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* *Reflection: Positive Reinforcement
Fractions in the Real World - Section 1: Think About It

I work hard to build a culture in my classroom where students are willing to take risks. Being wrong, in front of more than 20 of your peers, can be tough on a middle school student if a supportive culture is not in place.

I teach this lesson early in the school year. I use a number of moves to reassure kids that making mistakes is a normal part of math class, and something that needs to happen so that we can all learn together. Here are some of things I'll say often:

**Before students start to work**- "This problem might feel tricky at first. It's my job to teach you this material today, but I want you to give it a shot and struggle a bit before we talk."**To encourage more hands**- "I'm going to wait for some more hands. Be willing to take a risk. What's the worst that can happen? You share an incorrect answer? So what! We will use it and learn from it"**To encourage more hands,**I'll narrate as hands go up - "Hector is willing to take a risk and share his thinking. Sophie has something to share about this problem"**When an incorrect answer is shared**- "Alexis, I'm glad you shared that with us, thank you. I saw a number of you get to this answer, and it shows a really common mistake when we work with this kind of problem. Let's figure this out together..."

*It's Okay to Struggle*

*Positive Reinforcement: It's Okay to Struggle*

# Fractions in the Real World

Lesson 4 of 6

## Objective: SWBAT represent and solve in-context, complex word problems using a visual model or computational procedures.

#### Think About It

*7 min*

Students work independently on the Think About It problem. Students are likely struggle to come to an answer with this problem. That's okay! The goal of this problem is to have students access the different problem solving strategies they've worked on so far this year.

If students are able to come up with the appropriate algorithm or visual model for this problem during their work time, use this work to start the Intro to New Material section.

After students have a chance to try this problem, I ask them what strategies they used to try to get to an answer. They'll likely say: bar models, other visuals to help us represent the problem, number lines, annotation of the problem, estimation, number sentences.

#### Resources

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#### Intro to New Material

*15 min*

In this lesson, students will solve problems that involve fractions and all four operations. I use the Think About It problem to start the instruction in this lesson.

For this particular problem, the visual works well because of the numbers used. However, students will solve similar problems later in this lesson that will be more difficult to solve using only the visual model. Therefore, as I walk through the problem with students, I create a visual model and use the algorithm simultaneously.

After solving the Think About It problem, I guide students through the Intro to New Material problem set. I'll focus on sense-making with students, asking often 'What information do we know from the problem?' and 'What question are we trying to answer?' For this lesson, I expect students to create visual models for each problem. Later in this unit, there will be a lesson where I'll allow students to pick any problem solving strategy to solve. For this lesson, though, I want to continue to push students' comfort with visual models.

**Steps for Solving/Modeling Fraction Word Problems**

1) Read and annotate what you know.

2) Determine what the question is asking you.

3) Draw a picture that reflects the problem and label everything that you know.

4) Use the diagram and the context of the problem to determine what operations and equations you need to use.

5) Solve using the standard algorithms.

6) Recontextualize your answer in the context of the problem and include units.** **

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#### Partner Practice

*20 min*

Students work in pairs on the Partner Practice problem set. As they work, I circulate around the classroom and check in with each group. I am looking for:

- Are students drawing a correct bar model that represents the problem (if strategy chosen)?
- Are students writing a number sentence to solve the problem?
- Are students answering in a complete sentence?
- Are students checking their work using estimation or multiplication?

I'm asking:

- What are you looking for in this problem? How is that represented in your model? In your number sentence?
- How did you know what step to do first?
- Which strategy did you use to solve this problem? Why did you pick that strategy?
- How else could you have gone about solving?
- What does this number mean, given the contest of this problem?

Before students move on to independent practice, we talk about Problem 5 from this problem set. I ask students what operations they needed to solve this problem, and then ask them what made this problem a little different from the others. I want students to talk about the order of operations here - they needed to add/subtract before completing the division in this problem.

#### Resources

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#### Independent Practice

*15 min*

Students work on the Independent Practice problem set.

For Problems 1 and 2, I expect students to draw models like we did for the Think About It problem. If, as they're working, students appear to be stuck with these problems, I'll encourage them to use the Think About It problem as a resource.

Problems 3 and 4 work under the assumption that students are comfortable with finding the area of a rectangle. You may consider adding the formula for area to this problem, if your students need this support. The units are yards and gallons in these two problems, but students are only manipulating the numbers in yards. It might confuse students to have gallons appear. When this happens, I rely on our problem-solving framework, asking: what do we know, what are you being asked to find?

#### Resources

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#### Closing and Exit Ticket

*8 min*

After independent work time, I have students talk with their partners about how they solved Problem 7. This is a problem with which students are likely to be successful. Some students will have used the standard algorithm, some may have drawn a picture, and some may have reasoned about the problem. Once students have talked to one another, I have the class share out the strategies that they employed.

Students then work independently on the Exit Ticket to close the lesson.

#### Resources

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##### Similar Lessons

Environment: Urban

###### Fractions Review: Simplifying Fractions

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*Resources(12)*

Environment: Urban

Environment: Urban

- 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: Whole Numbers Divided by Fractions Using Models
- LESSON 2: Fractions Divided by Whole Numbers Using Models
- LESSON 3: Fraction Division Using the Standard Algorithm
- LESSON 4: Fractions in the Real World
- LESSON 5: Division with Mixed Numbers
- LESSON 6: Fraction Division Word Problems