Identify the Constant of Proportionality from an Equation

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Objective

SWBAT identify the constant of proportionality from an equation.

Big Idea

Students will use MP1, 2, 3, 4, 6, and 8 to solve problems involving identifying the constant of proportionality from an equation.

Bell Ringer

10 minutes

Hand students the bell ringer as they enter the room. For this bell ringer, students will work on problems, 1 and 2.  Save 3 and 4 for homework. 

Before starting this bell ringer, go over the homework from the lesson on identifying the constant of proportionality from a graph.  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 x and y values and how to use that information to identify these values plotted on a coordinate grid.

3. How to solve for unit rates.

Students will sit in their I.T.T seats and begin right away using MP1, MP2, and MP6 to grapple through two problems. Allow students 10 minutes forIndividual Think Time. 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 identify unit rates in equations.  Students may be intimidated on the first read of the questions.  Encourage students to scaffold the questions by highlighting important information, box numeric values, and read the question as if they were the ones in each scenario.  In their thinking, students will want to get in the habit of labeling the value of each variable. Students will appreciate that they do not need to solve for a value. 

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 be sure they know that they are not solving for a value. Students should show understanding that unit rates can be read in several ways.  For example in question 1, Bryce is making $10.50 per hour.  This can also be read as for every hour Bryce makes $10.50.  The word “per” is critical with unit rates.  This can be an identifiable cue that students are working with unit rates.  When developing student thinking with constant of proportionality, this is an early concept that students should understand.  Students should be able to break the equation down and know that 10.5h is equivalent to $10.50 for each hour.  “Each” representing every 1 hour he will earn $10.50.  Low learners may need to be refreshed on the decimal representation of 10.5 is equivalent to monetary value of $10.50. 

A common mistake is students mistaking the value as being $10.05.  The understanding gained here will help when students need to solve algebraic equations and expressions.  

Whole Group Discussion

20 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. In question 1, students with little understanding may lead toward response D.  Students may see 10.5 and choose $5.10/hr because both have the same digits.  They will reorder the digits because they are unable to understand how to identify the amount per hour, and the equivalent monetary value.  To spark debate I would ask the students how much is Bryce making each hour.  

Closing

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.  For example, for question 1, I would start with tying in our discussion conversation of each hour and the money made.  It is important for students to identify how to read rates and what that looks like.  

HOMEWORK

Have students solve question 3 and 4 from the bell ringer.  The link and pdf are ideas of homework questions you can use to create your own word problems.