Multistep Tape Diagrams, Part 2

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SWBAT solve multi-step ratio problems, using tape diagrams

Big Idea

Tape diagrams can show ratio relationships and be used to reason about solutions to problems.

Think About It

5 minutes

Students work in pairs on the Think About It problem.  This problem mirrors the work we did in the previous lesson.  Partners will have an idea about how to solve, and many groups will be able to get to the solution of this problem.  

After 3 minutes of work time, I show an exemplar tape diagram on the document camera and think aloud about how I solved this problem.  

Guided Practice

15 minutes

The material in this lesson is the same content we worked on in the previous lesson.   There is not any new material.  Rather than run an Intro to New Material section in this lesson, I facilitate guided practice immediately following the Think About It problem.  The goal of this lesson is to give students more practice with the multi-step tape diagrams.

To start the Guided Practice section, I read problem one out loud and ask students to think about how to get this problem started.  I then call on hands for each step of the problem.  In addition to asking students 'what do we do next?' I am also asking things like 'what do we know?,' 'how can we represent that?' 'what are we trying to find out,' and 'why did you chose to do do that?'  

In between problems 1 and 2, I ask students to show me on their thumbs how they feel about working without me on these problems.  I expect to see mostly thumbs up (I'm ready to rock it!) or thumbs sideways (this is still a little tricky, but I am going to keep working at it).  I then cold call students to get the 2nd problem done.  The only question I ask is 'what's next?' 

Partner Practice and Discussion

20 minutes

Students work in pairs on the Partner Practice problem set.  As they are working, I circulate around the classroom.  I am looking for: 

  • Are students correctly creating tape diagram from a given ratio with equally sized rectangles and labeling?
  • Are students correctly drawing the new portion of the scenario?
  • Are students correctly solving for each part or total using division or multiplication?
  • Are students showing clear, logical work?
  • Are students providing an answer to the specific question?


I am asking:  

  • What does the ratio mean in this problem?
  • How can you represent this?
  • What is the value of each part?  How do you know?
  • If both terms have the same amount, how would this be represented in a tape diagram?
  • How do you use the value that is added to find each part?
  • Why did you divide by X?
  • What is the question asking you to find?


After 10 minutes of work time, I ask for a student to share his/her work for problem two on the document camera.  The student explains to the class the steps he/she took to find the solution.

Students then complete the check for understanding problem independently.  I have students clap out their answer choice, and then cold call on a student to show the tape diagram on the document camera. 

Independent Practice

15 minutes

Students work on the Independent Practice problem set.  As they are working, I am looking for and asking the same questions I used during Partner Practice.  

As I circulate, I pay careful attention to how students are solving problems 4 and 5.  These are a different problem type - we are given the total for the group.  There isn't anything being added in our situation.  Therefore, students should not be adding any new rectangles to the tape diagrams.  I've included this problem to ensure that students are reading carefully and really working to make sense of the problems they encounter.

Closing and Exit Ticket

10 minutes

After independent work time, I bring the class back together and we discuss problem number 4.  First, I ask them to raise their hand if they started to add a new portion to the tape diagram.  I then have them turn and talk with their partner about why we don't need to add anything new to our model.  After 1 minute of talk time, I ask for 1-2 students to share out why we aren't adding anything here.  I then ask for a student to explain how we would solve this problem.  As the student explains, I am modeling by creating my own tape diagram and solution, based on what the student is sharing with the class.  

Students work independently on the Exit Ticket to end the lesson.  Here's a completed Exit Ticket Sample.