Using Rates

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SWBAT use unit rates to solve mathematical or real life problems

Big Idea

This lesson is designed to get students connecting their learning about unit rates to real life examples.


15 minutes

The students will be working on a problem from Illustrative Math.  The problem is as follows:

Joe was planning a business trip to Canada, so he went to the bank to exchange $200 U.S. dollars for Canadian (CDN) dollars (at a rate of $1.02 CDN per $1 US). On the way home from the bank, Joe’s boss called to say that the destination of the trip had changed to Mexico City. Joe went back to the bank to exchange his Canadian dollars for Mexican pesos (at a rate of 10.8 pesos per $1 CDN). How many Mexican pesos did Joe get?

This problem is a great connection to real-world.  The confusion may come in when students see the CDN abbreviation.  Please explain to them that because Canada uses the dollar too, we call it CDN to differentiate between the two. Students can use any strategy they choose to solve this problem.  The end result is that Joe will get 2203.2 pesos for his $200 U.S.

If students finish early, have them explain their solution: What you did and why you did it.  Additionally, students that finish early or are clearly understanding the concept, can work with other students that may be struggling.

Give students time to justify their answer with a partner (SMP 3).  This would be a good time to use a HUSUPU to partner students up randomly.

Unit Rate discussion

10 minutes

I’m going to use Think-Pair-Share for each of these questions.

Begin reviewing by asking students what is the difference between a rate and a unit rate?  I’m looking for students to say that a unit rate is a special rate because it is a per 1 ratio.

Next, ask them when is finding the unit rate is important?  I’m looking for responses like when you need a per hour, minute, mile answer and most importantly when we need to compare rates.

Finally, I’m going to ask them to make a list of unit rates found in their daily lives?  We will add this to chart paper so that it can be available throughout the unit.


Taking Unit Rates One Step Farther

30 minutes

I will complete 3 problems with the students.  I will use the ratio table, tape diagram, and double number line in my examples.  Today, I’m going to focus on finding both unit rates.  For example if the problem says I travel a certain amount of miles in a certain amount of hours.  I’m going to find the per mile and per hour rate for the last guided practice problem.  Most students will struggle with this because it is not something they are familiar with.  Allow them to visually represent the problem then they can use a calculator to find the actual dollar amount.

 Slide 6:  This slide is asking them find both unit rates.  I will show them all 3 ways to do this.  It will be helpful to have a calculator ready so that they are not caught up with the computation part.  The most important part here is that see that there are two unit rates:  $5/hour or .2 hour/$1 (per hour and per dollar rates).  Stretch the students by asking them how much time she would have to earn $1.00 (12 minutes) or what does .2 of an hour mean (SMP 4)

 and (SMP 6)

If students struggle with tape diagrams, you can give them a manipulative to use.  I like to use uni-fix cubes because they are large and easily manipulated.  I would also give these students problems that divide out easily so they can get the concept down without worrying about decimal or fraction answers. 

Ratio and Rates Round table

20 minutes

The students will be completing a Roundtable with their tablemates.  Before moving on to a new problem, students much check the answer to the previous problem and peer tutor as needed. 


10 minutes

I’m going to have the students think about their learning today and make a connection to their daily lives. 


In your notes, respond to this question in writing:  When making a purchase at the store, what are some things we need to know?  How is what you need to know connected to your learning?

 I will be looking for students to make the following connections:

Getting the best deal

Cost per pound/ounce/can

Cost when buying more than 1

Cost for 1/2 pound