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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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- 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!