Unit Concept Map
Grade Level: 8th Grade Pre-Algebra
Subject: Mathematics
Course Essential Question:
Unit Topic:
Linear relationships with two variables
Unit Essential Question:
How are proportional relationships, lines and linear equations related?
PA Standards/Anchors(Assessment Anchor/Eligible Content)
MO.8.B-E.2.1.1
Graph proportional relationships, interpreting the unit rate as the slope of the graph.
Compare two different proportional relationships represented in different ways.
Example: Compare a distance-time equation to determine which of two moving
objects has greater speed
MO.8.B-E.2.1.2
Use similar right triangles to show and explain why the slope m is the same between
any two distinct points on a non-vertical line in the co-ordinate plane.
MO.8.B-E.2.1.3
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.
Concepts
 Recognize how proportional relationships can be
represented graphically and as an equation.
 Identify the relationship between similar triangles and slope
of a linear function graph
 Relate slopes and their meaning in real life situations.
Skills
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Graph data from proportional relationships.
Identify vertical and horizontal change between points on a
graph.
Calculate rate of change from two given points on a graph.
Calculate rate of change.
Calculate slope of a line.
Interpret the meaning of a line on a graph.
Calculate slope and locate y-intercept using a graph or an
equation.
Recognize positive and negative slopes on a graph.
Formative Assessments
Summative Assessment
Vocabulary
 corresponding sides
 proportion
 rate of change
 similar figures
 slope
 unit rate
 x-axis
 y-axis
 y-intercept
 y=mx
 y=mx+b
Resources
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Quick checks.
Turn and talk or Partner
Share.
Use of white boards to
for quick check of
student understanding.
Quiz-Quiz-Trade
Matching game - where
students will match a
graph to an equation.
Each student holds a
card with either a graph
or an equation on it.
Their task is to find the
student with the card
that matches their card.
Ticket out the door.
End of class quizzes
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Teacher made test.
To include:
Multiple choice, short
answer, constructed
response, and/or
construct a graph
questions.
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Prentice Hall
Mathematics PreAlgebra
Study Island
Graph paper
Graphing Calculator
Calculate slope from a
data table, a graph, and
a linear equation.
Construct a graph from
a linear equation.
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Benchmark test on
Study Island.
Key Lesson Questions
1. How is unit rate calculated from a graph? And
how are unit rate and slope related?
5. How can similar right triangles be used to show
and explain why the slope m is the same between
any two distinct points on a non-vertical line in the
co-ordinate plane?
2. How can unit rate or slope be calculated from
a data table or a linear graph?
6. How does the equation y=mx represent a line
through the origin?
3. How can slope represented in different forms
be compared?
7. How does the equation y=mx+b represent a
line intercepting the vertical axis at b?
4. How are proportions used to determine
similarity in triangles?