##
* *Reflection: Developing a Conceptual Understanding
Proportional and Nonproportional Relationships - Can you find the constant? - Section 2: Explore

As a way to introduce the concept of a constant speed or rate, I had students work in groups to complete the tortoise speed investigation. For my advanced block, I was able to just give them brief instructions and then they were able to complete the investigation and answer the questions as a group. For my regular blocks, I found that I had to break down the investigation into parts and almost walk them through it. I set the scene by saying that the tortoise moves 10.5 inches in 3 seconds, use what you have learned so far this year to determine how far the tortoise can go in 1 second. All groups were successful with that. Then, we took a look at the table, and I guided the students through filling out the first couple columns, and then groups were able to finish. I did the same with the ratios. I gave all groups a few minutes to ponder the questions, and finally I asked the students to come up with a word that would describe the tortoise's rate of speed, and after a few minutes I gave them a hint that the word started with "c." In each of my blocks at least one person was able to come up with the word "constant" which I then shouted excitedly, as that word is so important and key to determining if a relationship is proportional - that I wanted kids to see how meaningful the word was to me :)

*Tortoise Investigation Reflection*

*Developing a Conceptual Understanding: Tortoise Investigation Reflection*

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

Lesson 5 of 14

## 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?

*60 minutes*

#### Launch

*10 min*

**Opener: **As 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**).

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#### Summary

*5 min*

Instructional Strategy - Table Discussion**: **To 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!

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- UNIT 1: Introduction to Mathematical Practices
- UNIT 2: Proportional Reasoning
- UNIT 3: Percents
- UNIT 4: Operations with Rational Numbers
- UNIT 5: Expressions
- UNIT 6: Equations
- UNIT 7: Geometric Figures
- UNIT 8: Geometric Measurement
- UNIT 9: Probability
- UNIT 10: Statistics
- UNIT 11: Culminating Unit: End of Grade Review

- LESSON 1: Introduction to Unit Rates - Learn to be a smart shopper!
- LESSON 2: Unit Rates with Complex Fractions
- LESSON 3: Unit Rates Fluency - Practice makes Perfect!
- LESSON 4: More Unit Rates Fluency - Practice, Practice!
- LESSON 5: Proportional and Nonproportional Relationships - Can you find the constant?
- LESSON 6: Equations of Proportional Relationships - Who needs a table?
- LESSON 7: Equations of Proportional Relationships - Fluency Practice!
- LESSON 8: Graphs of Proportional Relationships - What are the two important characteristics?
- LESSON 9: Graphing Proportional Relationships - Fluency Practice
- LESSON 10: Problem Solving Connections - Can you apply what you know about proportional reasoning?
- LESSON 11: Proportional Reasoning Review - Remember Hollywood Squares?
- LESSON 12: Proportional Reasoning Test - Time to Put it All Together!
- LESSON 13: Proportional Reasoning Remediation/Enrichment
- LESSON 14: Proportional Reasoning Retest - REWIND and Try Again!