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# Finding Equivalent Ratios

Lesson 2 of 3

## Objective: SWBAT find equivalent ratios.

*40 minutes*

#### Hook

*5 min*

The purpose of the Hook is to garner students interest in the upcoming topic. I will share a short story with students.

*When I was in high school, I ran track. I was a sprinter, not a long distance runner. My best friend, Michelle, was also on the track team, but she was a long distance runner. Since I'm a competitive person, I always tried to keep up with her when we practiced. However, Michelle simply had a greater endurance for long distance. For every 3 laps I ran, Michelle ran 5 laps.*

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#### Do Now

*10 min*

Previously, students were introduced to writing and interpreting ratios. The Do Now relies on their previous knowledge of ratios.

**Do Now**

**In my story of running track, what was the ratio of my laps to my friend Michelle's laps. How many different ways can you write/represent this ratio?**

After about 5 minutes, I will randomly select students to show an example on the board.

**Possible Answers**

1)3 to 5

2)3 : 5

3)3/5

4)For every 3 laps you ran, Michelle ran 5 laps.

5) Students may use a ratio table

6) Students may draw a tape diagram.

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#### Lesson

*15 min*

**Example 1 - **See Equivalent Ratios - Example 1

Continuing from the Hook and Do Now, this lesson will focus on using tape diagrams to find equivalent ratios.

*Let's use a tape diagram representation of the ratio 3 to 5. How can we determine how many laps Michelle ran if I ran 264 laps?*

I will give students a few minutes to discuss the problem with their group and then we will reconvene. If students are unable to develop a strategy on their own, I will offer them a few leading questions.

*Does each box represent the same number of laps?*- Students should realize that each box represents the same number.

*How can we determine how many laps each box represents?*- Students should understand that if you divide the total number of laps that I ran by the number of boxes that represent this amount, you will arrive at the value of each box.

*Once we know the number of laps for each box, how can we use this to determine the number of laps that Michelle ran?*- Students should understand that we can multiply the value of each box by the number of boxes representing Michelle's laps to determine the total amount of her laps.

I will lead students through another example to ensure that they understand how tape diagrams can be used to find equivalent ratios.

**Example 2 - On Jonathan's Social Studies test the ratio of problems he answered correct to problems he answered incorrectly is 2 : 9. If he answered 26 questions wrong, how many did he answer right? Use a tape diagram to determine your answer.**

#### Resources

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#### Exit Ticket

*10 min*

The exit ticket is an assessment of students' understanding of using tape diagrams to find equivalent ratios. Students will receive a sheet of paper on which to solve the below problem on.

**Exit Ticket**

**Jose and Tamara are decorating a for a party. They have two different color streamers, red and blue. The ratio of length of red to length of blue is 2 to 3. If there is 38 ft of red streamer, how many feet of blue do they have? Use a tape diagram to show your work.**

Students will have 5 - 7 minutes to answer the question. I will collect the tickets and use them to determine scaffolding and grouping for future lessons.

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- UNIT 1: First Week of School
- UNIT 2: Properties of Math
- UNIT 3: Divisibility Rules
- UNIT 4: Factors and Multiples
- UNIT 5: Introduction to Fractions
- UNIT 6: Adding and Subtracting Fractions
- UNIT 7: Multiplying and Dividing Fractions
- UNIT 8: Algorithms and Decimal Operations
- UNIT 9: Multi-Unit Summative Assessments
- UNIT 10: Rational Numbers
- UNIT 11: Equivalent Ratios
- UNIT 12: Unit Rate
- UNIT 13: Fractions, Decimals, and Percents
- UNIT 14: Algebra
- UNIT 15: Geometry