Unit Rate Problems (Part 1 of 3)

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SWBAT solve unit rate problems by creating and extending a table or double number line diagram.

Big Idea

If we know the unit rate in a relationship, we can find any equivalent ratio easily.

Think About It

5 minutes

In this lesson, students are using what they've learned about unit rate to find equivalent ratios. At the start of class, I will ask students to work independently on the Think About It problem.  I expect students to easily complete part A.  Some students will struggle to articulate their thoughts for part B.  If this happens, I plan to ask "how far can you walk in 7 hours?"  When they respond with 21 miles, I will ask how they found this.  


Intro to New Material

15 minutes

After we fill in the brief notes, we complete the one example in the Intro to New Material section.  

I have students guide me through the steps to start my double number line diagram.  We represent the original relationship of 2 pounds for $6.  The problem asks how much 15 pounds would cost, so I ask students what the scale factor would be.  Some students will be able to figure that 7.5 is the scale factor, but many students will struggle because it is not a whole number scale factor. 

I add the unit rate to my double number line and then ask students how we can use this to find the cost of the 15 pounds of beans.  

With double number lines, it is important to ensure that students work backwards on the number lines when plotting the unit rate.

Partner Practice and Discussion

15 minutes

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

  • Are students annotating the problem?
  • Are students drawing the correct models?
  • For double number lines, are students correctly placing the unit rate?
  •  Are students using their displays to answer the questions asked?

I'm asking:

  • How did you figure out that equivalent ratio?
  • How can these displays help you answer rate questions?
  • Why did you need the unit rate?
  • How did you find the unit rate?


After 10 minutes of work time, the class comes back together to discuss problem 3.  This is the only one of the set where they should need to calculate unit rate to be able to answer the question.  I will cold call on a succession of students to help me create the visual model as a way to check for understanding.

Afterward, I will ask students to complete the check for understanding question. After the students complete the task, I will pull a popsicle stick as a way to pick a student work sample to show on the document camera.

Independent Practice

20 minutes

I will have students work on the Independent Practice for about a 20 minute section of my lesson, today. As they work, I am able to circulate around the room and check in with each individual student.

After 20 minutes, we come together as a class to discuss Problem 6.  Like with most good math problems, there are multiple ways to arrive at the answer for this problem.  I start the discussion by having students turn and tell their neighbor how they chose to problem solve.

I will then ask students to share out their strategies with the class. As new ideas are introduced, and I will share a sample for each pathway that I hear.  I expect most students will use unit rate to find how far Joseph jogs in 9 hours.  Some students will use skip counting to express multiple equivalent ratios.  Advanced students will determine the scale factor to get to the answer.

Closing and Exit Ticket

7 minutes

To close the lesson, I ask students to think about how they'd explain to someone new to our class why unit ratios can make finding equivalent ratios an easier task.  After 45 seconds of think time, students turn and share their thoughts with their partners.  Then, I will have 2-3 students share what they discussed with their partners.  

Students complete the Exit Ticket to end the lesson.