Fractions in the Real World

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Objective

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

Big Idea

To solve multi-step problems, we need to work step-by-step, making sure to keep track of what we are solving for.

Think About It

7 minutes

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.

Intro to New Material

15 minutes

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.   

Partner Practice

20 minutes

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.  

 

Independent Practice

15 minutes

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?

Closing and Exit Ticket

8 minutes

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.