# Proportional and Nonproportional Relationships - Can you find the constant?

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## Objective

Students will be able to distinguish between proportional and nonproportional relationships.

#### Big Idea

You have heard of moving at a constant speed or doing something at a constant rate - but did you know that was a proportional relationship?

## Launch

10 minutes

OpenerAs students enter the room, they will immediately pick up and begin working on the opener.  Instructional Strategy - Process for openers  This method of working and going over the opener lends itself to allow students to construct viable arguments and critique the reasoning of others, which is mathematical practice 3

Learning Target:  After completion of the opener, I will address the day’s learning targets to the students.  In today’s lesson, the intended target is, “I can distinguish between proportional and nonproportional relationships.” Students will jot the learning target down in their agendas (our version of a student planner, there is a place to write the learning target for every day).

Thoughts from Me! This lesson requires that students look for repeated reasoning, which will help them to determine if a relationship is proportional or not (mathematical practice 8). Students will be required to develop models for real world problems (mathematical practice 4) as well as reason through problems (mathematical practice 2).

45 minutes

## Summary

5 minutes

Instructional Strategy - Table DiscussionTo summarize this lesson, I will have students have a table discussion on the question:  To determine if a relationship was proportional or not, we looked for a constant ratio.  What do you think the technical term for this constant ratio is?  In the next lesson, we will move towards identifying the constant of proportionality, k, and writing equations.  This summary activity is a lead in to that. I am almost confident that no groups will come up with “constant of proportionality,” but it is fun to see! I am not going to tell them if no one gets it, they will have to stay tuned tomorrow!