MathematicsLinear Functions &
Linear Models

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Unit Information

Content Map: Linear Functions & Linear Models

Checklist: Linear Functions & Linear Models Checklist

Unit 5.6: Examples and Explanations of Standards

Prerequisites: As identified by the CCGPS Frameworks

  • determining unit rate

  • applying proportional relationships

  • recognizing a function in various forms

  • plotting points on a coordinate plane

  • characteristics of a proportional relationship

Unit Length: 29 Days

Resources by Concept: (click on a concept)

Concept 1: Graph Linear Functions & Compare Different Representations
Lesson Standards:
  • CC.8.EE.5 (1) Graph proportional relationships, interpreting the unit rate as the slope of the graph.
  • CC.8.EE.5 (2) Compare two different proportional relationships represented in different ways.
Essential Questions:
  • How can the same mathematical idea be represented in a different way? Why would that be useful?
  • What does the slope of the function line tell me about the unit rate?
  • What does the unit rate tell me about the slope of the function line?
  • How can the properties of lines help me to understand graphing linear functions?
Key Vocabulary:
proportional relationship
Slope
Rate of change
linear
Resources:
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Concept 2: Rate of Change & Initial Value
Standards:
  • CC.8.F.4 (1) Construct a function to model a linear relationship between two quantities.
  • CC.8.F.4 (2) Determine the rate of change and initial value of a linear function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph.
Essential Questions:
  • When two functions share the same rate of change, what might be different about their tables, graphs and equations? What might be the same?
  • What is the significance of the patterns that exist between the triangles created on the graph of a linear function?
  • How does a change in one variable affect the other variable in a given situation?
Key Vocabulary:
Unit rate
initial value
Resources:

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Concept 3: Rate of Change & Initial Value (y = mx + b)
 Standards:
  • CC.8.EE.6 (1) Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane.
  • CC.8.EE.6 (2) Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
  • CC.8.F.3 (1) Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line.
Essential Questions:
  • How can I find the rate of change from a table, graph, equation, or verbal description?
  • How can I find the initial value from a table, graph, equations, or verbal description?
Key Vocabulary:
congruent figures
Resources:
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Concept 4: Non-Linear Examples
Standards:
  • CC.8.F.3 (2) Give examples of functions that are not linear.
Essential Questions:
  • How do I recognize non-linear functions in a graph?
  • How do I recognize non-linear functions in a table?
  • How do I recognize non-linear functions in a chart?
Key Vocabulary:
Non-linear
Resources:
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Concept 5: Interpreting the Meaning of Rate of Change and Slope
Standards:
  • CC.8.F.5 (1) Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., whether the function is increasing or decreasing, linear or nonlinear).
  • CC.8.F.5 (2) Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
  • CC.8.F.4 (3) Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Essential Questions:
  • How can I write a function to model a linear relationship?
  • How can I sketch a graph given a verbal description?
  • How can I describe a situation given a graph?
  • How can I use a linear model to solve problems?
Key Vocabulary:
Resources:
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