Eighth Grade

Power Standards

• Define, evaluate and compare linear and non-linear functions. (8.F.1-3)
• Compare properties of two functions of the same type, each represented in a different way. (8.F.2)

Concepts and Skills

* Power Standard Content

• Input-output relationship of functions
• * Compare two functions represented differently (table, graph, equation, description)
• * Understand, interpret and construct equations in y=mx+b notation
• * Describe the relationship between two variables from their graph
• Recognize the connection between exponential equations and growth/decay patterns in tables and graphs
• Construct equations to express exponential patterns that appear in data tables, graphs, and problem situations

Language Usage

• A student in 8th grade will demonstrate the ability to apply and comprehend critical language by understanding, interpreting and constructing linear and non-linear functions.

Content-Specific Vocabulary

• Input
• Output
• Function
• Equations
• Variable
• Linear
• Non-linear
• Table
• Graph
• Exponential
• Notation
• Growth patterns
• Decay patterns
• Multiplicative
• Additive

Process-Specific Vocabulary

• Compare
• Understand
• Interpret
• Construct
• Describe
• Properties
• Recognize

Essential Understandings

• Linear, exponential and quadratic relationships have specific properties.
• Exponential relationships are multiplicative while linear relationships are additive.
• Tables, graphs and equations are tools for modeling real-world situations and solving problems.

Factual Guiding Questions

• How do you create an input-output table for a given function?
• What do each of the variables in the standard equation y=mx+b represent?
• What would the graph look like for different types of functions?
• What is an exponential equation?

Conceptual Guiding Questions

• What is the difference between inputs/outputs of a function versus a relation that is not a function?
• How do you compare two functions when looking at tables, graphs, and equations?
• How are growth/decay patterns in tables and graphs connected to exponential equations?

Engaging/Debatable Guiding Questions

• What is the relationship between linear and non-linear functions?
• When would you use the different functions in real-world situations?