1. Five lemons cost $1.80 Do Now 12.2.13 What is the cost per lemon ?
At this rate, how much will it cost to purchase 9 lemons?

2. We will calculate1 unit rates.
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.
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
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. 12 8
12 : 8 8 4
8 : 4
1 find the answer mathematically
Vocabulary

3. 8 4 2 1 0.50 1 Unit Rates 1 a b 2 granola bars per3 dollar 1
Concept Development
A unit rate shows the relationship between a quantity and one unit of another quantity.
An equivalent2 ratio table can be used to organize the information.
Two unit rates can be found given one ratio.
Animated
Darla bought 8 granola bars for $4.
Unit Rates
Which of the following are unit rates? How do you know?
A 45 tree logs on 5 trucks
B 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?
CFU
÷ 8
÷ 4 8 4 2 1
0.50 1
granola bars
dollars
Unit Rates
÷ a
÷ 4
÷ b
÷ 8 a b a b 1
1st Unit
2 granola bars per3 dollar 1 b a
2nd Unit
$0.50 per granola bar
2 equal value
3 for every 1
Vocabulary
÷ b
÷ a

4. Skill Development/Guided Practice
A unit rate shows the relationship between a quantity and one unit of another quantity.
An equivalent ratio table can be used to organize the information.
Two unit rates can be found given one ratio.
Create an equivalent ratio table using the given units and quantities.
Identify the unit quantity. (write 1)
Determine4 the division or multiplication which produces 1.
Apply the operation to the other quantity.
Interpret5 the unit rate.
Calculate unit rates. 1 2 3 5 4
How did I/you identify which would be the unit quantity?
How did I/you determine the related quantity.
CFU 2 4
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 2 = 1 2 4 = 1 2 5 5 = 1 5 20 = 1 4
pounds (lb)
miles (mi) 4 4 2 = 2 4 = 1 20 20 5 = 4 20 = 1
dollar $
minutes (min)
$2 per pound
4 minutes per mile
half-pound per dollar
Quarter-mile per minute
4 figure out 5 explain
Vocabulary

5. Skill Development/Guided Practice (continued)
A unit rate shows the relationship between a quantity and one unit of another quantity.
An equivalent ratio table can be used to organize the information.
Two unit rates can be found given one ratio.
Create an equivalent ratio table using the given units and quantities.
Identify the unit quantity. (write 1)
Determine the division or multiplication which produces 1.
Apply the operation to the other quantity.
Interpret the unit rate.
Calculate unit rates. 1 2 3 5 4
How did I/you identify which would be the unit quantity?
How did I/you determine the related quantity.
CFU 2 4
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. 12 12 6 = 2 2 = 1 14 14 2 = 7 7 = 1
miles (mi)
miles (mi) 78 78 6 = 13 13 2 =
6.5 98 49 7
minutes (min)
minutes (min) 98 2 = 49 7 =
6.5 minutes per mile
7 minutes per mile
Application
Who runs a faster mile? How do you know?

6. 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 2 1 3 4 5
5. James bought 12 pounds of almonds for $54. Amina bought her almonds for $4.25 per pound. Who got a better deal? How do you know? 12 12 = 1
pounds (lbs) 54
dollar ($) 54 12 =
4.5
Amina got a better deal. She only paid $4.25 per pound while James paid $4.50 per pound.
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? 12 12 = 1
gallons
Application
Why is the better deal in question 5 lower but the better mileage in question 6 higher? 27
miles (mi)
324
324 12 =
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.

7. New Machine: 87.5 boxes per hour Old Machine: 102.4 boxes per hour
Relevance
A unit rate shows the relationship between a quantity and one unit of another quantity.
An equivalent ratio table can be used to organize the information.
Two unit rates can be found given one ratio. 1
Calculating unit rates helps people make smart comparisons.
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: boxes per hour 2
Calculating unit rates will help you do well on tests.
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?

8. 6 1 54 9 ratio unit rate one unit quantity
A unit rate shows the relationship between a quantity and one unit of another quantity.
An equivalent ratio table can be used to organize the information.
Two unit rates can be found given one ratio.
Skill Closure
Create an equivalent ratio table using the given units and quantities.
Identify the unit quantity. (write 1)
Determine the division or multiplication which produces 1.
Apply the operation to the other quantity.
Interpret the unit rate.
Calculate unit rates. 1 2 3 5 4
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. 6 6 = 1
vans
9 students per van 54 54 6 = 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.
Word Bank
ratio
unit rate
one unit
quantity
Summary Closure
What did you learn today about calculating unit rates? (Pair-Share)
Use words from the word bank.

9. Independent Practice
A unit rate shows the relationship between a quantity and one unit of another quantity.
An equivalent ratio table can be used to organize the information.
Two unit rates can be found given one ratio.
Create an equivalent ratio table using the given units and quantities.
Identify the unit quantity. (write 1)
Determine the division or multiplication which produces 1.
Apply the operation to the other quantity.
Interpret the unit rate.
Calculate unit rates. 1 2 3 5 4
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?
$0.80 per pound
1.25 pounds per dollar
1 week = 7 days 10 10 = 1 10 8 = 1 1 4 4 4 = 1 1 7 =
1 day
pounds (lb)
weeks
2240
2240 4 =
560
560 7 = 80 8
dollar $ 8 10 =
0.8 8 = 1
dollars $
$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. 14 14 2 = 7 7 = 1
360
360 2 =
180
180 6 = 30
geese
miles
ducks 84 84 2 = 42 42 7 = 6 12
gallons 12 2 = 6 6 = 1
6 ducks per goose
30 miles per gallon (30 mpg)

10. 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? 10 10 4 = 2 1 2 10 = 1
330
330 3 =
110
110 5 = 22
apples
students
cups of sugar 4 4 = 1 1 4 10 = 2 5 15
teachers 15 3 = 5 5 =
2 and a half apples for every cup of sugar
22 students to every 1 teacher 2 5
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. 2 5
 15 = 6
She will need 6 cups of sugar.

11. 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. 15 15 3 = 5 5 = 1 48 48 4 = 12 12 = 1
marbles
homeruns
cents 75 75 3 = 25 25 5 = 5
attempts (at-bats)
240
240 4 = 60 60 12 = 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.

12. 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 5 = 1 1 3 =
1 ft 12 =
yards
1 foot
1 inch
Lucy’s talking minutes 18 18 4 = 4 1 2
dollars $ 90 90 5 = 18 18 3 = 6 6 12 = 1 2
Richard’s talking minutes 4 4 = 1
$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. 18 6 1
Students
Muffins 25 1 3 3
Teams $ 75