Comparing Rates

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SWBAT: • Use information to create a rate table or a line graph • Use tables and graphs to compare rates

Big Idea

What was Diane’s speed for each segment of her triathlon? Students use line graphs and tables to compare rates.

Do Now

5 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to practice comparing rates.  I want students to realize that a gas mileage that is higher is better because you can go further with one gallon of gas.

Students participate in a Think Pair ShareI call on students to share their ideas.  I push students to explain that the Honda Civic has better gas mileage which will end up saving you money on gas over time.

Group Work Strategies

3 minutes

My goal is for students to be able to engage with difficult math problems and persevere in solving them.  I am not always available to help and I don’t want students to depend on me as their first resource when their work gets confusing.  Instead, I want students to develop strategies that they can use when they get stuck.

I explain this goal to my students and I have them brainstorm strategies that they can use when their group gets stuck.  I ask students to share out ideas with the class.  Some students may mention they can look back in their notes to review skills.  Other students may share that they can talk about what they know and what they need to figure out.  Students may mention strategies like creating a visual with their information.  It may work that students could skip the question and come back to it later. 

I mention to students that if they continue to be stuck, they need to work on developing a specific question to ask me.  Stating, “We don’t get it” does not tell me what you and your group are wondering about and what you have figured out already.



Athlete of the Week Introduction + Group Work Time

35 minutes


  • I use the student work from the previous lesson to Create Homogeneous Groups.
  • I have rulers and markers ready for students to use with the line graphs.
  • I also print out extra copies of the line graphs in case students want extra copies.
  • Each group receives a Group Work Rubric.

Students move into groups.  We read through the introduction of the problems.  We begin problem 1 together.  I want students to recognize that they can use the rate of 30 meters/ 5 seconds to create equivalent rates.  Other students may notice that the distance is increasing by 30 meters with each 5 seconds, so they may add 90 + 30 = 120.  This does not work, since the time changes from 15 to 25 seconds. 

For question b, I want students to pick a value of Wendy’s data and write it as a rate in meters/seconds.  Other students may calculate a unit rate.  If a student offers a unit rate, I ask them to explain their reasoning to the class.

Depending on how the students are doing, I may choose to complete part c together, or I may allow groups to start working together. For part c, I want students to recognize that Yoshie is faster.  She can go 70 meters in 11 seconds while Wendy can only go 60 meters in 10 seconds.  In 11 seconds, Wendy would go less than 70 meters.  Other students may use Wendy’s unit rate of 6 meters/ 1 second to realize that she will go 66 meters in 11 seconds.  Other students may realize that Yoshie will go 350 meters/11 seconds while Wendy will go only 330 meters/ 11 seconds.  Students should be able to recognize that the student who is faster is the student who goes farther in the same amount of time.

While groups are working, I walk around to monitor student progress and behavior.  Students are engaging in MP1: Make sense of problems and persevere in solving them, MP2: Reason abstractly and quantitatively, MP4: Model with mathematics, and MP6: Attend to precision. I am looking to see what strategies groups use to answer problem 3a-c.  I will use these observations to choose students to share during the closure.

If students are struggling, I may ask the following questions:

  • What strategies did you brainstorm earlier in the lesson?
  • What specifically is your question?
  • How do you know if someone is faster?
  • What strategies did you use in the previous lesson when you were trying to see who was faster?
  • What do you notice about the graph?
  • Is distance the x or y value? 
  • How can you figure out the distance traveled?

If students successfully complete questions 1-3, they can move on to questions 4 and 5. 

Closure and Ticket to Go

7 minutes

I ask students to share out how they calculated the distance traveled and speed for the different segments of Diane’s triathlon.  I call on a few students to come up to the document camera to show and explain their group’s work.   

I have students look at problem 5. Some students may have worked on this with their group.  I ask students to participate in a Think Pair Share.  I want students to be able to explain why one graph matches a rate.  I ask students which family is traveling fastest.  Some students may mention steepness, while other students may use specific data points to make their case.  Which family is traveling the slowest?  How do you know?

Instead of giving a Ticket to Go I collect student work to look at and I pass out the HW Comparing Rates.