Review 4: Converting Measurements Using Ratios

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Objective

SWBAT use ratios to convert measurement units by multiplying or dividing

Big Idea

Why are there two systems of measurement? How do we move between units in the same system? Students create and use foldables to convert measurement units.

Do Now

5 minutes

See the Do Now video in my Strategy Folder for more details on how I begin class.  For this do now, problem one is having students determine what operation is necessary to solve the problem and then also estimate their answer.  Problem 2 is testing whether students remember the meaning of mode. 

I ask a student to share what operation is needed to solve problem one. I am looking for a student to share that if each person’s lunch costs about $2, then you would have to multiply the cost of one lunch by the number of lunches.  Students could estimate before calculating or calculate after they estimate.  For number 2, I have a student read the problem and identify an answer that is incorrect.  I am looking for a student to be able to tell me why a student might have incorrectly picked an answer.  For example, if someone picked B – 19 he/she probably got confused and thought the mode was the middle value of a data set, instead of the value that occurs most often.

 

Systems of Measurement Reading Passage & Discussion Questions

15 minutes

After the Do Now, I have a student read the objectives for the day.  I tell students that they will be reading an article about measurement systems, creating a foldable as a resource, and using that resource to convert measurements.   I ask students why it is important to be able to convert measurement units.  Students will likely share about the importance of being able to change one measurement into different units when designing or building something. 

Before I have students read the article independently, we turn to page 5 and 6 to preview the discussion questions.  I remind students to text mark while they are reading.    Also I preview the foldable page , show students where the materials are to create the foldable, and I review behavioral expectations for using the materials.   It often helps my students if I post a “To Do” list on the board with the tasks they need to complete in order.   One for this class may look like: 1) Read article and answer discussion questions, 2) Create foldable, 3) Read over example problems on p. 8, 4) Complete practice problems (p. 9-10).

When students are reading and answering questions, I circulate and monitor.  I will ask students who I know struggle with reading and vocabulary what they are reading about and what they are text marking.  If they are not text marking I’ll ask them what they are looking for in the text.  If they struggle I will go back to the discussion questions and read them with the student. 

After students have been reading and answering questions for 10 minutes, I announce that they should be close to finishing the reading and the questions.

Creating the Foldable

15 minutes

After students have been reading/answering questions for 15 minutes, I tell them they should be moving on to creating their foldable.

Students use page 6-7 to create their foldable.  I circulate to answer questions.  I share exemplar foldables with students who struggle to create theirs.  I announce every 5 minutes how much time they have to complete their foldable. 

ALTERNATIVE: If you would rather, you can create a foldable and copy it for your students rather than have students create their own.

Using Ratios to Convert Measurements

15 minutes

After students have had 15 minutes to work on their foldable I stop the class.  We turn to page 8 and read through/complete the two examples using their foldables as a resource.  Students are demonstrating MP 5: 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 tell students that when I am checking answers I will not give a student a star if they have not created and labeled equivalent ratios.  Here students are engaging with MP6: Attend to precision.  Students must carefully select and convert units.

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, which they have grown comfortable with over the school year.

Students work on problems on page 9-10 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 # 8 and #11 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.  

Also the last 2 problems on page 10 are more difficult because they each involve 2 conversions.  I am looking to see how students attack these problems.  Does a student create a new ratio that shows the relationship between the two units (ie. 1 quart/4 cups)?  Does a student first change the gallons to pints with a set of ratios and then change pints to cups using another set of ratios?  I note which students are using which strategies so that I can revisit their work during the closure.

 

Closure

10 minutes

See the Closure video in my Strategy Folder for more details.   I ask students to share strategies for #8.  Some students may express their answer as 5 10/12 feet or 5 5/6 feet.  Other students may express their answer as 5 feet and 10 inches.  I ask whether these answers are equivalent.  I ask whether the answer 5.10 feet would also work because some students still struggle with turning a remainder into a decimal.    

I pick 2 students (that I identified while I was circulating during work time) to share their strategies and thinking around question 21 on page 10.  I have them show and explain their thinking.  I ask students if they agree or disagree with the thinking.  My goal is to show students multiple ways of solving the same problem.