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# Introducing Ratio Reasoning & Percentages

Lesson 12 of 20

## Objective: SWBAT solve problems involving percentages using the concept of ratios and proportional relationships

## Big Idea: A Percent is a Ratio Too?! Showing students how percentages and ratios are related and how problems involving percentages can be solved by using ratio relationships

*70 minutes*

#### Curriculum Reinforcer

*5 min*

The Curriculum Reinforcer is basically a quick three to five question quiz containing information from previously taught standards that will allow you to determine areas in which your students may need to review. When I create my Curriculum Reinforcers, I make sure to mix up the types of problems. I use multiple choice, open-ended questions, as well as questions that require constructed responses. I may provide a mixture all in one day or, I may have all multiple choice one day and a mixture the next. It all depends on what I am looking for my students to be able to do. Often times, I also mix the standards however, there are times when I don't. I mix them so that I can see how well my students are fairing in more than one standard. In those instances when I don't mix up the standards, I am trying to see if the students are able to understand the standard when it is presented in a variety of ways.

#### Resources

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#### Engagement

*5 min*

To start off this lesson, I will present, “The Ring Toss Challenge,” which requires the students to convert between fractions and percentages. “The Ring Toss Challenge,” is attached to this section of this lesson.

While presenting, “The Ring Toss Challenge,” I will ask the students the following questions:

- Who won the challenge?
- How do you know?
- So what game are they going to play next?

The mathematical Practice standards evident in this section: **MP1, MP3, and MP6 **

After going through this engagement activity, we will then transition to learning about percentages and how percentages relate to the concept of proportional relationships.

#### Resources

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To start off this lesson, I will ask the following question, “What is a percentage and what does it represent?” If the students seem stuck, I will then say, “think about the opening activity and how percentages represented the situation presented.

The purpose of asking this question is to make my students think about whether or not they truly understand what a percentage is and the purpose of a percentage. During this lesson, not only will the students learn how to solve percent proportions but, they will also come away with a true working knowledge of the meaning as well as other “take aways” as listed below:

- Although a percent is one number it represent a part to whole ratio, all by itself.
- Because percentages are part to whole ratios, they can be changed into decimals, and fractions.
- Finding a percent of a number is like finding a fraction of a number.
- A percentage written as a fraction is that percentage as the numerator and 100 as the denominator then, simplify.
- A percentage written as a decimal is that percentage with the decimal placed two digits to the left.
- Percentages are commonly used to make comparisons.
- Another common use for percentages involves money in situations dealing with taxes, gratuity, bank accounts, sales… etc.
- We can solve some problems involving percentages using proportions.

To accomplish the transfer of this knowledge to my students, we will engage in dialogue that will provide examples of each of the bullet points above. I will also provide the students with several examples.

- The first example will involve finding the percent of a number.
- The second example will be a word problem where I will show students how they would use the same concept of finding the percent of a number in a real world context.
- The third and last problem that I will model will present a circle graph. And, using that circle graph, I will have to answer a question involving percent.

Mathematical practice standards evident in this portion of this lesson: **MP1, MP2, MP4, MP6, MP7, & MP8**

To view the problems that I will be modeling, Please see the attached PowerPoint.

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#### Try It Out

*10 min*

To practice percentages in connection with the concept of proportions, I will have the students complete two problems. The problems that they will complete are as follows:

1. What is 32% of 60?

2. Troy wants to buy a jersey of his favorite MLS team, The jersey is 30% off the original price. If the original price of the jersey is $35, what is the amount Troy will save?

While they are completing these problems, I will travel the room to observe student work to determine if there is anything that I may need to reteach before moving on. I will also answer any questions that the students may have.

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#### Independent Exploration

*20 min*

To practice this concept of using proportions to solve problems involving percentages, my students will complete the worksheet attached to this section of this lesson.

This worksheet requires students to find the part and the whole of a given quantity in relation to the percentage given. This worksheet also requires the students to be able to solve problems involving percentages in real world context. **(MP1)**

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#### Closing Summary

*20 min*

Selected students will present their answers to the worksheet that they completed during the independent exploration.

These students will present their answers under the document camera. When presenting their work, they will need to discuss the method they chose to solve their problem and take the class through their solution step by step. They will also need to be prepared to answer questions coming from their peers as well as me, their teacher.** (MP3 and MP6)**

To close out the lesson and determine if students truly understood what they were taught today, they will complete the following ticket out the door.

Ticket Out The Door:

What is 0.55% of 220?

#### Resources

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- LESSON 1: Ratios & Proportions: Unit 2 Pre-Assessment
- LESSON 2: Understanding Ratios
- LESSON 3: Ratios, Rates, and Unit Rates
- LESSON 4: Equivalent Ratios
- LESSON 5: Ratios & Proportions
- LESSON 6: Using Ratios to Solve Problems
- LESSON 7: Ratios, Rates, and Unit Rates in the Real World
- LESSON 8: Ratios on the Coordinate Plane
- LESSON 9: Representing Proportional Relationships in Different Ways (2 Day Lesson)
- LESSON 10: Ratios in a Storybook (3 Day Lesson)
- LESSON 11: Quiz 1: Ratios & Proportions
- LESSON 12: Introducing Ratio Reasoning & Percentages
- LESSON 13: Percent Problems in Context
- LESSON 14: Proportional Relationships & Geometry
- LESSON 15: Ratios & Conversion Factor
- LESSON 16: Unit 2 Station Review (2 Day Lesson)
- LESSON 17: Quiz 2: Ratios & Proportions
- LESSON 18: Unit 2: Reviewing Deficit Areas
- LESSON 19: Unit 2 Assessment
- LESSON 20: Student Self-Assessment: Reflecting on Ratios & Proportions