Ratios & Conversion Factor

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Objective

SWBAT solve problems involving the conversion of measurements by using the concept of ratio relationships

Big Idea

Conversion Excursion: Using ratio relationships to solve problems involving converting one measurement unit to another

Curriculum Reinforcer

5 minutes

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories

Engagement

5 minutes

For the opening activity, we will play a quick game. I will ask students, "How many of you remember your conversion factors?" I will then explain what a conversion factor is while also explaining that I do not want any of them to blurt out any of the conversion factors because we are getting ready to play a game and if they blurt out, then they will be disqualified from winning a prize. After providing this disclaimer, I will proceed to explain that a conversion factor is a type of ratio that tells us how many unit of one kind fit into a unit of another kind... For example, how many inches are in a foot. I will then ask, "Does everyone understand what I mean by a conversion factor?" Once, I am satisfied that all my students understand what I am talking about then I will give them 2 minutes to write down as many conversion factors as they can remember from the previous school year. After the two minutes have passed, they will need to flip their paper over and put down their pencils. At this point, I will collect the papers while asking, "Why do you think I wanted you to do this activity today?" The students should answer that they believe that we will start converting units of measurement to other units of measurement. I will then make a big show of going through the papers to find the student or students who remembered the most. Those students who remembered the most will get a prize out of my supply closet.

Instruction & Teacher Modeling

10 minutes

For today's instructional piece, I will first explain the significance of conversion factors.

  • Conversion Factor - Tells us by what amount the units used to measure an objects proportions change when that same object is being measured using different units. The object itself does not change in size but, the units used to measure the object does change in size. Conversion factor is a type of ratio.

 

After explaining this, I will then demonstrate this truth using common objects in the classroom. I will measure one object using inches and then I will go back and measure that same object using centimeters.

During the instructional portion of this lesson, I will present my students with three conversion chars. These charts will display the following:

  • Conversion factors for customary units
  • Conversion factors for metric units
  • Conversion factors necessary to convert between customary and metric units

The presentation of these three charts is for the purpose of conveying to my students that ll conversion factors are a type of ratio that can be used to solve problems that require converting by following the four problem solving steps to setting p and solving a proportion. This four step was introduced in a previous lesson.

Using the conversion factors presented in the charts, I will demonstrate to students how to solve problems that require converting from one unit of measure to another by using the concept of ratio relationship. I will complete three examples... One for each of the presented charts (one for converting within the customary system of measurement, one for converting withing the metric system of measurement, and one for converting between the two systems).

The examples that I will use for my demonstration are as follows:

  1. How many yards are in 4 feet?
  2. How many deciliters are in 48.7 kiloliters?
  3. How many centimeters are in 7 inches?

For each problem, I will provide a visual solution to illustrate the meaning of the problem and then I will solve the problems using ratios and proportions.

Try It Out

10 minutes

I will have my students attempt to convert measurements by trying the following problems:

  1. How many cups are in 9 pints?
  2. How many decagrams are in 324.7 centigrams?
  3. How many centimeters are in 50.8 inches?

During this time, I will be traveling the room to check to see if students are grasping the concept.

Then we will go over the answers to each of the problems. Those students who show that they are still struggling with the concept will work in a teacher led group so that I may have an opportunity to get rid of any misconceptions they may have and fill in any gaps in skills and prerequisite knowledge necessary to successfully complete the task for today.

Independent Exploration

20 minutes

For the independent practice, I am providing three options that can be used in many ways (i.e. different students can complete different assignments according to their ability and learning style, they can be used on different days so that students can explore this concept over more than one day, or they can be used during different parts of one lesson that would last for more than one day).

OPTION 1: This option is a task that highlights the concept surrounding ratio by measuring using unconventional means. For example, students will measure the length and width of a rectangle using nickels, M&M's, beans, paper clips... etc. Basically, you can have the students use any small object as a unit of measure and then, you would have the students create their own conversion factor based upon the different measurement. For instance one conversion factor might end up being 1 paper clip = 2.5 beans.

OPTION 2: This option is a task that is similar to the OPTION 1 task in that you are measuring using unconventional means. However, you are basically using your own body.

OPTION 3: This option is a worksheet. This worksheet can be used as a way of assessing student understanding individually while the other two options require a collaboration among the students.

 

My students will complete all three of these options. I will first have them complete Options 1 and 2, and I will use Option 3 as a formative assessment that they will complete individually.

These assignments will be completed over a two day period. I will have my students complete option 1 on day 1, option 2 will be completed on the second day after a brief review of the concept, and option 3 will be used at the end of day 2 to check for mastery.

 

Closing

20 minutes

To close out this lesson, the different students groups will present their work. Using the authentic responses to the presentation, I will facilitate a discussion using strategic questioning and well placed comments to foster a deeper understanding of the concept taught in this lesson. 

Students should be able to convey what they have learned by explaining their work while using precise mathematical language. By now, my students realize that their work will be critiqued and should be ready to defend their solution strategies or concede their inaccuracies thereby correcting their thinking and understanding.