Contributor: Marlene Vogel. Lesson ID: 10794
Is your family spending grocery and utility money the most efficient way? By going to the grocery and using your toilet, you'll learn how to choose the right rates in math.
The Big Shake
A group of people has organized The Big Shake. The plan is to have citizens from New York to Los Angeles line up and pass a handshake from east to west.
Here's how you can figure out your estimation for The Big Shake:
The focus of this lesson is how to choose the appropriate rate and unit when solving a math problem, so let's solve this problem at the end of the Get It! section!
What is a rate?
According to Jenny Eather at A Maths Dictionary for Kids, rate is when you compare two measurements with different units.
It is important to know the appropriate rate to use in a situation.
For example, it is more appropriate to use miles-per-hour instead of feet-per-minute when talking about how fast a car is moving. However, when you are discussing the movement of a snail, it is better to use the rate of inches-per-minute instead of miles-per-hour.
We use miles-per-hour when discussing the movement of a car because cars can move long distances in a short period of time. We use inches-per-minute when discussing a snail because snails move slowly and it would take a long time for us to measure how far a snail moved in an hour.
Sample rate problem
Below is a sample problem that will help you learn how to choose the correct rate when solving a math problem:
Suppose you want to examine your family's electricity and water use. You plan to find out how efficiently your family uses these resources, and what changes you might make to increase efficiency. Name rates that will be helpful in carrying out your plan.
Think about what rates to use when examining your family's energy use.
You are going to keep track of how much electricity your family uses.
Normally, you could measure water usage by gallons. However, it is difficult to measure how much water your family uses in your home by gallons as your plumbing is hidden in the house and underground.
Discuss this with your teacher.
Excellent! A good way to measure how much water is being used during a shower is to time how long the shower is running.
What is a reciprocal rate?
An important point to know about rates is that they can be reciprocal. Simply put, a reciprocal is the opposite of the original rate. For example, as you have read earlier, car speed is measured in miles-per-hour. A reciprocal for that rate is hours per mile.
Sample reciprocal rate problem
Here is a sample problem to help you see how reciprocal rates work:
Stephen recycles 25 pounds of newspapers, cans, and bottles per week. Give a reciprocal rate that has the same meaning.
You can solve the problem by writing the rates as fractions.
Pounds per week would be written as the following fraction:
25 pounds | |
1 week |
The reciprocal rate is written as:
1 week | |
25 pounds |
Knowing how to write a rate in the reciprocal form will help you solve problems later on.
To find a unit rate, you divide the numerator in the fraction by the denominator.
For example, imagine that you are filling up a 10-gallon container with water from a hose.
1 minute | |
2 gallons |
Now you can figure out how long it takes for 1 gallon of the container to be filled with water.
Your final answer will be 0.5 minute per gallon. This is your unit rate.
Now, you can complete the problem at the beginning of the lesson. Access The Big Shake Answer Key, found in Downloadable Resources in the right-hand sidebar, to check your answers when you are done:
In the Got It? section, you will find activities to help you practice the skill of choosing the appropriate rate.