Converting Rates

Contributor: Marlene Vogel. Lesson ID: 10797

How do you rate your ability to convert rates instead of units? Can you convert feet-per-minute to inches-per-second? Mow your lawn and try multiple exercises to learn rate conversion made easy!

categories

Middle School

subject
Math
learning style
Visual
personality style
Lion, Beaver
Grade Level
Middle School (6-8)
Lesson Type
Dig Deeper

Lesson Plan - Get It!

Audio:

Plastics are everywhere. You drink from them, wear them, sit on them, look through them — you get the idea! If you drink from, say, 3 bottles of water a day, how many is that per year? In your lifetime? Better learn how to convert rates for the real story!

Drastic Plastic

According to 50 Simple Things You Can Do to Save the Earth, the average person in the United States uses about 190 pounds of plastic every year. Answer the four questions below (You can complete this assignment after completing the lesson):

  1. What are two reciprocal conversion factors that involve pounds and ounces?
  2. What is an appropriate conversion factor to find the number of ounces of plastic used by each person in a year?
  3. How is converting rates different from converting units?
  4. How could you convert your answer in Question 2 to give the number of ounces of plastic the average person in the United States uses each day? What is the number?

When you are ready, check your answer with the Drastic Plastic Answer Key, found in Downloadable Resources in the right-hand sidebar.


Before continuing, if you missed, or need to review, the previous Related Lessons in our Dimensional Analysis series, find them in the right-hand sidebar.

An important point to know about rates is that they contain two units. Examples of rates are miles-per-hour and gallons-per-minute.

Converting rates differs from converting units in that, when you are converting rates, you have an extra step. When converting rates, you will need to convert one of the two units in order to calculate the answer. Below is a sample problem that will take you through the process of converting a rate:

It takes more than 5,000,000 trees to print one week's worth of newspapers for the United States. How many trees per day is this?

In this problem, you are asked to convert trees per week into trees per day. See below to set up your problem:

To be able to answer the question properly, you will need to convert from weeks to days. This is the extra step mentioned in the explanation above:

Now, it is time to put the information from the problem into the formula that you put together. Your problem should look like this:

In the step above, you are taking the information from the problem (5,000,000 trees per week) and converting it to x amount of trees per day. You need to convert your original fraction of trees per week by multiplying it with week per days (number of days in a week). You will now simplify your problem. See below:

Simplify by cancelling out 1 week in both the numerator and the denominator. You will be left with what is seen below:

Now, divide your numerator by your denominator. This will give you your answer. It takes 714,285 trees to print one day's worth of newspapers for the United States.


Now that you have seen the process for converting rates, it is time to try one on your own.

A standard shower head uses about 6 gallons of water per minute. How many ounces per second is this? (Hint: A gallon contains 128 fluid ounces.)

Follow the steps below to solve the problem.*

  1. Set up your problem using words.
  2. Make sure you include your conversion in the problem.
  3. Insert the numerical values into your problem.
  4. Simplify
  5. Divide
  6. Arrive at your answer! Pat yourself on the back for a job well-done!
  • Did you realize you had to do two conversions in this problem?

You needed to convert from gallons to ounces, and you needed to convert from minutes to seconds.

Great job!

You can now move on to the Got It? section, where you will find some activities to help you practice your new skill of converting rates.

*The entire process set up in numerical form, including the answer, is located in the Go! section at the bottom of this lesson.

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