Tape Diagrams

Tape Diagrams

Introduction to Tape Diagrams

Opening

Introduction to Tape Diagrams

A store sells 10 comedy DVDs for every 90 action DVDs.

This relationship can be shown using a tape diagram. In the tape diagram, each unit (each square) represents 10 DVDs. There is 1 unit of comedy DVDs and 9 units of action DVDs.

There are different ways to arrange the tape diagram. You can see the ratio between the two quantities of DVDs more easily in Tape Diagram 2.

  • What is the ratio of action DVDs to comedy DVDs?
  • What is the ratio of comedy DVDs to action DVDs?

Math Mission

Opening

Use tape diagrams to represent ratios and solve problems about ratios.

Carlos’s DVD Collection

Work Time

Carlos's DVD Collection

Carlos has a DVD collection. The ratio of action DVDs to mystery DVDs in his collection is 5:2. The tape diagram shows this ratio.

  • If Carlos has 45 action DVDs, how many mystery DVDs does he have?
  • Use the tape diagram to help you solve this problem.

Ask yourself:

  • How many DVDs do 5 units in the tape diagram represent?
  • How many DVDs does 1 unit in the tape diagram represent?
  • How many DVDs do 2 units in the tape diagram represent?

Emma’s DVD Collection

Work Time

Emma's DVD Collection

Emma has a DVD collection. The ratio of drama DVDs to mystery DVDs in her collection is 7:3.

  • Make a tape diagram that represents the situation above.
  • If Emma has 28 drama DVDs, how many mystery DVDs does she have? Use your tape diagram to find the solution.

Ask yourself:
 

  • Create a tape diagram with two strips of tape.
  • Create one strip of tape to represent the drama DVDs. How many units should you divide the strip into?
  • How would you create a second strip of tape to represent the mystery DVDs?
  • How many DVDs does each unit in your tape diagram represent?

Prepare a Presentation

Work Time

Prepare a Presentation

Explain how you made the tape diagram for Emma's DVD collection and how you used tape diagrams to help solve both problems.

Challenge Problem

Emma bought 4 more drama DVDs and some more mystery DVDs at a yard sale. The ratio of drama DVDs to mystery DVDs in her DVD collection is now 8:5.

  • How many mystery DVDs did she buy? Draw a tape diagram and use it to solve this problem.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about the different approaches your classmates used in making their tape diagram, and how students used the tape diagrams to solve the two ratio problems.

As your classmates present, ask questions such as:

  • How did you determine the number of units to divide each strip of tape into?
  • Could you have divided the tape into a different number of units?
  • Can you explain how your tape diagram represents the ratio in the problem?
  • Do you think using a tape diagram made it easier to solve the problem?

Tape Diagrams and Ratios

Formative Assessment

Summary of the Math: Tape Diagrams and Ratios

Write a summary about how tape diagrams can be used to represent ratios and how they can be used to solve ratio problems.

Check your summary.

  • Do you explain what a tape diagram is?
  • Do you describe how a tape diagram can represent a ratio?
  • Do you discuss how tape diagrams can be used to solve ratio problems?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

Tape diagrams help me "see" ratios because ...