Unit Plan 13 (Grade 8 Math): Comparing Functions—Multiple Representations

Focus: Compare functions given as rules, graphs, or tables; determine rates of change and initial values.

Grade Level: 8

Subject Area: Mathematics (Functions)

Total Unit Duration: 5 sessions (one week), 45–60 minutes per session

I. Introduction

This week, students become “function translators,” moving smoothly among rules (equations or verbal), graphs, and tables to compare how different functions behave. The spotlight is on two big ideas: the rate of change (how fast the output changes per 1 unit of input) and the initial value (the output when the input is 0, when that makes sense). Students decide which function grows faster, starts higher, or fits a given situation better—and explain why.

Essential Questions

• How can I recognize and compare rate of change and initial value when functions are shown in different ways?
• What do “faster,” “steeper,” or “starts higher” mean in terms of slope and intercept or in a real context?
• How do I justify which function is best for a situation using evidence from a rule, graph, or table?

II. Objectives and Standards

Learning Objectives — Students will be able to…

1. Identify rate of change and initial value from a rule (for example, in y = mx + b), a graph (slope and y-intercept), a table (change in y over change in x), or a verbal description.
2. Compare two functions presented in different representations and determine which has the greater rate of change and/or larger initial value.
3. Explain comparisons in context, using correct units and clear language (for example, “Plan A costs 2.50 dollars per pound; Plan B costs 2.80 dollars per pound.”).
4. Recognize when a relation is not linear and describe how a non-constant rate of change affects comparisons.

Standards Alignment — CCSS Grade 8

• 8.F.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an equation, determine which function has the greater rate of change.

Success Criteria (student-friendly)

• I can find the rate of change and initial value from a rule, graph, table, or description.
• I can say which of two functions changes faster or starts higher, and explain why using units.
• I can tell when a function is not linear and describe how that changes my comparison.
• I can justify my decision with clear evidence from the representation.