##
* *Reflection: Flexibility
Determine The Graph of a Proportional Relationship - Section 2: Problem Solving

When we arrived at this section of the lesson it seemed right to change the order of work. I asked students to first examine the various tables and determine if the relationships were proportional or not. This was a nice review and tie in to the previous two lessons:

Determine Equivalent Ratios: Scale Factor Between Ratios

Determine Equivalent Ratios: Scale Factor Between Terms

This also allowed us to know right away whether or not we were graphing a proportional relationship or not. The lesson is already set up so that the first question is to determine the proportional relationship, but sometimes my students miss these details in text Having the discussion first on the various tables allowed us to make the determination and then label the tables as proportional or not proportional.

Once this was done, we could spend our energy on graphing points and determining the two characteristics of a proportional relationship graph.

*Identifying Proportional Relationships in a Table*

*Flexibility: Identifying Proportional Relationships in a Table*

# Determine The Graph of a Proportional Relationship

Lesson 8 of 12

## Objective: SWBAT determine if a graph represents a proportional relationship

*35 minutes*

#### Introduction

*15 min*

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.

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#### Problem Solving

*15 min*

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

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#### Exit Ticket

*5 min*

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**.

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##### Similar Lessons

###### End of Grade Review: Tables, Graphs, and Equations of Proportional Relationships

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- LESSON 1: Proportional Relationships of Whole Numbers
- LESSON 2: Proportional Relationships With Decimals
- LESSON 3: Proportional Relationships With Fractions
- LESSON 4: Finding Distances on Maps
- LESSON 5: Scaling a Recipe
- LESSON 6: Determine Equivalent Ratios - Scale Factor Between Ratios
- LESSON 7: Determine Equivalent Ratios - Scale Factor Between Terms
- LESSON 8: Determine The Graph of a Proportional Relationship
- LESSON 9: Determine Equivalent Ratios - Common Unit Rate
- LESSON 10: Writing The Constant of Proportionality Equation
- LESSON 11: Writing Equations for Proportional Relationships
- LESSON 12: The Distance Formula