Relate the Graph of a Proportional Relationship to a Table

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Objective

SWBAT relate graphs of a proportional relationship to a table.

Big Idea

Allow students to practice MP1, MP2, MP3, MP4, and MP6 to decide whether two quantities are in a proportional relationship.

Opening Video

Bell ringer

20 minutes

Hand students the bell ringer as they enter the room.  Students will sit in their Individual Think Time seats and begin right away using MP1, MP2, and MP6 to grapple through two problems. Allow students 10 minutes for I.T.T. Students will need to write their thinking strategies in their interactive notebooks. They will use this to share during pair up time.  Walk the room to check for understanding.  Students should show that they are able to test for equivalent ratios in a table, or graph on a coordinate plane and observe whether the graph is a straight line through the origin. 

Once students have worked individually for 10 minutes, have students discuss their work with their pair up partners.  Students should have 10 minutes to discuss their thinking and compare their responses.  Students should be able to guide one another through the process of solving each of these questions. This will put into practice MP3.  For struggling learners, you may want to check for vocabulary understanding.  During this time it will be important to check that students understand where the origin is, and it’s importance in proportional relationships, how to plot points on a coordinate grid, how to read a coordinate grid, how to identify ordered pairs in a table in order to plot on a coordinate grid, understand what a coordinate plane is, understand how to test for equivalent ratios, and what the significance is of a straight line when proving proportional relationships.  

Whole Group Discussion

10 minutes

During this time, students groups should have the opportunity to share out their pair up time discussions, and reveal each of their responses.  You may not have time to have each student share.  As you filter through the room during pair up time, attempt to identify a group who has understanding, some understanding and little understanding.  During the whole group discussion have students debate their responses and defend their thinking.  This again will practice MP 3. As the facilitator of the discussion, you can head the discussion with open ended questions that will evoke students to defend.  For example, a student may say I chose C for question 1 because there is a constant change between the x values and a constant change between the y values.  You may ask:

“How does the constant change prove the table has a proportional relationship?”  This will allow students to think deeper.

For question 1, students may attempt to choose C because they may see that the x values increase by 1, and the y values increase by 2 each time.  Have students graph those ordered pairs and discuss the results.  Students should see that there will not be a straight line.  This will be a great time to discuss the importance of a linear line in relationship to proportional reasoning. 

Closing

10 minutes

Close the lesson with students leaving the room with the correct process in answering each question.  Use strategies that were discussed during the whole group discussion and show how to solve each problem correctly.  Have your students correct any mistakes.

 

Homework

This is an option for you to use to create your own or you can find two or three questions that students can do at home to reinforce understanding.