Determine The Graph of a Proportional Relationship

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Objective

SWBAT determine if a graph represents a proportional relationship

Big Idea

Students look for two key features of graphs that are proportional.

Introduction

15 minutes

The purpose of the introduction is to reacquaint my students with the coordinate plane.  They have had very little practice graphing so far this year.  So, before we dig into how proportional relationships look we need to review graphing.

We'll start with a review of terms.  I want to see if students can match key vocabulary to a coordinate plane.  They must know the terms x-axis, y-axis, and of course origin.

Next I will have the students graph 6 different points.  As any teacher with a little experience will see, students still confuse the ordered pairs.  They often are confused by graphing any point on an axis; they might mistakenly graph point E (3,0) on the y-axis.  It is important for students to place the points and label them with the letters to make it easier for me to determine how well they can graph.  

If I see a need, I will come up with a few more points to graph.

Problem Solving

15 minutes

Here is where students explore the key features for the graph of a proportional relationship.  The point of this activity is for them to conclude how the graph looks on their own by comparing a few different sets of data (MP8).  I give them the guidance that they are looking for a particular shape and starting location.  I may have to ask students to connect their points to the y-axis.  So that we can see that the graph should pass through the origin.

As students are working I will be initially checking their graphs for accuracy.  Fortunately, these are all quadrant I graphs so that reduces complexity a bit.  Some students will have a difficult time graph (1, 2.5) as they won't know what to do with 2.5.  I'll ask where does 2.5 fall between 2 and 3.  Hopefully, this well help them see that it belongs half way between 2 and 3.  I may have to ask what is 2.5 as a mixed number.

Students work through 4 sets of data to finally conclude the characteristics of a proportional relationship's graph.

As a quick check for understanding I will pull up this online graphing calculator.  I will input various values and ask students to determine whether or not they represent proportional relationships.

Some of the values may be similar to these:

y=3x

y=1/3x

y=3x + 5

y=1/3x + 5

y=1/x

y=x^2

y=x^3

 

Exit Ticket

5 minutes

For the exit ticket students must identify whether or not a graph is proportional.  They must include an explanation to qualify their answers.  Each problem will be worth 2 points: 1 for a correct answer and 1 for a valid explanation. A score of 6 out of 8 will be considered the minimum level of success.  

An example answer for #1 is to circle not proportional.  Then the student could say "the graph is not a straight line".  This is a simple way to have students practice MP3.