##
* *Reflection: Data Analysis
Problem Solving Connections - Can you apply what you know about proportional reasoning? - Section 2: Explore

For some very odd reason, the biggest misconception I encountered was students deciding to calculate the unit rate and then multiply it by ten?! I sat with one group, and when I asked why they multiplied by ten, they said because 4 miles per hour didn't sound fast - well, then it hit me, they were trying to make the unit rate into miles per hour - but really it was given to them in miles per minute! I was concerned going into the lesson that I was going to have to walk them through it, but I was pleasantly surprised. I partnered the kids homogeneously and they were able to dive right in.

I have stuck with the kids not being able to use calculators, and it has been really helpful I think in tweaking their skills with rational numbers. Instead of freaking out that the table consisted of fractions, they just got to work :)

# Problem Solving Connections - Can you apply what you know about proportional reasoning?

Lesson 10 of 14

## Objective: Students will be able to apply aspects of proportional reasoning including unit rates, graphs, tables, and equations to work a real world problem.

## Big Idea: If it doesn't apply, I don't care - heard that before? Well, this lesson applies what students have learned about proportional reasoning!

*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 apply what I know about unit rates and proportional relationships to solve a real world problem.” 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

*5 min*

Instructional Strategy - Table Discussion**: **To summarize this lesson, I will have students have a table discussion on the question: What are all the ways you can identify the constant of proportionality?

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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!