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# Part to Part Ratios Using Tape Diagrams and Tables

Lesson 2 of 13

## Objective: SWBAT represent a ratio using a tape diagram and a ratio table to determine the value of a part given the value of the other part

## Big Idea: There are multiple ways to represent proportional relationships and reason about solutions to problems.

*65 minutes*

#### Think About It

*5 min*

Students work independently on the Think About It problem. The problem starts by having students practice what they learned in the previous lesson. It then has students extend their thinking, by asking them to apply the rate to an equivalent ratio. After 3 minutes of work time, I have students share out how they tried to figure out the number of Wilson racquets in the last part of this problem. Some students will create equivalent fractions, while others will draw models.

As we conclude this warmup, I frame the lesson by letting students know that we will be using two models in this lesson - tape diagrams and tables.

#### Resources

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#### Intro to New Material

*20 min*

In this lesson, students will use a tape diagram or a ratio table to solve for a given value by making equivalent ratios until they find an equivalent ratio pair.

In all of the problems in this lesson, we will use an additive relationship. Some students are able to make the jump to a multiplicative relationship, but in this lesson I want students to physically build out the diagrams. In future lessons, we will just represent the given ratio and then create an equivalent ratio, but here we stay concrete.

To start the introduction of new material, I model how to create a tape diagram for the Think About It problem. You can see the problem solved step by step. The steps that I follow:

- Write the given units separately.
- Next to the first unit, draw however many equally sized boxes represent the first part of the ratio.
- Next to the second unit, draw however many boxes represent the second part of the ratio (keeping them exactly the same size as the unit above).
- Decide what the known term of the second ratio is. Decide how many groups of the given ratio you would need to add to get to that term. Draw them next to the given ratio boxes.
- However many groups you made of the first term, make that many groups of the second term also drawing the boxes.
- Count the boxes for the unknown part of the ratio. Include units.

Students help me create the tape diagram for the first problem in the Intro to New Material. For the second problem, I guide students to create a ratio table.

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Students work in pairs on the Partner Practice problems. As they work, I circulate around the room. I am looking for:

- Are students correctly identifying the terms and putting them in the correct order?
- Are students correctly identifying the proportional relationship?
- Are students correctly filling in all of the equivalent ratios?
- Are students using the model that the problem asks for?
- Are students drawing tape diagrams correctly (equally sizes boxes, etc.)?

I am asking:

- How did you know what the relationship was?
- How did you know what the rest of the ratios would be?
- What does your ratio represent?

I pay close attention to the organization of the tape diagrams. If students do not line up their boxes, they may lose track of what they need to draw. I created an example of the potential mistake.

After 10 minutes of partner work time, students work independently on the final check for understanding problem. I have one student who feels confident about his/her tape diagram share his/her work on the document camera. I then have one student who feels confident about his/her ratio table share his/her work on the document camera.

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#### Independent Practice

*15 min*

Students work on the Independent Practice problem set. As they work, I circulate around the room and I look for and ask the same questions I used during the partner practice.

Students need to annotate and take care to organize their work. A Student Sample is included here.

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#### Closing and Exit Ticket

*10 min*

After 15 minutes of independent work time, I bring the class back together for a conversation. We discuss Problem_7 from the Independent Practice problem set. This problem can be difficult for students because it involves the repeated addition of a fraction. Strategies that students share may include converting the fraction to a decimal, adding 2 1/2 repeatedly in the margin, or drawing pictures.

Students work independently on the Exit Ticket to end the lesson.

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on the intro new material section the key idea reads: A ratio table is a table the represents___________ relationships between different ratios. Is the "the" suppose to be "that" and is the blank equal? I have early AM brain so please help. Thanks this is a wonderful lesson!

| one year ago | Reply

I love the structure of the lesson and is actually how I'm trying to restructure my room right now. I did notice however that in the "Intro to New Material" section, the table example isn't proportional. The first column is 4 shells for $2 which is 4:2 and the second column is 6 shells to $4. Thanks for the materials though! Making my first year a lot easier!

| 2 years ago | Reply

Is number 9 on the independent practice supposed to be 600 gallons?

If there are 10 gallons for every 20 miles, that means 2 miles per gallon, so if you go 1200 miles, that would be 600 gallons.

I may have the "after school on a Monday" brain so please excuse me if I just blew that out the water.

| 2 years ago | Reply

Hi Carla! I'm getting ready to teach ratios and these resources look great! Is there any way you could send this lesson and Lesson 1 of this Unit to me in Word format? It would be super helpful to my instruction and my kids! Thanks! My e-mail is kareemkalil@hotmail.com.

Kareem

| 3 years ago | Reply*expand comments*

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- UNIT 1: Number Sense
- UNIT 2: Division with Fractions
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Coordinate Plane
- UNIT 5: Rates and Ratios
- UNIT 6: Unit Rate Applications and Percents
- UNIT 7: Expressions
- UNIT 8: Equations
- UNIT 9: Inequalities
- UNIT 10: Area of Two Dimensional Figures
- UNIT 11: Analyzing Data

- LESSON 1: Describing Ratios
- LESSON 2: Part to Part Ratios Using Tape Diagrams and Tables
- LESSON 3: Tape Diagrams - Part to Part and Part to Total Ratios
- LESSON 4: Part to Total Ratios Using Tape Diagrams and Tables
- LESSON 5: Multistep Tape Diagrams, Part 1
- LESSON 6: Multistep Tape Diagrams, Part 2
- LESSON 7: Comparing Ratios
- LESSON 8: Ratios and Double Number Lines
- LESSON 9: Ratios and Scale Factors
- LESSON 10: Graphing Ratios
- LESSON 11: Unit Rate
- LESSON 12: Converting Measurements In the Same Sytem Using Ratios
- LESSON 13: Converting Measurements in Different Systems Using Ratios