Making the Most of Rates and Unit Rates!

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SWBAT find rates and unit rates using tools such as tables, tape diagrams and double number lines. Students will also be able to use rate language (each, to, per, for each)

Big Idea

Students will be making sense of problems and looking for structure in this lesson about real life rates and unit rates.


15 minutes

I’m going to have students warm up with a problem from Illustrative Math called Boys and Girls.  The problem is:

The ratio of the number of boys to the number of girls at school is 4:5.

a. What fraction of the students are boys?

b. If there are 120 boys, how many students are there altogether?

This problem has students looking at ratios as a fraction (so they will need to know that a fraction is a part to whole relationship) and also finding equivalent ratios.  In order for students to fully understand their thinking, I’m going to have them explain their steps and say why they took the steps that they took. I’m also going to have them apply a tool from their tool box to use for this problem.

 Give students time to interact with a partner to go over their answers.  You can use the HUSUPU tool to get them into pairs. 

Introducing Rates

10 minutes

To begin the instruction for the day, I’m going to give the students a partial list of rates we use in our daily lives. I will be using the “special” words (per, each, in ) for rate as I discuss each of them.  When I’m done, I’m going to have students work with their tablemates to come up with 3 more rates they have heard in daily lives.  When students have completed their lists, add them to the board as a visual for today’s learning. You can also do an “I have that” to increase their list if needed.  One student says a rate, if you have it, you say “I have that”. If you don’t, then you add it to your list. 


10 minutes

There are two vocabulary words the students need to understand:  rate and unit rate

Rate is a special kind of ratio that compares two types of measurements.  This concept can be difficult for students so it may be a good idea to point out how the two quantities are different.

Unit Rate is a ratio of two measurements in which one of the measurements is a single unit.  Ask the students what another word for single is?  Next, ask students if all unit rates are rates? (Let them discuss with their partner), then ask them if all rates are unit rates? (Again, discuss with a partner) (SMP 1)

Let's do some problems!

35 minutes

During this part of the instruction, I’m going to give the students a variety of rate problems to convert into unit rates.  Students will be encouraged to use whatever strategy they are most comfortable with during the “your turn” part of the power point.  While I’m modeling instruction I will be using different strategies so I will appeal to all members of the class. The strategies I will be using for this lesson are double number lines, tape diagrams and ratio tables. Also, during the modeling portion, I will be repeating the phrase “If I only had one _____ then…. (SMP 6)   This will continually reinforce the vocabulary of unit rate. After working on the unit rate problems, students will be working a variety of problems that address rate and other ratio problems.


10 minutes

I’m going to have students write about a time when finding a unit rate would be very important.  If time permits, I will have them share with a partner to hear different opinions.