Unit Rate Problems (Part 2 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 of a ratio relationship, we can find any equivalent ratio easily with any whole number value.

Think About It

8 minutes

To begin, I ask students to work with partners on the Think About_It problem.  Students can create either a double number line or a ratio table to solve.  The sample here includes work from a student who chose to create a ratio table on the Think About It problem.

After 3-4 minutes of work time, I bring the class together.  I pull a popscicle stick as a way to cold call a student whose work will be shown on the document camera.  The student walks the class through how the problem was solved.  If the student didn't get to a solution (or arrives at an incorrect solution), the class uses the work as a starting point to get to the correct answer.


Guided Practice

15 minutes

Students worked on unit rate problems in the previous lesson, so there is no new material in this lesson.  Rather, I am giving students more practice with using unit rates to find equivalent fractions.  The problems in this lesson require students to use decimals and fractions in their work, which is difficult for some of my students. 

The Guided Practice section of this lesson includes problems that I model with double number lines and ratio tables.

For problem A, I model the solution using fractions.  With problem B, I use decimals.  I decide to do this so that my students have examples of each method that they can consult as they work.  

Partner Practice and Discussion

15 minutes

As usual, students work in pairs on the Partner_Practice  problem set.  As students work, I circulate around the room.  I am looking for:

  • Are students explaining their thinking to their partner?
  • Are students writing their work in the work space?
  • Are students drawing the models correctly?
  • Are students writing the correct decimal or fraction for each unit in their double line diagram or table?
  •  Are students using their displays to answer basic questions?

 I am asking:

  • How did you figure out that equivalent ratio?
  • How can these displays help you answer ratio questions? 
  • What's the unit rate?
  • How did finding the unit rate help you to figure out the equivalent ratio?

I make sure I am keeping an eye on the students' double number line, to be sure that they place the unit rate to the left of the starting equivalent ratio.  The work on the Partner Practice needs to include correct models, arithmetic, and the answer to the problems.

After 10 minutes of partner work time, students complete the check for understanding independently.  I have the class clap out their answer, so I can get a quick sense of student mastery.  I then have one student display his/her work from the CFU on the document camera. 

Independent Practice

20 minutes

Now I will give students time to work on the Independent Practice problem set. 

On problem number one, some students may decide to find the miles per hour for the unit rate. This problem, however, is best solved by finding hours per mile.  As students annotate the problems, I have them circle the unit that the problem gives us for the equivalent fraction - this is the one we use for the unit rate (so, for problem one, it tells us Andrew is traveling 22 miles, so we want to find the unit rate for one mile).

If students are working quickly, they can be encouraged to create both models for the problems.

Closing and Exit Ticket

8 minutes

After independent work time, I bring the class back together for a conversation.  I like to talk about problem 4a from the independent practice.  

There are many ways the students can determine that Daniel is incorrect in his thinking.  I have students first vote about Daniel's line of thinking - thumbs up if he's correct and thumbs down if he's incorrect.  My expectation is that the majority of students will show that Daniel's thinking 

I have students share with their partner how they knew Daniel's thinking was incorrect.  Then, 3-4 students share out their thinking (more, if there are more than 3-4 kids who want to share!).  Students may talk about unit rates, scale factor, number sense, or partitioning in their thinking.

Students complete the Exit Ticket independently to close the lesson.