## Lesson: Rates Introducing the Concept

Your students may have encountered rates and ratios before, but they will need to do a thorough review of these concepts before proceeding to use them to solve problems.

Prerequisite Skills and Concepts: Students should have a basic understanding of ratios — how to write them and how to simplify them. Students should also have an ability to work with fractions and find equivalent fractions.

• Say: Today we are going to look at a special type of ratio called a rate. Does anyone know what I mean by rate?
Students may say that a rate is a ratio in which the quantities being compared use different units, such as dollars per ounce or miles per hour. If they don't give you this answer, tell them what a rate is.
• Say: Rates are commonly found in everyday life. The prices in grocery stores and department stores are rates. Rates are also used in pricing gasoline, figuring how fast a person runs or a car moves, and in hourly wages or monthly fees.
• Say: Two important ideas are unit rates and unit prices. Does anyone know what a unit rate is?
Students will probably not know what a unit rate is, so provide them with the following explanation.
• Say: When we have a unit we have one of something. A unit rate is a rate for one of something. We write the rate as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you would run an average of 7 yards in 1 second. Both of the rates, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
• Ask: Now that you know what a unit rate is, what do you think a unit price is?
Students will say that it is the price of one item. If they don't, tell them what it is.
• Ask: What is the unit price of 10 pounds of potatoes that cost \$2.80?
Help students calculate that the unit price is \$0.28 cents per pound by dividing the price by 10.
• Write the following problem on the board: “One grocery store advertises carrots on sale for \$1.14 for 3 pounds, while another store has carrots on sale for \$0.78 for two pounds. Which store has the better buy?”
• Ask: What are we trying to find in this problem?
Students should say that we are trying to find out which is the better buy for carrots.