*Contributor: Marlene Vogel. Lesson ID: 12895*

What are nurses doing when they feel a pulse? How do drivers know when they're near the speed limit? How's your water bill calculated? All of these measure rate, so learn to be a top-rated calculator!

categories

subject

Math

learning style

Kinesthetic, Visual

personality style

Lion, Beaver

Grade Level

Middle School (6-8)

Lesson Type

Skill Sharpener

**Did you know? **Tug boat captains use *rates* to determine how long it will take to sail to a destination. You may not become captain of a boat, (or a hotel owner!), but you do have rates!

Before sailing into this lesson, **Find your rate**.

To complete this activity, you will need someone to work a stop watch and tally for you. You can choose to either hop on one foot or do jumping jacks. Whichever activity you choose to complete, your helper needs to set your timer for one minute and tally how many hops or jumping jacks you complete in that one-minute time span. Write that amount down on a piece of paper in the form of a ratio (Example: 50 hops / 1 minute). Then, answer the following questions:

- How many hops or jumping jacks can you complete in 5 minutes?
- How many hops or jumping jacks can you complete in 30 minutes?
- How many hops or jumping jacks can you complete in 60 minutes?

Instructions for how to calculate are in the* It's Great to Know Rate! Answer Key* found in **Downloadable Resources** in the right-hand sidebar. Do not *skip* ahead!

This lesson will help you refresh your math skill of calculating rate.

Take a moment to refresh your memory of this math skill, then complete the activity below it:

**Refresh your memory**

Remember, working with math problems involving *rate* is like working with math problems involving *ratio*. The difference is, when working with ratio you are comparing two quantities of the same unit. Working with rate involves working with two quantities with *different* units.

For example, when working with rate, you could be working with the two units of miles and gallons of gas. Suppose you are going to take a trip, and you fill the tank of your car before leaving. Now, suppose you have completed your drive and you note that you have driven 98 miles and have used 4 gallons of gas. With this information, you can calculate how many miles you can drive on one gallon of gas and calculate how much gas you will need to drive 100 or more miles. Take a moment to refresh your memory by reading the rest of this problem below and how to find the rate:

You know that it took 4 gallons of gas to drive 98 miles. How many miles can you drive on 1 gallon of gas?

**Step One** Write the given information in the form of a fraction:

98 miles | = | x miles | |||

4 gallons of gas | 1 gallon of gas |

**Step Two**

- To find a rate larger than the given rate, you will need to multiply.
- To find a rate smaller than the given information, you will need to divide.

- When you look at the denominators, you can see that you are going from 4 gallons of gas to 1 gallon of gas.
- You will use division to calculate the answer to this problem.
- You will divide the denominator by a number that will result in getting the answer of 1 for this problem.
- You already know that if you divide the number 4 by the number 4, you will receive the answer of 1. Remember, during this step, whether you are multiplying or dividing, whatever you do to the numerator of the given information, you will also do to the denominator of the given information, and vice-versa. For this problem, since you divided the denominator by the number 4, you will need to divide the numerator by the number 4 as well (See below):

4 | ÷ | 98 miles | = | x | |

4 | 4 gallons of gas | 1 gallon of gas |

4 | ÷ | 98 miles | = | 24.5 | |

4 | 4 gallons of gas | 1 gallon of gas |

As you can see, once you perform the division, you receive the answer of 24.5. This means that you can travel 24.5 miles on 1 gallon of gas!

- CHALLENGE QUESTION: When would you use the process of calculating rate in a real-life situation? (Possible answers are located at the end of the
*Go!*section. Don't skip ahead.)

In the *Got It? *section of this lesson, you will find a genuine hands-on activity that will help you continue to refresh your memory and skills for finding rate.