Converting Measurements Using Ratios

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Objective

• Use ratios to convert measurement units using multiplication or division. • Apply knowledge of measurement conversions to solve word problems.

Big Idea

How much taller is Lebron than Dwayne? Students use ratios to convert measurements and apply this knowledge to word problems.

Do Now

5 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 students to think about how they would figure out exactly how much taller Lebron is than Dwayne.  I want students to realize that they must first have the measurements in the same units, before they can compare the heights. 

Students participate in a Think Pair Share.  I call on students to share out information they need and ideas for answering the question.  This is not a time when we are figuring out the answer.  We will revisit this question during the closure.  Listening to student responses helps me gauge students’ experience with converting measurements.

Did you know...?

5 minutes

Note:

  • Before this lesson, I fill out and copy 1 foldable for each student.  Rather than spend class time creating the foldable, I want students to spend time applying the conversion facts in order to solve problems.  The foldable will serve as a great resource that students can keep in their binders.

I call on students to read the text.  I want students to briefly hear about the history of the metric system.   Then I ask students to review the conversion lists on the next page.  Students need to be familiar with measurement conversions so they are able answer more complicated questions.  Using the incorrect units can cause problems!  I briefly tell them about NASA’s mistake that caused the Mars Orbiter to crash.  NASA’s team was using metric units to use the thrusters, while Lockheed Martin (a company helping the mission) was sending NASA data about the thrusters in customary units.  As a result, the Mars Orbiter, which cost $125 million, crashed.

 At this point, I pass out foldables to students and briefly explain how they can be used as a resource.

Brain Pop Video

7 minutes

I pause the video so students have time to write down their notes. At the end I ask students, “What does it mean when Tim said that metric units increase by a factor of 10?”  If students are stuck, I have them turn to their metric conversions for length in their foldable.  I want students to realize that as they move from one unit to the next larger unit, the unit is 10 times as big.  For example, a centimeter is 10 times bigger than a millimeter.  1 cm = 10 mm.  I mention that units that have the prefix deci-, deka-, and hecto- are less common.

Conversion Check-in

3 minutes

I explain to students that they will be expected to have the conversions on this page memorized for the PARCC assessment.  I give students a minute to answer the conversions.  Then they use a different color pen/pencil to check their answers.

Using Ratios to Convert Measurements and Practice

10 minutes

Together we read through and complete the two examples using the foldables as a resource.  Students are engaging in MP5: Use appropriate tools strategically.  I do want students to memorize the measurement conversion facts, but until then I want students to use the foldable as their tool and focus their work on creating equivalent ratios.

 I stress to students that by using ratios we can see what units we have and what units we want to have and then change them.  I stress that for each problem students must create a ratio showing the relationship between the measurement units you are given and the units you want to convert to.   

I do not teach students to multiply when changing a “smaller” unit to a “larger” unit, or vice versa.  I believe that this short cut does not help students; rather it is one more procedure that they are likely to mix up or forget.  By using ratios, I believe students are able to understand that converting measurements is just creating equivalent ratios.

Students work on problems on page 1-8 independently using their foldables.  I circulate, looking to see that students are first creating a ratio showing the relationship between the 2 units and then an equivalent ratio converting the units.  Students may struggle with 6-8 because the answers have a whole number and then a fraction/decimal.   I let students struggle with these, reminding them to use their strategies that they have for working with equivalent ratios.   

Apply What You Know

10 minutes

We read through problem 1 together.  I have students work on it in partners for a couple minutes, and then we come back together.  I have students raise their hands to show which answer they believe is correct.  A common mistake is for students to divide by 10 instead of multiply by 10.  This can be prevented if students set up and label the ratio of grams to milligrams and then set up the other ratio using 150 grams.   I ask students to explain why people may have chosen choice, a, b, or d.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Students work on the other problems independently.  As students work, I walk around to monitor student progress.  I am looking to see that students are taking the time to set up and label their ratios.  Students are engaging in MP1: Make sense of problems and persevere in solving them and MP5: Use appropriate tools strategically.

If there is time, I ask students to share their thinking about problem 3.  I call 1-2 students up to show their work under the document camera and share their thinking.

Closure and Ticket to Go

10 minutes

I ask students to return to the do now problem about Lebron and Dwayne.  Students participate in a Think Pair Share about how to solve this problem.  Students work with their partner for a few minutes to solve it.

We come together and students share out their thinking.  Some students may have converted the measurements to meters and subtracted, finding that Lebron is 0.1 m taller.  Other students may have converted the measurements to centimeters, finding that Lebron is centimeters taller.  If either of these ideas does not come up, I will share them with students and ask what they think.  I want students to realize that both of these answers are correct, since 10 cm = 0.1 m.   If I have time, I will offer the idea of subtracting 193 – 2.03 to find the difference in height.  I want students to realize that this is not correct, since one measurement is in centimeters and the other is in meters.

I pass out the Ticket to Go and the HW Converting Measurements Using Ratios.