*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

subject

Math

learning style

Visual

personality style

Lion, Beaver

Grade Level

Middle School (6-8)

Lesson Type

Dig Deeper

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* by Earthworks Group, 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):

- What are two reciprocal conversion factors that involve pounds and ounces?
- What is an appropriate conversion factor to find the number of ounces of plastic used by each person in a year?
- How is converting
*rates*different from converting*units*? - 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:

trees | to | trees | |||

week | day |

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:

trees | x | week | = | trees | |

week | days | days |

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

5,000,000 trees | x | 1 week | = | x trees | |

1 week | 7 days | 7 days |

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:

5,000,000 trees x 1 week | |

1 week x 7 days |

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

5,000,000 trees | |

7 days |

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.

- Set up your problem using words.
- Make sure you include your conversion in the problem.
- Insert the numerical values into your problem.
- Simplify
- Divide
- 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. Check out the entire process, including the answer, on the *Shower Conversion Answer Sheet* found under **Downloadable Resources** in the right-hand sidebar.

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.

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