I explain what an equation like y = 3x + 2 means in a real context?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Identify independent and dependent variables in a context and describe how they change together.
- Create tables of (x, y) ordered pairs from a rule or from data; plot points on the coordinate plane.
- Write an equation that expresses y in terms of x (for example, y = kx, y = mx + b) and explain the rate and initial value in words with units.
- Analyze patterns in tables/graphs to describe how y changes as x increases (increasing, decreasing, constant; “for every 1 in x, y changes by …”).
- Check reasonableness by plugging values into the equation and comparing with the graph or table.
Standards Alignment — CCSS Grade 6
- 6.EE.9: Use variables to represent two quantities that change in relationship to one another; write an equation to express one quantity (dependent) in terms of the other (independent); analyze the relationship using tables, graphs, and verbal descriptions.
Success Criteria — Student Language
- I can name which quantity is independent (x) and which is dependent (y).
- I can make a table of ordered pairs and plot them correctly.
- I can write y in terms of x and tell what the rate and initial value mean in units.
- I can use my equation to predict and check with the graph or table.
- I can explain the relationship in a clear sentence (“For each 1 hour, the distance increases by 5 miles.”).