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* *Reflection: Unit Exams
Proportional Reasoning Remediation/Enrichment - Section 2: Explore

Today was an early release day at my school, so I had to whip right through this lesson. The weather was great, so I sat the proficient students out on my patio to work on a performance task so that I could focus on the students who were not proficient.

There were lots of "I can't believe I did that" and "oh my god" when I passed back the tests. Students were embarrassed that they had used subtraction to determine whether a relationship was proportional given a table rather than setting up ratios. I also gave the students a pointer when finding the constant of proportionality given a graph, I had them draw horizontal line from any point on the graph to the y-axis, circling the number of the y-axis they ran into, and a vertical line to the x-axis, circling the number on the x-axis they got to. By doing that, they were able to physically see that the y was over the x (because when you do that the y will always be higher on the paper than the x). Hopefully that will help them remember y always goes on top!!

*Explore Reflection*

*Unit Exams: Explore Reflection*

# Proportional Reasoning Remediation/Enrichment

Lesson 13 of 14

## Objective: Students will be able to represent proportional relationships via graphs, equations, tables, and words.

## Big Idea: Uh-oh...scores weren't as good as you were hoping? This lesson recaps PR and gets kids ready for a retest!

*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 represent proportional relationships via graphs, tables, equations and words. I can calcuate unit rates and use them to solve problems.” 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).

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#### Explore

*45 min*

**Proportional Relationships Overview: **Proportional Reasoning Remediation Video

**Proficient Students - Leaky Faucets Performance Task: **Students that were proficient (and since I am doing full class retesting, I am setting proficiency at 90%) will work with a partner on the "Leaky Faucets" performance task. This task requires students to work together (**mathematical practice 3**), perservering through a task (**mathematical practice 1**) that applies proportional reasoning to an every day problem (**mathematical practice 2**). Students will show their work through a variety of forms - equations, tables, graphs (**mathematical practice 4**), looking for patterns (**mathematical practice 7**) to help the character solve his problem! I have an outdoor patio, so, weather permitting, I will have the proficient students sit out on the patio and work while I work with the non-proficient students.

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#### Summary

*5 min*

**Instructional Strategy - Table Discussion: **To summarize this lesson, I am going to have students participate in a table discussion. The most common error the first time students took the test was remembering to set up their ratio as y:x; thus, my question is: "when calculating the constant of proportionality, what always goes over what?" I will walk around as students discuss, and then I will have tables hold up white boards simultaneously with their answers.

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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!