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: 

 Connected Mathematics Variables & Patterns
Lesson p. 36 Analyzing Graphs & Tables 1st part only

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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:
NonLinear Examples 
Standards: 
 CC.8.F.3 (2) Give examples of functions
that are not linear.

Essential Questions: 
 How do I recognize nonlinear functions in
a graph?
 How do I recognize nonlinear functions in
a table?
 How do I recognize nonlinear functions in
a chart?

Key Vocabulary: 
Nonlinear

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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