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# Graphs of Proportional Relationships - What are the two important characteristics?

Lesson 8 of 14

## Objective: Students will be able to determine if the graph of a relationship is proportional, and thus state the constant of proportionality and equation for the relationship.

## Big Idea: Is your graph a straight line? Does it pass through the origin? This lesson helps you determine if graphs are proportional!

*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 determine if a graph represents a proportional relationship, and I can determine the constant of proportionality from a graph and the equation for proportional 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! **In this lesson, students will be looking for patterns and repeated reasoning, and drawing conclusions (**mathematical practices 7 and 8)**. Using real world problems, students will create graphs (**mathematical practice 4**) and given a graph, students will be able to determine an equation and whether or not the relationship is proportional (**mathematical practice 2**). It will be important that students pay close attention to precision (mathematical practice 6), and use tools (calculator, graph, table) as needed (**mathematical practice 5). **

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#### Summary + Homework

*10 min*

Instructional Strategy - Table Discussion**: **To summarize this lesson, I will have students have a table discussion on the question: What are the two characteristics of the graph of a proportional relationship?

**Homework:** As students are having their table discussion, I will pass out the night’s assignment. I have left additional time within this lesson for students to begin on the assignment, as I want to make sure they have a good grasp on it before they get home.

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*Responding to Liz Brown*

I agree. I had a particularly hard time with one section of the notes. I also wanted to check myself on the homework because I had a couple of kids present a very good argument for their answer compared to mine. Great Lesson!!

| one year ago | Reply

Loved this lesson. It was perfect for my students to bring what I had taught together for better understanding. Thank you for the post of the lesson. Wonderful examples, note page, and homework. My struggling students felt more confident after the lesson and performed much better than when first taught.

| one year ago | Reply

I like all your lessons that I have seen so far. Thank you for the good help.

| one year ago | Reply*Responding to R Gillespie*

I am glad you have found them useful!

| 2 years ago | Reply

Do you have the keys for the resources? I would especially like the key to the notes.

| 2 years ago | Reply*expand comments*

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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
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- 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!