Understanding tape diagrams

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SWBAT use tape diagrams to solve a variety of problems.

Big Idea

Using a tape diagram is one of the key models for ratios and proportions.

Do Now (Memory Box)

10 minutes

I’m going to have students write down everything they remember about ratio tables.  The purpose of this activity is to get the students thinking about their prior learning.  By creating an opportunity for students to write their thoughts on paper creates a meaningful application between their visual and written notes.  If students are struggling with this, have them put their pencils down.  Open up their notes and give them 2 to 3 minutes to look over their notes.  Do not write anything down.  When the time is up, have ALL students go back to their memory box and add to their information. It is helpful to remind students that they can use pictures and words to fill up their memory box. (SMP 1: thinking deeply about a concept, SMP 3: using assumptions and previously established results, SMP7: discerning patterns and structure)

Guided Practice

30 minutes

How does it work:  The students will be introduced to a problem that can be solved using a tape diagram.  The problem is a real life scenario involving a compound called Gack which is a combination between silly putty and jello-0. 

Slide 3:  The key focus in this slide will be to get the students to understand where the 5 parts came from.  Allow students time to think about this information.   After thinking about it, have them share with a partner.  Bring this question up to the group.  “How did we arrive at 5 parts in this problem and how do you know”?  Students should be looking at the visual of a tape diagram and see that there are 3 parts of glue to 2 parts starch for a total of 5 parts.

Slide 4:  This slide represents the total amount of cups needed (40).  Ask the students “if 40 cups are needed, then how many does EACH part represent?”  Again, allow time for think-pair-share.  The students should arrive at each part is worth 8 parts. 

Slide 5:  This slide represents the solution.  Instead of me telling them what the solution is, I’m going to show the slide and let the students make their own observations (SMP7) and then ask them to explain what is happening in this situation (SMP 8) in order to get their answer.

Students should see that if each part is worth 8, then we can go back to the original ratio and multiply the amount of parts (8) by the original parts (3 and 2).  So the solution is 24 parts glue and 16 parts starch for a total of 40 cups all together.  The answer makes sense. 

Your Turn

35 minutes

During this time, I’m going to allow students to grapple with the problem on their own.  They should first work independently, then as students finish, they can do a HUSUPU to compare answers with a partner. While students are working on these problems, I’m going to encourage them to use the tape diagram as a model of their understanding and thinking (SMP5). Since these tape diagrams are being added to the tool box, I want them to have as much exposure as possible.  Students may ask to use a ratio table or some other visual model.  If they do ask, I would go ahead and let them, but ask them to also represent it using a tape diagram as this is the target learning for the day.

Classroom management tips:  During this time, students will be working at varying levels.  Some will finish early, while others will struggle.  For those that finish before you are ready to move on to the next question, have them write down their steps to solving the problem.  (what did I do, and why did I do it).  This will solidify their learning by getting them to think about their thinking.  For students that struggle, you could always pair them up with a student that has clear thinking and understanding of the concept.  Allow some peer tutoring time.

When all students have completed the problem, bring students to the board to explain how they solved the problem. Encourage students to ask about steps that don’t make sense or comment on ideas that made solving the problem easier.  


15 minutes

I’m going to use a tool called Connect 3 (math tools, 2012).  This tool can be used to show relationships between vocabulary or mathematical content.  The students will be showing a relationship between ratio table, tape diagram, and double number line.  On each solid line in between, they are to come up with one sentence that identifies the relationship between the concepts.  In the middle, they can write a brief summary of all 3 concepts or discuss their uses. The beauty of this tool is that it hits the meat and potatoes of the vocabulary.  Students will need to think about their relationship and sum it up in one coherent sentence.  This supports SMP1 by monitoring and evaluating progress and willingness to consider the approaches of others and SMP 6 by creating carefully formulated explanations. 

When students have completed their Connect 3, allow them time to share with a partner to compare their thoughts.