1

Name: ____________________________________________________ Period: _________

Rates, Ratios & Proportions Packet

Two weeks ago, two flowers were measured at 8 inches and 12 inches, respectively. Today, they are 11 inches and 15 inches tall. Did the 8 inch or 12 inch flower grow more? Show your reasoning.

1) Which class team has more girls? Explain your reasoning.

Team A: Team B:

2

2) Which fish tank has more goldfish? Explain your reasoning.

Tank C: Tank D:

3) Which group has more circles? Explain your reasoning.

Group E: Group F:

4) Shelley has two dogs, Ollie and Sandy. When she brought them home as puppies, Ollie weighed 4 pounds and Sandy weighed 7 pounds. Now Ollie weighs 8 pounds and Sandy weighs 11 pounds. Did Ollie or Sally grow more?

3

A. How many posters per minute can each of the students make?

B. Which student makes the most posters per minute? The least?

C. If Selena makes 8 posters in 80 minutes, how does this change your answers to Parts A & B?

D. Matt joins the group, and it takes him 6 minutes to make each poster. How many posters can he make in 30 minutes?

4

A. Jason is putting the volunteers into two groups: those who can work 6 hours or less and those who can work 7 hours or more. 1. Write a ratio that Jason can use to compare the number of students in the two groups.

2. What can Jason determine from this ratio?

B. After sending out flyers, Jason has found 96 people willing to volunteer at the animal shelter.

1. About how many of the volunteers are able to work 6 hours or less?

2. About how many of the volunteers are able to work 7 hours or more?

5

A) 1. Determine which volunteer is the fastest at making blankets.

2. How many hours will it take each volunteer to make all of his or her blankets? Show your reasoning.

DOGS

Name Weight (in pounds) Food (in cups)

Beauty 24 2

Scruffy 48 4

Sport 36 3

Fifi 12

Honey 5

B) Kai is responsible for feeding the animals at the shelter. He makes a table to record the

amount of food each dog gets.

C) 1. Write ratios for Beauty, Scruffy and Sport that compare the dog’s weight to the amount of food that the dog receives.

2. Compare the ratios and explain what the comparison tells you about how the dogs are fed.

3. Complete the table for Fifi and Honey.

4. Explain how to use a ratio to find the amount of food any new dog at the shelter should receive.

CATS

Name Weight (in pounds) Food (in cups)

Star 9 3

Frisky 6 2

Patch 12 4

Whiskers 3

Blackie 5

D) Kai is responsible for feeding the animals at the shelter. He makes a table to record the amount of food each dog gets.

1. Write ratios for Star, Frisky, and Patch that compare the cat’s weight to the amount of food that the cat receives.

2. Complete the table for Whiskers and Blackie.

E) The shelter has a different food for older dogs. An older dog weighing 22 pounds gets 2 cups of the food, and an older dog weighing 55 pounds gets 5 cups of the food. Make a table showing the amounts of food to feed older dogs weighing 33 pounds, 44 pounds and 77 pounds.

6

F) Challenge: To estimate the time it will take students to complete a 10-mile walk-a-thon to raise money for the animal shelter, four friends record the distances they walk and their times.

Name Miles Walked Time in Minutes

Sean 3.6 80

Ava 2 30

Reece 5.5 132

Gail 0.6 18

1) Who walked faster, Reece or Gail?

2) At these rates, who will finish the walk-a-thon first, and how long will it take?

3) One of the friends can walk a mile in 24 minutes. Who is it?

4) If the four friends team up for a walking relay in which each team member walks 5 miles, how long will it take the team to finish the relay?

7

Best Buy on Cat Food #1 The pictures on the following page are of 2 pet stores: Bob’s Best Buys and Maria’s Pet Emporium. As you can see, both stores are having a sale on cat food. Bob’s ad reads: “This week only: 12 cans of Kitten Gourmet for $15.” Maria’s ad reads, “Super Sale: 20 cans of Kitten Gourmet for $23.” Both stores are offering the same brand of cat food but are pricing it differently! Advertising is often confusing, isn’t it? Each store wants you to think that it has the best sale price. Which store has the better price? What is the unit price per can? How much better is the price? Can you work this problem out in more than one way? Cat Food Workspace:

8

9

Best Buy on Rabbit Food #2 Bob’s Best Buys and Maria’s Pet Emporium are having another sale, but on rabbit food. Bob’s ad reads: “This week only: 10 cans of Bunny Gourmet for $14.” Maria’s ad reads, “Super Sale: 8 cans of Bunny Gourmet for $12.” Both stores are offering the same brand of rabbit food but are pricing it differently! Advertising is often confusing, isn’t it? Each store wants you to think that it has the best sale price. Which store has the better price? What is the unit price per can? How much better is the price? Can you work this problem out in more than one way? Rabbit Food Workspace:

10

The Price of Birdseed #1 At Bob’s Best Buys you can scoop your own mixture of birdseed and weigh it. He sells it by the pound. Bob also sells packaged birdseed with the weight marked on the bag. Some customers prefer to make their own mixture; others buy the packaged sizes. Some customers buy large bags because they have large yards with many bird feeders. Other people prefer to buy small bags for a pet. At the checkout, Bob weighs the bag and charges by the pound. The problem is that most customers want to know the price before they get to the checkout. Bob would like to post a chart that would tell people the price once they know the weight. Bob sells five pounds for $8.00 and he charges the same rate no matter how much you buy- there are no discounts for larger quantities. Bob sells bags packaged at the following weights: ¼, ¾, 1, 2, 3, 5, 8, 13, 21, 34 and 90 pounds. Customers also need to know the price for either weight that they scoop themselves. Make a chart that Bob can use in his store. Birdseed #1 Workspace:

11

The Price of Birdseed #2 At Maria’s Pet Emporium you can scoop your own mixture of gourmet birdseed and weigh it. She sells it by the pound. Maria’s also sells packaged gourmet birdseed with the weight marked on the bag. Some customers prefer to make their own mixture; others buy the packaged sizes. Some customers buy large bags because they have large yards with many bird feeders. Other people prefer to buy small bags for a pet. At the checkout, Maria weighs the bag and charges by the pound. The problem is that most customers want to know the price before they get to the checkout. Maria would like to post a chart that would tell people the price once they know the weight. Maria sells five pounds for $11.00 and she charges the same rate no matter how much you buy- there are no discounts for larger quantities. Maria sells bags packaged at the following weights: ¼, ¾, 1, 2, 3, 5, 8, 13, 21, 34 and 90 pounds. Customers also need to know the price for either weight that they scoop themselves. Make a chart that Maria can use in her store. Birdseed #2 Workspace:

12

Using Ratios to Save Money Decide which of the following is a better buy. Show your reasoning. 1. a) 3 ounces of cheese for $2.00 or b) 4 ounces of cheese for $3.00 2. a) 13 apples for $1.60 or b) 14 apples for $1.75 3. a) 5 eggs for 70 cents or b) 6 eggs for 80 cents 4. a) 12 ounces shampoo for $2.95 or b) 15 ounces shampoo for #3.25 5. If 6 chocolates cost $0.96, how much money would 22 chocolates cost?

13

14

15

.

16

.

17

.

.

3. In a class of 24 sixth graders, 25% walk to school, 1

8 ride bicycles to school,

1

3 take the bus

to school, and the remainder of the class are driven to school by their parents or guardians.

a) Make a circle graph to illustrate the information given in the problem.

b) How many students in the class walk to school? Explain your reasoning.

c) How many students in the class ride bicycles to school? Explain your reasoning.

d) What fraction of the class is driven to school by their parent or guardian? Explain your

reasoning.

e) What percentages of the students in the class walk, ride bicycles or the bus, or are

driven to school by a parent or guardian? Explain your reasoning.

18