Fraction Division Word Problems

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Objective

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

Big Idea

Division has different meanings depending on the context.

Think About It

7 minutes

Students work in pairs to solve the Think About It problem, using any strategy they'd like.

After 3 minutes of work time, students come back together and share their strategies for arriving at a solution.  There are a variety of strategies students might access to solve this problem:

Guided Practice

15 minutes

The content in this lesson is not new, as students have had the opportunity to divide with fractions throughout this unit.  This lesson, then, has a Guided Practice problem set, rather than an Intro to New Material section.  

The steps that students will take to problem solve in this lesson:

Steps for Solving/Modeling Fraction Word Problems

1)      Read and annotate what you know.

2)      Determine what the question is asking you.

3)      Pick an appropriate strategy to solve.

4)      Solve using the standard algorithms.

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

7)      Check for accuracy and reasonableness. 

 

 This lesson occurs early on in the school year.  In this lesson, I focus on problem annotation, organization of work space, and representing the problem.  I'll work all year with students on our problem solving framework, which requires students to understand, plan, solve, and check (UPSC).  

The sense making questions I ask after the students read and annotate the problem are:  What does this problem tell us?  What did you annotate (along with showing the annotations on the document camera)?  What is the problem asking us to find?  Are there any words in this problem you don't know?  Are those words essential to understanding this problem?

Partner Practice

20 minutes

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

  • Are students annotating the problems?
  • Are students drawing a visual model that represents the problem when necessary?
  • Are students writing a number sentence to solve the problem?
  • Are students answering in a complete sentence?
  • Are students using multiplication to check their work? 
  • Are students correctly using the standard algorithm to divide?
  • Are students simplifying their answer, when appropriate?
  • Are students finding the correct answers?

I'm asking:

  • How did you know to draw the model like this?
  • Why is this the number sentence that goes along with the problem? 
  • Tell me about your annotations.
  • What's the problem asking you to find?
  • Were there any unfamiliar words in this problem?  Were they essential to your understanding? 
  • How did you check your answer?
  • How did you make this into a division problem to solve?

 

Asking students about unfamiliar words serves two purposes.   One, I want to help build vocabularies.  But, two, I want students to internalize the idea that unknown words might not be a roadblock to finding a solution to the problem.  For example, later in the year my students will see an area problem about spreading mulch in a garden.  My students may not be familiar with the word 'mulch,' but they can still understand the problem and apply the  mathematical concept needed to solve.  

 

Independent Practice

15 minutes

Students work on the Independent Practice problem set.  

As I circulate, I ask questions of students about Problem 4.  I'll ask which item is more expensive, the book or the magazine?  I'll talk to students about the strategy they're trying to use.  I'll make sure that students are expressing their answers as money amounts, and not as fractions.  

One of the reasons I'm able to have rich conversations with students about their work is because I've taken the time to work out problems and have anticipated student misconceptions.

There are a number of strategies students might use to find the cost of the book:

 

Closing and Exit Ticket

8 minutes

After independent work time, I have the class come back together to share some work.  I ask for a volunteer to share out the problem (s)he wrote for problem 5.  Once a student shares, I ask the class to vote with thumbs up/thumbs down on whether or not the word problem we heard goes along with the given number sentence.  I'll cold call on a student with the correct thumb (up if the problem is correct, and down if the problem is incorrect) to explain why the story problem does or does not work.  If the shared problem is incorrect, we'll work as a class to improve and fix it.

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