Calculating Unit Rates

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Objective

• Use data to calculate and compare unit rates.

Big Idea

How long does it take each student to make one bracelet? How many bracelets can each student make in an hour? Students practice finding and using unit rates to answer questions.

Do Now

7 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 to see what strategies students will use to fill in the table and find the unit rate.  Some students may create a rate of 150 miles/ 5 gallons and divide to find that the car travels 30 miles/1 gallon.  Other students may work with the two distances to find the other distances.  For instance, if the car travels 150 miles using 5 gallons of gas, then for 10 gallons they would multiply 150 by 2.  They could also divide 180 by two to find the distance the car can travel using 3 gallons of gas.  I am interested to see what kind of strategies students use to find the unit rate.

Students participate in a Think Pair ShareI call on students to share their different ways of filling out the table and finding the miles per gallon.  I ask students, “What do we call it when one of the measurements in a rate is 1?”  I want students to understand the difference between a rate and a unit rate.

Miles Per Gallon

10 minutes

Notes:

  • Students will work in partners.  Before the class, I use the data from the 2 previous lessons to create partner pairs.
  • I Post a Key around the room.

We work through problem 2 together.  I ask, “How can we use the data in the table to fill in the blanks?”  Similar to the do now, students will use different methods to calculate the missing data and this is great.  I give partners a couple minutes to do their calculations and then we share out.  I ask, “How can we use this data to know how many miles per gallon Car B gets?”  Students may use different data points to find the unit rate.  I show students how we can use the unit rate to find out how far the car can travel with 17 gallons of gas.  I stress to students that it will help them keep track of units and measurements if they create equivalent rates that are labeled.  A common mistake is for students to set up the rates with different units in the numerator or denominator.  Another common mistake is for students to take one piece of the rate to multiply it without understanding what they are doing.  Some students may also struggle with unit rates that include a decimal.  Most students can use their division and multiplication skills to work through the problems.  If students are still struggling to multiply and divide with decimals, I let them use a calculator.  Even if a student uses a calculator they must first set up and label the equivalent rates.

For part d, the important question is “What data can we compare?”  In order to compare rates, we needs to compare rates that share a common measurement.  For instance we can compare the distance both cars can travel with 1 gallon, but we can’t compare the distance Car A travels using 3 gallons and the distance Car B travels using 5 gallons.  I make a connection to comparing fractions.  One way we compare fractions is by creating a common denominator.  To compare rates, each rate must have a common measurement.

Work Time

20 minutes

I explain that students are going to apply these strategies to more problems.  I ask students to review their strategies if they get stuck from the previous lesson (Comparing Rates). 

As students work, 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, and MP6: Attend to precision.  If a partner pair completes a problem, I briefly look over it to check for glaring mistakes.  If the students are on track, I send them to check their work with the key.

If students are struggling, I may ask one or more of the following questions:

  • What specifically is your question?
  • What is a unit rate?
  • How can you calculate a unit rate?
  • What are you trying to find out?
  • What do you know?
  • What can you compare?
  • What strategies did you use in questions 1 and 2 in this packet?
  • What do you notice about the graph?

If students successfully answer questions 3-5, they can work on the extra practice problems.  

Closure and Ticket to Go

13 minutes

I ask students, “What is the difference between a rate and a unit rate?” and “When is it helpful to use a unit rate?”  I want students to recognize that if they can calculate a unit rate, they can find other calculations easily.

Then I tell students to turn to the strawberry graph on page 6.  I ask them, “What can you tell about the prices of strawberries at store A, B, C, and D just by looking at the graph?”  Students participate in a Think Pair Share.  I want students to recognize that Store D has the cheapest strawberries because it has the flattest graph and that Store A has the most expensive strawberries because it has the steepest graph.  Other students may share the cost per pound of strawberries of each store.  The important part is that students are able to justify their ideas using data from the graph.

With about 6 minutes left, I pass out the Ticket to Go and the HW Calculating Unit Rates.