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999 West Dundee Road
Wheeling, Illinois 60090

Phone: 847-537-8270

Superintendent: Dr. Michael Connolly

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Mathematics

Functions

Critical Content

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

 

Critical Language

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

 

Concept-Based Connections

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?