Finding Equivalent Ratios

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SWBAT find equivalent ratios.

Big Idea

Students use tape diagrams to find equivalent ratios.


5 minutes

The purpose of the Hook is to garner students interest in the upcoming topic.  I will share a short story with students.

When I was in high school, I ran track.  I was a sprinter, not a long distance runner.  My best friend, Michelle, was also on the track team, but she was a long distance runner.  Since I'm a competitive person, I always tried to keep up with her when we practiced.  However, Michelle simply had a greater endurance for long distance.  For every 3 laps I ran, Michelle ran 5 laps.


Do Now

10 minutes

Previously, students were introduced to writing and interpreting ratios.  The Do Now relies on their previous knowledge of ratios.  

Do Now

In my story of running track, what was the ratio of my laps to my friend Michelle's laps. How many different ways can you write/represent this ratio?

After about 5 minutes, I will randomly select students to show an example on the board. 

Possible Answers

1)3 to 5

2)3 : 5


4)For every 3 laps you ran, Michelle ran 5 laps.

5)  Students may use a ratio table

6) Students may draw a tape diagram.



15 minutes

Example 1 - See Equivalent Ratios - Example 1

Continuing from the Hook and Do Now, this lesson will focus on using tape diagrams to find equivalent ratios.

Let's use a tape diagram representation of the ratio 3 to 5.  How can we determine how many laps Michelle ran if I ran 264 laps?

I will give students a few minutes to discuss the problem with their group and then we will reconvene. If students are unable to develop a strategy on their own, I will offer them a few leading questions.

  • Does each box represent the same number of laps?
    • Students should realize that each box represents the same number.
  • How can we determine how many laps each box represents?
    • Students should understand that if you divide the total number of laps that I ran by the number of boxes that represent this amount, you will arrive at the value of each box.  
  • Once we know the number of laps for each box, how can we use this to determine the number of laps that Michelle ran?
    • Students should understand that we can multiply the value of each box by the number of boxes representing Michelle's laps to determine the total amount of her laps.

I will lead students through another example to ensure that they understand how tape diagrams can be used to find equivalent ratios.

Example 2 - On Jonathan's Social Studies test the ratio of problems he answered correct to problems he answered incorrectly is 2 : 9.  If he answered 26 questions wrong, how many did he answer right?  Use a tape diagram to determine your answer.


Exit Ticket

10 minutes

The exit ticket is an assessment of students' understanding of using tape diagrams to find equivalent ratios.  Students will receive a sheet of paper on which to solve the below problem on.

Exit Ticket

Jose and Tamara are decorating a for a party.  They have two different color streamers, red and blue.  The ratio of length of red to length of blue is 2 to 3.  If there is 38 ft of red streamer, how many feet of blue do they have?  Use a tape diagram to show your work.

Students will have 5 - 7 minutes to answer the question.  I will collect the tickets and use them to determine scaffolding and grouping for future lessons.