Converting Measurements in Different Systems Using Ratios

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SWBAT convert measurement units within different systems by using ratio tables and unit rates.

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.  After 2 1/2 minutes of work time, the class comes together for a quick discussion.  I ask students what the problem tells us, and what we're being asked to find.  I ask them what model we can use to solve this problem, and then display a student sample on the document camera.  I ask students what makes this problem a little more difficult, and we talk about how to apply a scale factor that is a fraction.  

In the previous lesson, students converted between units of measurement within the same system.  In this lesson. students will convert between units of measurement within different systems.  

Guided Practice

15 minutes

In this lesson, there isn't new material for students to master.  Therefore, this lesson doesn't have an intro to new material section.  Instead, I lead students through some Guided Practice before they are released to partner practice.  We practice using both ratio tables and double number lines, with which students are proficient.  

This lesson provides a great opportunity to talk about the reasonableness of the answers we get, based on the size of the scale factor.  Students should practice articulating that a scale factor less than 1 will result in an answer that is smaller than the starting amount (assuming the starting amount is greater than 1).  

Like in the previous lesson, 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.  As students work, I circulate around the classroom.  I am looking for:

  • Are students correctly labeling the double number lines or ratio tables?
  • Are students multiplying or dividing the terms by the correct units?
  • Is the arithmetic correct?
  • Are students using the appropriate operation?
  • 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?
  • What information are you given?
  • How do I know that my answer makes sense given the conversion?
  • Should I have more than my original units or fewer?
  • Is there a second step to this problem? (in some cases)


After 10 minutes of partner work time, I ask for 2 volunteers to show work from one of the partner practice problems.  Students give positive and constructive feedback on the models and answers.  

Students then work on the check for understanding problem on their own.

Independent Practice

15 minutes

Students work on the Independent Practice problem set.  If students are struggling, I ask the questions that I used during the Partner Practice section of the lesson.

The steps students should be taking: 

1) Write the units being converted

2) Write the given ratio

3) Write the known value for the conversion 

4) Find the scale factor

5) Apply the scale factor to find the unknown value

As the student work sample shows, students create visual models for each conversion problem.  

Closing and Exit Ticket

7 minutes

After independent work time,  I bring the class back together for a conversation.  First, we discuss Problem 3.  This problem requires students to analyze the numerical answer that they find in order to determine if Billy is tall enough for the ride.  When I ask students to share the answer they got, I will often get an answer of 139.7 cm. While this represents an accurate calculation, it is an incomplete answer. The correct answer should include the fact that Billy is tall enough for the ride.

Before the end of class, we will also talk about Problem 8, because I want students to work with a fraction and discuss this procedure. I take the time to model this problem and show all of the arithmetic steps on the document camera.  

Finally, students work independently on the Exit Ticket to end the lesson.