What are we going to do? What does calculate mean? Calculate means __________.

1. Learning Objective We will calculate1 unit rates. What are we going to do? What does calculate mean? Calculate means __________. CFU Activate Prior Knowledge A ratio shows the relationship between one quantity and another quantity. a b Write the ratio in a:b form and form. 1. There were 12 buckets of water balloons and 8 kids. Write the ratio of buckets to kids. 2. Darla bought 8 granola bars for $4. Write the ratio of granola bars to dollars. Students, you already know that the relationship between quantities is called a ratio. Now, we will use the ratio to calculate the unit rate. Make Connection 12 8 8 4 12 : 8 8 : 4 1 find the answer mathematically Vocabulary

2. Concept Development • A unit rate shows the relationship between a quantityand one unit of anotherquantity. • An equivalent2 ratio table can be used to organize the information. • Two unit rates can be found given one ratio. CFU Which of the following are unit rates? How do you know? A 45 tree logs on 5 trucks B 4.5 pounds in every 1 box C $1:3ft D 32 miles per hour E 7cm:$2 In your own words, what is the difference between a ratio and a unit rate? Animated Darla bought 8 granola bars for $4. Unit Rates ÷ 8 ÷ 4 2 1 0.50 1 8 4 granola bars dollars Unit Rates ÷ a ÷ b ÷ 4 ÷ 8 1 a b a b 1st Unit a b 2 granola barsper3dollar 2 equal value 3 for every 1 Vocabulary 1 2nd Unit $0.50 per granola bar ÷ b ÷ a

3. Skill Development/Guided Practice • A unit rate shows the relationship between a quantityand one unit of anotherquantity. • An equivalent ratio table can be used to organize the information. • Two unit rates can be found given one ratio. How did I/you identify which would be the unit quantity? How did I/you determine the related quantity. CFU Calculate unit rates. 2 Create an equivalent ratio table using the given units and quantities. Identify theunit quantity. (write 1) Determine4 the division or multiplication which produces 1. Apply the operation to the other quantity. Interpret5 the unit rate. 1 4 2 3 4 5 1. Dean bought 2 pounds (lbs) of bananas from A-Market for $4 to make a banana smoothie after his bike ride. Calculate both unit rates: cost($) per pound(lb) pounds(lbs) per $ 2. Dean just finished his bike ride. His smartphone biking app says he traveled 5 miles in 20 minutes. Calculate both unit rates: minutes per mile miles per minute 2 1 5 1 pounds (lb) miles (mi) 4 2 1 20 4 1 = = = = = = = = dollar $ minutes (min) 20 4 20 4 5 5 2 1 1 2 4 2 5 5 2 4 2 4 20 20 $2 per pound 4 minutes per mile 4 figure out5 explain Vocabulary half-pound per dollar Quarter-mile per minute

4. Skill Development/Guided Practice (continued) • A unit rate shows the relationship between a quantityand one unit of anotherquantity. • An equivalent ratio table can be used to organize the information. • Two unit rates can be found given one ratio. How did I/you identify which would be the unit quantity? How did I/you determine the related quantity. CFU Calculate unit rates. 2 Create an equivalent ratio table using the given units and quantities. Identify theunit quantity. (write 1) Determine the division or multiplication which produces 1. Apply the operation to the other quantity. Interpret the unit rate. 1 4 2 3 4 5 Strategy: Reducing down to a unit rate. Mario and Tracy are training to run a marathon (about 26.2 miles). 3. Mario ran 12 miles in one hour and 18 minutes (78 minutes). Find Mario’s minute-per-mile running rate. 4. Tracy ran 14 miles in one hour and 38 minutes (98 minutes). Find Tracy’s minute-per-mile running rate. 1 1 14 7 12 2 miles (mi) miles (mi) 7 6.5 98 49 78 13 minutes (min) minutes (min) = = = = = = = = 14 7 2 12 78 13 49 98 6 2 2 7 2 6 2 7 7 minutes per mile 6.5 minutes per mile Application Who runs a faster mile? How do you know?

5. Skill Development/Guided Practice (continued) How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 1 2 3 5. James bought 12 pounds of almonds for $54. Amina bought her almonds for $4.25 per pound. Who got a better deal? How do you know? 4 5 1 12 pounds (lbs) 4.5 54 dollar ($) Amina got a better deal. She only paid $4.25 per pound while James paid $4.50 per pound. Application 6. Almaz bought a new car. Her new car gets 32 miles per gallon. Her old car could go 324 miles on a single tank of 12 gallons. Which car gets better gas mileage? How do you know? Why is the better deal in question 5 lower but the better mileage in question 6 higher? = = = = 1 324 12 12 54 12 gallons 12 12 12 12 27 miles (mi) 324 The new car gets better gas mileage. The old car gets 27 miles to the gallon while the new one gets 32 miles to the gallon.

6. Relevance • A unit rate shows the relationship between a quantityand one unit of anotherquantity. • An equivalent ratio table can be used to organize the information. • Two unit rates can be found given one ratio. Calculating unit rates helps people make smart comparisons. 1 A manufacturing warehouse has two boxing machines. Yesterday, the old machine produced 512 boxes of items in 5 hours and the new machine produced 700 boxes of items in 8 hours. The new machine made more boxes yesterday, but the old machine made more boxes per hour. New Machine: 87.5 boxes per hour Old Machine: 102.4 boxes per hour Calculating unit rates will help you do well on tests. 2 Does anyone else have another reason why it is relevant to calculate unit rates? (Pair-Share) Why is it relevant to calculate unit rates? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why? CFU Sample Test Question: 17. Evelyn bought 42 t-shirts for her students. If she wants to calculate the cost per shirt, what other information does she need?

7. A unit rate shows the relationship between a quantityand one unit of anotherquantity. • An equivalent ratio table can be used to organize the information. • Two unit rates can be found given one ratio. Skill Closure Calculate unit rates. Create an equivalent ratio table using the given units and quantities. Identify theunit quantity. (write 1) Determine the division or multiplication which produces 1. Apply the operation to the other quantity. Interpret the unit rate. 1 2 3 4 5 1. The school rented 6 vans to transport students to the local zoo. There will be enough seats for 54 students. Find the unit rate of students per van. Word Bank ratio unit rate one unit quantity 6 1 vans 9 students per van 54 9 student Access Common Core Describe how you found the unit rate in the question above. I divided the number of students by the number of vans to show how many students would be in a single van. = = 54 6 6 6 Summary Closure What did you learn today about calculating unit rates? (Pair-Share) Use words from the word bank.

8. Independent Practice • A unit rate shows the relationship between a quantityand one unit of anotherquantity. • An equivalent ratio table can be used to organize the information. • Two unit rates can be found given one ratio. Calculate unit rates. Create an equivalent ratio table using the given units and quantities. Identify theunit quantity. (write 1) Determine the division or multiplication which produces 1. Apply the operation to the other quantity. Interpret the unit rate. 1 2 3 4 1. 10 pounds of pork meat is on sale for $8. Calculate both unit rates: cost($) per pound(lb) pounds(lbs) per $ 2. Lisa is looking for a summer job. Her friend, Harrison, told her about being a camp counselor. He said he worked for 4 weeks and made $2240. If Lisa became a camp counselor, how much money would she make per week? How much money would she make per day? 5 $0.80 per pound 1.25 pounds per dollar 1 week = 7 days 4 1 1 day 10 1 1 weeks pounds (lb) 80 560 2240 8 1 dollars $ 0.8 dollar $ $560 per week $80 per day 3. A large pond has 14 geese and 84 ducks. How many ducks are there for every goose?Hint: Consider reducing down to a unit rate. • The Curry family drove 360 miles on 12 gallons. Find the unit rate of miles per gallon (mpg) of the Curry family’s car. • Hint: Consider reducing down to a unit rate. = = = = = = = = = = = = = = = = 2240 180 360 560 8 8 4 1 1 7 14 10 10 6 84 42 12 1 30 2 2 10 8 4 8 7 7 10 4 2 2 7 7 4 6 6 14 7 360 180 geese miles 6 84 42 12 6 1 ducks gallons 6 ducks per goose 30 miles per gallon (30 mpg)

9. Periodic Review 1 • Juanita left her secret recipe for apple pie on her desk. Maria peeked over and saw “10 apples” and “4 cups of sugar” in the recipe before looking away. Find both unit rates of apples per cup of sugar and cups of sugar per apple. 2. A middle school has 330 students and 15 teachers on staff. What is the unit rate of students per teacher? 22 330 110 1 2 10 students apples cups of sugar 1 15 5 1 4 teachers 2 and a half apples for every cup of sugar 22 students to every 1 teacher cup of sugar per apple Access Common Core If Maria wants to bake apple pies using 15 apples, which unit rate above could she use to find out how many cups of sugar she should use? Explain why you chose this unit rate. How many cups of sugar will she need? She should use the 2/5 cup of sugar per apple rate She needed to know how many cups of sugar to use for a number of apples. = = = = = = = = 330 110 4 4 1 2 2 2 10 10 5 15 5 5 2 3 4 10 5 4 10 5 3 5  15 = 6 She will need 6 cups of sugar.

10. Periodic Review 2 1. Valerie is a softball star that set a record for homeruns in a season (48) and homeruns in a game (4). If Valerie went up to bat 240 times this season, find her attempts per homerun. 2. Geoffrey bought 15 marbles for 75 cents. Find the unit rate of marbles per quarter. Find the unit rate of marbles per nickel. 1 15 5 marbles 1 48 12 homeruns 75 25 cents 5 240 60 attempts(at-bats) 5 25 cents = 1 quarter 5 cents = 1 nickel Valerie averaged 1 homerun for every 5 times she went up to bat. 5 marbles per quarter 1 marble per nickel Access Common Core Describe how you found the unit rate “marbles per quarter” in problem #2 above. I found how many quarters were in 75 cents. Then I divided the number of marbles by the number of quarters. = = = = = = = = 15 48 75 240 5 12 25 60 3 3 5 4 4 12 12 5

11. Periodic Review 3 1. Relationship specialists say that when talking to a friend, you should not talk too much more than your friend if you want to have a happy friendship. During a 22-minute phone call, Lucy talked for 18 minutes and Richard talked for 4 minutes. For every 1 minute Richard talked, how many minutes did Lucy talk? 2. Salvador ordered a metal pipe for the farm. The pipe was 5 yards long and cost $90. Find the cost per yard, cost per foot, and cost per inch. 1 yard = 3 feet 1 foot = 12 inches 5 1 1 foot 1 inch yards Lucy’s talking minutes 18 4 90 18 dollars $ 6 4 1 Richard’s talking minutes $18 per yard $6 per foot $0.50 per inch Access Common Core Write a word problem with the stated unit rate answer. Hint: Fill in the table first, then write your word problem. There are 18 students divided equally into three teams. How many students are on each team? Julio makes large muffins for his bakery every morning. He sold 25 muffins yesterday and made $75. How much does a muffin cost? 1. 2. = = = = = = = = 1 ft 5 18 4 90 1 1 1 6 18 4 4 2 2 12 5 5 3 12 3 6 1 18 25 Students Muffins 1 3 3 Teams $ 75

12. EDI – Cognitive, Teaching, and English Learner Strategies Cognitive Strategies Teaching Strategies Language Strategies Content Access Strategies

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