Understanding Unit Rates Math Notebook & pencil

Math Common Core MCC.6.RP.2 Understand the concept of a unit rate associated with a ratio with (b not equal to zero), and use rate language in the context of a ratio relationship.

Unit Rates The unit rate is the numerical part of the rate; the “unit” in “unit rate” is often used to highlight the 1 in “for each 1” or “for every 1.” Equivalent ratios have the same unit rate. Ratios have associated rates. For example, the ratio 3 feet for every 2 seconds has the associated rate 3/2 feet for every 1 second; the ratio 3 cups apple juice for every 2 cups grape juice has the associated rate 3/2 cups apple juice for every 1 cup grape juice. In Grades 6, students describe rates in terms such as “for each 1,” “for each,” and “per.”

Vocab Rate: A comparison of two quantities that have different units of measure. Unit Rate: A comparison of two measurements in which the second term has a value of 1.

Sample Jordan went to the store to buy peaches. The sign said “Peaches - $1.59 for three peaches.” At this rate, what is the cost of one peach? Draw a tape diagram or a double number line diagram to prove your answer.

Example #2 Is the following example a ratio or rate? [60 heartbeats per minute] Explain your answer. (6RP2)

Example #3 On a bicycle you can travel 20 miles in 4 hours. What are the unit rates in this situation (the distance you can travel in 1 hour and the amount of time required to travel 1 mile)? Try this one on your own. Raise your hand when you believe you have the answer. Do not blurt out your answer

Solution Solution: You can travel 5 miles in 1 hour written as and it takes of a hour to travel each mile written as . Students can represent the relationship between 20 miles and 4 hours.

Example #4 A simple modeling clay recipe calls for 1 cup corn starch, 2 cups salt, and 2 cups boiling water. How many cups of corn starch are needed to mix with each cup of salt?