Towering Fractions

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SWBAT apply the problem solving strategy of diagraming to solve problems of addition and subtraction.

Big Idea

Today students work to showcase their knowledge of working with fractions with unlike denominators.


20 minutes

For the class read aloud today, a guest reader from the community read the book The Man Who Walked Between Two Wires to the class.  This book is a great story about adventure, goal setting, and perseverance.  I like this story because there are various places when fractions are used to describe situations.

The story begins by saying that the towers are each 1/4 of a mile tall.  Pause at this point in the story and ask the students some story problems about fractions.

  • How tall would the towers be if they stood on top of one another?
  • How many towers would it take to make 1 mile?
  • If the school is 1/10 of a mile tall, how much taller is the tower in the story?


Be sure to ask questions with various levels of complexity, so all students are able to participate.  When the story is over, we quickly revisit these questions, a white board can be used to make a bar diagram to match each situation.  

The intention of this launch is to show the students that fractions are present in all situations, and to help engage students in problem solving with fractions.

Guided Practice

15 minutes

As the end of the unit approaches, my guided practice part of the lesson is much smaller.  It is more of a review than instruction.  I use this time to explain today's activity and model my expectations.  

Students solve story problems that are addition, subtraction, and/or multiple step problems involving fractions.  They use bar diagrams to represent their thinking and help make sense of the problem.

One of the MP's is ability to contextualize and decontextualize problems.  In making sense of quantities and relationships, students are applying abstract thinking (decontextualizing) the problem and representing it mathematically or deriving context from abstract to test their thinking. This means that as students solve problems, they are able to move back and forth between the work they are doing and the problem to analyze their progress.  Bar diagrams help students with this process.

I choose one to model the multiple step problems. Not all students will work with a multiple step problem today, but by choosing this problem I will be able to model both addition and subtraction bar diagrams.  I've shown this in explicit detail on the resource. The model problem will also serve as an anchor chart throughout the lesson, so students can refer to it for help.

 On the board, I post the directions for today's activity:

  • Solve the problem
  • Use a bar diagram to organize your thinking 
  • Write a solution sentence
  • Publish this work with a drawing to match the story.

Independent Practice

20 minutes

I have selected examples from the text book that are addition and subtraction story problems.  Before beginning the lesson, but without telling the students, I level the problems based on the various challenges they provide.

  • Some of the problems have fractions that one denominator is a multiple of the other.
  • Some have denominators whose common multiples are easy to identify. Others are more challenging.
  • Some problems are multiple step.


I give each student a problem that is targeted to their level. I want to make sure they have a problem they can feel successful with, that is challenging enough, but also something they can do on their own. (Extra copies of all problems are provided for students when they complete the first problem, because I know all students are capable of solving each of these problems.)  

Two copies of each problem passed out. Students work independently to solve the problem they are assigned.  If they complete one problem, they may select another from the pile.

When all students have had an opportunity to solve their assigned problem, I let them know that someone else in the class has been solving the same problem as well. 

Students find the classmate solving the matching problem and discuss their approach as well as their solution.  If they faced any challenges while solving, they share that too. 

Group Share

20 minutes

After students have discussed their solutions, they return to their seats for a group share.  At this time, students share something that was discussed in the partner share, including errors that were found.  

Then, a few students are invited to tell about their problem, without giving the answer.  

For the remainder of class, I meet with students in a quick conference about their work, while students solve more addition and subtraction of fractions problems.