Real World Practice with Rates and Unit Rates

Real –World Practice with Rates and Unit Rates 1

Warm Up OBJECTIVE: Students will use unit rates to compare quantities in reallife situations. Language Objective: Students will use vocabulary relating to rates like per and for every. Kyle can mow 3 lawns in 2 hours. If Kyle takes the same time to mow each lawn, how long does it take him to mow 1 lawn? Write a sentence! We’ll use a unit rate to solve this question: 2 hours 2 (60 minutes) = 120 minutes Hint: Convert the time from hours to minutes. 120 minutes 3 lawns = 40 minutes 1 lawn This means that Kyle can mow 1 lawn in 40 mins. Agenda 2

Launch Please watch the following video on Usain Bolt, the Olympic Gold Medalist in the Men’s 100 -meter spring. Answer the questions below! http: //vimeo. com/46634479 1) How fast does Usain run the 100 meter sprint? 9. 69 2) Does he run this race in seconds, minutes or hours? 9. 69 seconds 3) After how many meters can Usain tell if he will win a race? 4) What country is Usain from? After 70 meters Jamaica Agenda 3

Launch Hold up! How can we simplify thisthe rate? Let’s find Usain’s speed using rates and unit rates! We will compare distance (meter) to time (seconds). Step 1: Write a rate in fraction form 100 meters 9. 69 seconds Step 2: Simplify to write as a unit rate Let’s learn a trick to convert a rate to a unit rate! Yahhh! Tricks make math easier! Agenda 4

Launch Let’s learn a trick to convert a rate to a unit rate! REVIEW: 100 meters 9. 69 seconds Divideoperation is right!! What Let’s divide does the 100 meters bybar 9. 69 fraction to find a in unit represent the rate! ratio? We can write this as division problem: This unit rate means runsto 10. 32 per second. Step 2: Usain Simplify writeseconds as a unit rate This unit rate also means that in 1 second Usain Bolt runs 10. 32 meters. Agenda 5

Explore: Mini-Lesson Let’s find the unit rate of each real-world situation! (ex 1) Kenny goes to the grocery store and buys 5 pounds of Apples for $8. 40_ Step 1: Write a rate in fraction form. 5 pounds Step 2: Divide to find the unit rate. . $8. 40 ÷ 5 pounds = $1. 68 per pound What does this unit rate mean? Kenny paid $1. 68 $____ per ______ of apples. pound. Agenda 6

Explore: Try with a Partner Let’s find the unit rate of each real-world situation! (ex 2) Michelle is computer programmer who designs video games. She works 30 hours each week and makes $2, 535_ Step 1: Write a rate in fraction form. 30 hours Step 2: Divide to find the unit rate. . $2, 535 ÷ 30 hours = $84. 50 per hour Write a sentence to explain this situation. Michelle makes $84. 50 per hour Agenda 7

Explore: A New Challenge (ex 3) Cameron has 2 jobs offers as a camp counselor. At the YMCA, he will be paid $90 for working 8 hours. At the school’s day camp, he will be paid $78 for working 6. 5 hours. Brainstorm with your partner: Which job should Cameron take? Use your note’s from today to help you! Agenda 8

Explore: A New Challenge (ex 3) Cameron has 2 jobs offers as a camp counselor. At the YMCA, he will be paid $90 for every 8 hours of work. At a school day camp, he will be paid $78 for every 6. 5 hours of work. Brainstorm with your partner: How can we decide which job pays Cameron the most per hour? Create a table to organize your work! Write a sentence to answer question. YMCA Job School Job $90 ÷ 8 hours = $11. 25 per hour $78 ÷ 6. 5 hours = $12 per hour Cameron should choose the school job because he will make $12 per hour which is $0. 75 more than at the YMCA. Agenda 9

Explore: Practice with a Partner (ex 4) Maria is a clothing designer and needs to buy a lot of buttons to make her clothes! The following shows button advertisements from 2 different stores: Button R’ Us Button-Up! 55 Buttons for $5. 50 140 Buttons for $12. 60 Answer the following questions: a)What is the unit rate for buttons at Button R’ Us? b)What is the unit rate for buttons at Button-Up? c)Which store do you think Maria should buys buttons from? Agenda 10

Explore: Practice with a Partner Button R’ Us Button-Up! 55 Buttons for $5. 50 140 Buttons for $12. 60 Answer the following questions: a)What is the unit rate for buttons at Button R’ Us? $5. 50 ÷ 55 buttons = $0. 10 per button b)What is the unit rate for buttons at Button-Up? $12. 60 ÷ 140 buttons = $0. 09 per button c)Which store do you think Maria should buys buttons from? Explain your answer! Button-Up is cheaper than Button R’Us by 2 cents. Agenda 11

Challenge: Practice with a Partner Button-Up! 140 Buttons for $12. 60 Maria has decided to use the Button-Up! Company! Remember, she found a unit price of $0. 09 per button. How much would it cost her to buy 500 buttons? 500 buttons x $0. 09 per button = $45. 00 Agenda 12

Assessment Try on your own: Martina drives 360 miles in 6 hours and Carlos drives 248 miles in 4 hours. Who drives the fastest? Martina: 360 miles ÷ 6 hours = 60 miles per hour Carlos: 248 miles ÷ 4 hours = 62 miles per hour Carlos has a faster rate at 62 miles per hour! Agenda 13

Summary – Partner Work 1) Today, we learned that to compare rates, we can first find the ______ unit ______ rate. 2) A unit rate is a comparison of 2 different quantities 1 unit. where one measurement has only _____ 3) We can use unit rates to find things like how much a job pays per hour. What other real-world examples are there for using unit rates? Agenda 14