Unit Plan 12 (Grade 8 Math): From Patterns to Functions

Focus: Define function formally, identify functions from mappings/tables/graphs, and use input–output language.

Grade Level: 8

Subject Area: Mathematics (Functions)

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

I. Introduction

This week launches the formal idea of a function. Students move from familiar patterns and proportional rules to a precise definition: a function assigns each input exactly one output. They will test relations in multiple representations (mappings, tables, graphs, verbal rules) and use input–output language and basic function notation to communicate clearly.

Essential Questions

• What exactly is a function, and how is it different from a general relation or pattern?
• How can I tell from a table, graph, mapping, or rule whether the relation is a function?
• How does clear input–output language help explain real-world situations?

II. Objectives and Standards

Learning Objectives — Students will be able to…

1. State the formal definition of a function and explain it in their own words with examples and non-examples.
2. Decide if a relation is a function from a mapping, table, graph (vertical line test), or verbal rule.
3. Use input–output language and introductory function notation (f(x)) to describe and evaluate simple rules.
4. Identify domain (set of inputs used) and range (set of outputs produced) in context.

Standards Alignment — CCSS Grade 8

• 8.F.1: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and its corresponding output.

Success Criteria (student-friendly)

• I can explain: “A function gives one output for each input.”
• I can look at a table, mapping, or graph and tell if it is a function, and explain why.
• I can read and use f(x) in simple cases (for example, if f(x) = 3x + 2, then f(4) = 14).
• I can name the domain and range that make sense for a situation.