Converting Measurements In the Same Sytem Using Ratios

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SWBAT convert measurement units within the same system given by unit rates, by using ratio reasoning.

Big Idea

When converting measurements within or between systems of measurement, we are using the unit rate to find the unknown quantity.

Think About It

5 minutes

Students work independently on the Think About It problem.  Generally, students are aware that there are 12 inches in a foot, and are able to quickly complete this problem.  After a minute or two, I ask students for the answer and expect the student who answers to explain how (s)he arrived at the answer.  Students will say that they know that 1 foot is 12 inches.

I ask them to think about the previous lesson, which was on unit rate.  I ask students to make a connection between unit rate and the Think About It problem. 

Intro to New Material

15 minutes

In this lesson, students are using what they already know about ratios to convert units of measure within the same systems.  In the Intro to New Material  section, I model for students how to annotate and make sense of what we're being asked to find.

In this lesson, I coach students to include the unit rate/conversion fact in the ratio table before the other given information in the problem.  See the sample work for an example of how to set up the ratio tables.

For Problem D, I make sure we discus using decimals or fractions.  Students tend to use decimals in my class, but I see this problem as an opportunity to reinforce the idea that there are multiple pathways to get to a solution.  While my students compute 12 divided by 16, I work on my page to simplify the fraction 12/16.  We have a conversation about efficiency and being comfortable with using either .75 or its equivalent, 3/4.

The conversion facts are given to students throughout the student materials.  Another option would be to put all of the conversion facts at the end of the student materials, on a reference sheet (which is what my students would be given to reference on our state tests prior to the Smarter Balanced assessment).



Partner Practice and Discussion

15 minutes

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

  • Are students annotating the problems?
  • Are students correctly labeling and drawing  the double number lines and ratio tables?
  • Are students multiplying by the correct unit amount?
  • Are students showing clear, logical work?
  • Are students providing an answer to the specific question?
  • Are students checking for the reasonableness of their answer?  

I am asking:

  • What does the ratio mean in this problem?
  • What is the value of each part?  How do you know?
  • What is the question asking you to find?
  • How do you know your answer makes sense?
  • Should the number of units be more or less than the number you are converting? 


After 10 minutes of work time, I bring the class back together.  I show student work from the problem of the student's choice on the document camera.  

Students work independently on the check for understanding question.  Students show their answers on their fingers (1=A, 2=B, etc.)

Independent Practice

20 minutes

Students work on the Independent Practice problems. 

 After 15 minutes of work time, I have students turn and compare work with their partners for problem 8.  We then come back as a whole class to discuss the problem.  


Closing and Exit Ticket

10 minutes

After independent work time, I bring the class back together.  I ask students to turn and talk with their partner about how they might predict if their answer is going to be bigger or smaller than the number they are converting.  I have 2-3 students share their thoughts out with with class.  

Students work on the Exit Ticket to end the lesson.