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Ratios, Proportions, Unit Rate, and Rates of Change
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Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

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Page 1: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Ratios, Proportions, Unit Rate, and Rates of Change

Page 2: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Ratio

• A comparison of two numbers

• Can be written in two forms • The two numbers in a ratio are separated by a colon ( : )

A:B 2:3 25:56

• The two numbers written as a fractions

𝐴

𝐵

2

3

25

56

Page 3: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Examples of Ratios

What is the ratio of the child to the number of books?

1:4 or 1

4

Page 4: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Examples of Ratios

What is the ratio of bananas to monkeys?

7:3 or 7

3

Page 5: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Examples of Ratios

What is the ratio of the apple trees to the number of apples?

2:12 or 2

12

Page 6: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Proportion • A statement that two ratios are equal

• Can be written in two forms • Using a colon ( : )

A:B = C:D 2:6 = 1:3

• Two equal fractions

𝐴

𝐵 =

𝐶

𝐷

2

6 =

1

3

Page 7: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Proportional? How can you check if your ratios are proportional?

• Cross multiply

• If your two products are equal, you have a proportion

Ex: Are these two ratios proportional?

2 x 3 = 6 x 1

6 = 6

2

6 =

1

3

Page 8: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Proportional? How can you check if your ratios are proportional?

• Cross multiply

• If your two products are equal, you have a proportion

Ex: Are these two ratios proportional?

3 x 100 = 4 x 75

300 = 300

3

4 =

75

100

Page 9: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

How to solve proportions: Step 1 –

Cross multiply

Step 2 –

Divide

20 x N = 60 x 30

20N = 1,800

N = 90

20

30 =

60

𝑁

20 𝑁

20 =

1,800

20

Page 10: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

How to solve proportions: Jane ran 2 meters in 3 seconds. How many seconds will it take her to run 50 meters?

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑇𝑖𝑚𝑒

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑇𝑖𝑚𝑒 =

2 𝑚

3 𝑠

50 𝑚

𝑁 𝑠 =

Step 1 – Cross multiply Step 2 – Divide

Let’s set up our problem like this:

2 x N = 50 x 3 2N = 150 N = 75

2𝑁

2 = 150

2

Page 11: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Ratio and Proportion

In 2013 a Fort Worth middle school had 120 girls enrolled while 100 boys were enrolled as well. What is the ratio of girls to boys? What is the ratio of boys to girls?

Girls to boys:

120 : 100

Boys to girls:

100 : 120

The ratio from 2013 is still the same in 2014 but now there are 130 boys enrolled, how many girls are enrolled?

100 x N = 130 x 120

100N = 15,600

N = 156

120

100 =

𝑁

130

100𝑁

100 =

15,600

100

Page 12: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

At a concession stand 6 hot dogs cost $6.72. At this rate, how much would 8 hot dogs cost, in dollars and cents?

Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

Bell Ringer: 9-26-14

Page 13: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Unit Rate

Unit Rate or Unit Price

• Tells you the cost per unit (one). Ex. liter, kilogram, pound, slice, piece, gallon, etc.

• This tells you the cost of one item (One of whatever you want to buy)

• Helps you compare items to determine the best buy

Step 1 –

Just divide the price by the quantity (number of items); Set up as a proportion and use 1 in one of the spots.

Page 14: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Unit Rate Step 1 –

Just divide the price by the quantity (number of items); Set up as a proportion and use 1 in one of the spots.

A two liter bottle of water costs $3.80, how much does one liter cost?

2 𝐿𝑖𝑡𝑒𝑟𝑠

$3.80 =

1 𝐿𝑖𝑡𝑒𝑟

$ ?

3.80 x 1 = 3.80 then 3.80 ÷ 2 =

$1.90

Unit price for water is $1.90

Page 15: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Unit Rate

Which of the following is the better buy?

2 gallons of milk for $3.80 or 1.5 gallons of milk for $2.70

2 𝐺𝑎𝑙𝑙𝑜𝑛𝑠

$3.80 =

1 𝐺𝑎𝑙𝑙𝑜𝑛𝑠

$ ?

1.5 𝐺𝑎𝑙𝑙𝑜𝑛𝑠

$2.70 =

1 𝐺𝑎𝑙𝑙𝑜𝑛

$ ?

$1.90 $1.80

Unit price is $1.90 Unit price if $1.80

The better buy is 1.5 liters of milk for $2.70

Page 16: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Unit Rate

Which of the following is the better buy?

10 pencils for $4.00 or 6 pencils for $2.70

10 𝑃𝑒𝑛𝑐𝑖𝑙𝑠

$4.00 =

1 𝑃𝑒𝑛𝑐𝑖𝑙

$ ?

6 𝑃𝑒𝑛𝑐𝑖𝑙𝑠

$2.70 =

1 𝑃𝑒𝑛𝑐𝑖𝑙

$ ?

$0.40 $0.45

Unit price is $0.40 Unit price is $0.45

The better buy is 10 pencils for $4.00

Page 17: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Martha is well known for her famous chocolate chip cookie recipe. Each recipe makes 3 dozen cookies. Martha will disclose only parts of her chocolate chip cookie recipe. How many cookies will one recipe make? If Martha needs to make 126 cookies, how many cups of sugar and how many eggs will she need?

Bell Ringer: 9-29-14

Page 18: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Find The Following Unit Rates… • 8 Cokes for $6.50 ; 1 Coke for…

• 3 School Lunches for $5.85; 1 Lunch for…

Page 19: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

The Torres family is spending the day at the fruit market, here are the prices listed:

Oranges 22 for $2.42

Grapes 15 for $1.35

Apples 10 for $1.50

Pears 16 for $1.28

Joe’s Fruit Stand

1. What fruit should the family buy if they want the best

deal? 2. How much would 11 oranges cost?

Page 20: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

STAAR Questions

1 𝐺𝑎𝑙𝑙𝑜𝑛

4 𝑄𝑢𝑎𝑟𝑡𝑠 =

? 𝐺𝑎𝑙𝑙𝑜𝑛𝑠

74 𝑄𝑢𝑎𝑟𝑡𝑠 = _____

Page 21: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

STAAR Questions 53 – One-half gallon is equivalent to 4 pints. How many gallons are the equivalent of 72 pints?

A. 64 gal

B. 9 gal

C. 80 gal

D. 576 gal

Page 22: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

16 – Mr. Stein is purchasing 2.25 pounds of meat that costs $2.80 per pound. How much change should Mr. Stein receive if he gives the cashier $20.00?

F $6.30

G $13.70

H $14.95

J $2.52

Bell Ringer: 9-30-14

Page 23: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

STAAR Questions 13 – A recipe for a dessert requires 3 cups of strawberries for

every 11

2 cups of yogurt used. At this rate, how much yogurt

should be used if 2 cups of strawberries are used?

A. 1 cups

B. 9 cups

C. 3

4 cups

D. 1

2 cups

Page 24: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

STAAR Questions

6 - Sonny can walk 34

8 miles in 45 minutes. How many minutes does it

take Sonny to walk 1 mile? (Keep your answer as a fraction)

Page 25: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

32 - A package of 25 wristbands costs $5.25. At this rate, what is the cost of 1 wristband in dollars and cents?

Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

STAAR Questions

Page 26: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

53 - Freida drove 20 miles in 24 minutes. At this rate, how many miles did she drive in 6 minutes?

A. 1.2 mi

B. 7.2 mi

C. 5 mi

D. 2 mi

STAAR Questions

Page 27: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

43 - Jessica has a rectangular picture. The picture is similar to a rectangle that measures 4 inches by 6 inches. What could be the dimensions of Jessica’s picture? A. 8 in. by 10 in. B. 2 in. by 3 in. C. 5 in. by 7 in. D. 12 in. by 14 in

STAAR Questions

Page 28: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Kelly is selling cookies for a school fund raiser. The cookies cost $2.85 a box. She has collected $79.80. Approximately how many boxes of cookies has Kelly sold?

=

Bell Ringer: 10-1-14

Page 29: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Rate of Change • It’s the rate that describes how one quantity changes in

relation to another quantity

• A proportional relationship between two quantities is one in which the rate of change is constant, or one in which the ratio of one quantity to the other is constant

• Any two rates or ratios based on a given proportional relationship can be used to form a proportion

Page 30: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Number of Days

1 2 3 4 5

Amount of money earned

16 32 48 64 80

Chris earns money by dog sitting. Based on the table below, is the relationship between the amount Chris earns and the number of days a proportional relationship?

Step 1 – Write the rates (put the amount earned in the numerator and the number of days in the denominator)

Amount earned Numbers of days

Step 2 – Compare the rates. The rates are all equal, each rate is equal to $16 per day. This means the rate is constant, so the relationship is proportional. The constant rate of change is $16 per day.

= $16

1 𝑑𝑎𝑦

$16

1 𝑑𝑎𝑦

$16

1 𝑑𝑎𝑦

$16

1 𝑑𝑎𝑦

$16

1 𝑑𝑎𝑦

$32

2 𝑑𝑎𝑦𝑠

$48

3 𝑑𝑎𝑦𝑠

$64

4 𝑑𝑎𝑦𝑠

$80

5 𝑑𝑎𝑦𝑠

=

=

=

=

Page 31: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Time (mins) 1 2 3 4

Number of words 45 90 135 180

Based on the table below, is the relationship between time and the number of words typed a proportional relationship?

Step 1 – Write the rates (put the number of words in the numerator and the time in minutes in the denominator)

Number of words Time in minutes

Step 2 – Compare the rates. The rates are all equal, each rate is equal to 45 words per minute. This means the rate is constant, so the relationship is proportional. The constant rate of change is 45 words per minute.

= 45 𝑤𝑜𝑟𝑑𝑠

1 𝑚𝑖𝑛𝑢𝑡𝑒

45

1

45

1

45

1

90

2

135

3

180

4 =

=

=

Page 32: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Time (hours) 1 2 3 4 5

Distance (miles) 65 120 195 220 300

The table shows the distance I drove on one day of vacation. Is the relationship between the distance and the time a proportional relationship? Did I drive at a constant rate?

Step 1 – Write the rates (put the amount of miles in the numerator and the number of hours in the denominator)

Distance in miles Time in hours

Step 2 – Compare the rates. The rates are not equal, the speed changed. There is no constant rate.

= 65 𝑚𝑖𝑙𝑒𝑠

1 ℎ𝑜𝑢𝑟

60 𝑚𝑖𝑙𝑒𝑠

1 ℎ𝑜𝑢𝑟

65 𝑚𝑖𝑙𝑒𝑠

1 ℎ𝑜𝑢𝑟

55 𝑚𝑖𝑙𝑒𝑠

1 ℎ𝑜𝑢𝑟

60 𝑚𝑖𝑙𝑒𝑠

1 ℎ𝑜𝑢𝑟

120 𝑚𝑖𝑙𝑒𝑠

2 ℎ𝑜𝑢𝑟𝑠

195 𝑚𝑖𝑙𝑒𝑠

3 ℎ𝑜𝑢𝑟𝑠

220 𝑚𝑖𝑙𝑒𝑠

4 ℎ𝑜𝑢𝑟𝑠

300 𝑚𝑖𝑙𝑒𝑠

5 ℎ𝑜𝑢𝑟𝑠

=

=

=

=

Page 33: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

30 - Every 2 days a scientist spends 1.25 hours observing dolphins and 3.5 hours observing sea lions. At this rate, how many total hours will the scientist spend observing dolphins and sea lions in 6 days? F. 28.5 h G. 14.25 h H. 9.5 h J. 23.5 h

Bell Ringer: 10-2-14

Page 34: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two
Page 35: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two
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Page 38: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two
Page 39: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Time (minutes) 1 2 3 7 10

Water (gallons) 5 10 15 35 50

Most showerheads that were made before 1944 use 5 gallons of water per minute. Is the relationship between the numbers of gallons of water used and the number of minutes a proportional relationship?

Step 1 – Write the rates (put the amount of water in the numerator and the number of minutes in the denominator)

Water in gallons Time in minutes

Step 2 – Compare the rates. The rates are all equal, each rate is equal to 5 gallons per minute. This means the rate is constant, so the relationship is proportional. The constant rate of change is 5 gallons per minute.

= 5 𝑔𝑎𝑙𝑙𝑜𝑛𝑠

1 𝑚𝑖𝑛𝑢𝑡𝑒

5

1

5

1

5

1

5

1

10

2

15

3

35

7

50

10

=

=

=

=

Page 40: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Time (minutes) 1 2 3 7 10

Water (gallons) 5 10 15 35 50

Most showerheads that were made before 1944 use 5 gallons of water per minute. Is the relationship between the numbers of gallons of water used and the number of minutes a proportional relationship? We learned the constant rate of change is 5 gallons per minute. Now let’s write our information as ordered pairs (time, water used). Ordered pairs (X, Y) (1, 5), (2, 10), (3, 15), (7, 35), (10, 50) Next, let’s plot the order pairs on a graph

Page 41: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Ordered pairs (1, 5), (2, 10), (3, 15), (7, 35), (10, 50)

Time (min)

Wat

er u

sed

(ga

llon

)

2 4 6 8 10

10

20

30

40

50

60

Page 42: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Time (hour) 1 2 3 5 8

Total Cost ($) 45 90 135 225 360

A house cleaning company charges $45 per hour. Is this relationship a proportional relationship? Write the data in the table as order pairs (time, cost) Ordered pairs (X, Y) (1, 45), (2, 90), (3, 135), (5, 225), (8, 360) Next, let’s plot the order pairs on a graph

Page 43: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Ordered pairs (1, 45), (2, 90), (3, 135), (5, 225), (8, 360)

Time (hr)

Tota

l Co

st (

$)

2 4 6 8 10

100

200

300

400

500

600

Page 44: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

The table shows the distance I drove on one day of vacation. Is the relationship between the distance and the time a proportional relationship? Did I drive at a constant rate? Write the data in the table as order pairs (time, cost) Ordered pairs (X, Y) (1, 65), (2, 120), (3, 195), (4, 220), (5, 300) Next, let’s plot the order pairs on a graph

Time (hours) 1 2 3 4 5

Distance (miles) 65 120 195 220 300

Page 45: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Ordered pairs (1, 65), (2, 120), (3, 195), (4, 220), (5, 300)

Time (hr)

Dis

tan

ce (

mile

s)

2 4 6 8 10

100

200

300

400

500

600

Page 46: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

40 – Carrie missed 9.6% of the problems on a test. The test had a total of 125 problems. Which of the following is the best estimate of the number of problems Carrie missed?

F. 123

G. 13

H. 2

J. 113

Let’s Review for the 10/3/14 Test on Monday

Page 47: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

20 – A total of 40 people made cakes for a bake sale. Each person made 3 cakes. Mrs. Sánchez found that 15% of these cakes were chocolate. How many chocolate cakes were made for the bake sale?

F. 120

G. 6

H. 18

J. Not here

STAAR Questions

Page 48: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

STAAR Questions

9 – Of the 250 sheep in a flock, 34% are white. What is the total number of white sheep in the flock?

A. 85

B. 216

C. 165

D. Not here

Page 49: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

A student reads 65 pages per hour. Complete the table and tell me if the relationship is proportional or not.

Time (h) 3 5 10

Pages 585

Page 50: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Bell Ringer – Which is the better deal?

5 Snickers for $4.78 or 4 Twix for $3.80

Let’s Review for the 10/6/14 Test on Tuesday, yes, I pushed it back a day so you could study…

= =

Page 51: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

A babysitter makes $7.50 per hour. Complete the table and tell me if the relationship is proportional or not.

Time (h) 2 5

Money ($) 22.50 60

Page 52: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

Which rectangle is similar to a rectangle 2 inches wide and 3 inches long? A. 4 inches wide and 16 inches long B. 8 inches wide and 24 inches long C. 12 inches wide and 16 inches long D. 8 inches wide and 12 inches long

Page 53: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

9. The triangles are similar. What is the length of the longest side

of the larger triangle?

A. 9

B. 12

C. 15

D. 18

Page 54: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

A recipe for a dessert requires 5 cups of strawberries for

every 21

3 cups of yogurt used. At this rate, how much yogurt

should be used if 3 cups of strawberries are used?

A. 1 cup

B. 2 1

4 cups

C. 12

5 cups

D. 12

3 cups

Page 55: Ratios, Proportions, Unit Rate, and Rates of Changeimages.pcmac.org/SiSFiles/Schools/TX/Alvarado...Ratios, Proportions, Unit Rate, and Rates of Change Ratio •A comparison of two

A total of 28 people made cakes for a bake sale. Each person made 3 cakes. Mrs. Sánchez found that 25% of these cakes were chocolate. How many chocolate cakes were made for the bake sale?

F. 84

G. 24

H. 18

J. 21