0.2.10 Representing and Interpreting
Proportional Relationships (Part 1)
Lesson Objectives
Required Materials
Identify and explain correspondences between
different representations of a proportional
relationship.
rulers
Understand that for graphs of proportional
relationships on the same axes, the graph with
greater constant of proportionality is steeper.
Understand that proportional relationships are
represented by equations of the form
with
and their graphs lie on first quadrant lines
that pass through
.
Setup: Number Talk: Fraction Multiplication and Division (5 minutes)
Display one problem at a time. 1 minute of quiet think time, followed by a whole-class discussion.
Statement
Anticipated Responses
1.
1.
2.
2.
3.
3. 20
4.
4. 3
Setup: Tables, Graphs, and Equations (20 minutes)
Print version only: Arrange students in groups of 3. Assign each student in each group a letter: A, B, or C.
Statement
Anticipated Responses
Your teacher will assign you one of the following
1. And 2. Graph is created correctly.
points:
,
,
.
2. Tables are completed correctly.
1. Plot and label only your point on the graph
provided.
2. Use a ruler to line up your point with the origin,
. Draw the ray that starts at the origin and
goes through your point. Extend your line to the
edge of the available graphing space.
3. Complete the table with the coordinates of points
on your graph. Use a fraction to represent any
value that is not a whole number.
3.
:
or equivalent.
:
or equivalent.
:
or equivalent.
4. Answers vary.
5.
:
or equivalent.
:
or equivalent.
:
or
equivalent.
6. Answers vary. Connections should be made
between the point
that appears on both the
graph and in the table and the equation
.
x
0
1
2
3
4
5
6
y
NA
4. Write an equation that represents the relationship
between and defined by your point.
7
8
9
5. Set your graph and table next to the graph and
table of other members of your group. In the
tables, what things are the same and what things
are different? In the equation? In the graph?
6. What is the -coordinate of your graph when the
-coordinate is 1? Plot and label this point on your
graph. Where do you see this value in the table?
Where do you see this value in your equation?
7. Based on your observations, summarize any
connections you see between the table,
characteristics of the graph, and the equation.
Setup: Space Rocks (10 minutes)
Statement
Anticipated Responses
Meteor Perseid 245 was traveling through the solar
system. The graph shows the distance it traveled
after a given point in time.
Asteroid x traveling faster than Perseid 245.
Explanations vary.
Is Asteroid x traveling faster or slower than Perseid
245? Explain how you know.
Setup: Ticket Booth, Revisited (5 minutes)
Cool-down (5 minutes)
Anticipated Responses
Noah and Diego left the amusement park’s ticket
booth at the same time. Each moved at a constant
speed toward his favorite ride. After 8 seconds, Noah
1. The steeper graph represents the distance
traveled by Diego.
was 17 meters from the ticket booth, and Diego was
43 meters away from the ticket booth.
2. Answers vary. Sample response: Diego had gone
farther after 8 seconds. If you pick a time and look
at which graph represents a person who has gone
farther, that is the steeper graph. So that must be
Diego’s graph.
1. Which graph represents the distance traveled by
Noah, and which line represents the distance
traveled by Diego? Label each graph with one
name.
1. Explain how you decided which graph represents
which person’s travel.
Lesson Summary (5 minutes)
Let’s say that you know the point
about the relationship?
is on the graph of a proportional relationship. What else do you know