Determine the Constant of Proportionality Between the Sides of Right Triangles

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SWBAT identify the constant of proportionality between the sides of right triangles.

Big Idea

Students will use MP1, 2, 3, 4, 6, and 8 to solve problems involving identifying the constant of proportionality between the sides of right triangles in order to deepen their understanding of constant proportionality.

Bell Ringer

20 minutes

Hand students the bell ringer as they enter the room. For this bell ringer, students will work on problems, 1 and 2. 

Before starting this bell ringer, go over the homework from the lesson on identifying the constant of proportionality of an equation.  Review the big points of the lesson when going over the homework.  Some important key points to help with transition are:

1. Key vocabulary

2. How to identify unit rates in an equation

3. How to solve for unit rates.

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. 

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 this bell ringer, while you walk the room checking for understanding you will want to check that students are able to identify the value for the base and the height.  Students may see the height line as a hash mark and count that toward the base measure.  If students are able to set up the ratio correctly and reduce it appropriately they will be able to change their response accordingly.  This is a great way to see that students are using MP1 and 2.

Students may want to set up the ratio of 11/2 at first.  This is purely a miscount of the hash marks.  Students should recognize the ratio is 12/4.  Once they are able to write the ratio appropriately they should be able to reduce it to identify an equivalent ratio.  In turn by now their understanding of equivalent ratios will identify constant of proportionality. 

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. 


10 minutes

It is important for students to know the correct process and correct answers in order for them to correct misguided thinking.  Go through the correct process in responding to each question.  Students will correct mistakes