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DAILY MATH WARM-UPS7th GRADE CCSS-ALIGNED

WARM-UP NUMBER

CCSS TOPIC ✓

1 6.NS.26.NS.3

fluently divide multi-digit numbersfluently add, subtract, multiply, and divide decimals

26.NS.46.RP.16.RP.2

common factors, least common multipleunderstand the concept of ratiosunderstand the concept of unit rate

3 6.RP.3 ratio and rate reasoning

4 6.EE.16.EE.2

evaluate expressions with exponentsread, write, and evaluate expressions with variables

5 6.EE.36.EE.4

apply properties to exponentsidentify equivalent expressions

6 6.NS.16.NS.5

divide fractions by fractionsunderstand positive and negative whole numbers

7 6.NS.6 understand rational numbers

8 6.NS.7 order rational numbers

96.EE.5 6.EE.66.EE.7

use substitution to solve equationsuse variables in equationssolve equations with variables

10 6.EE.7 6.EE.8

solve equations with variableswrite and graph inequalities

11 6.EE.9 6.G.1

independent and dependent variablesarea of polygons

12 6.G.2 6.G.3

volume of rectangular prismsdraw polygons on the coordinate plane

13 6.G.46.G.4

represent 3-D figures with netsfind surface area using nets

146.SP.16.SP.2 6.SP.3

recognize statistical questionsunderstand that data has a distributionrecognize center and variation in data

15 6.SP.5 summarize data

16 6.SP.4 display data

*Warm-up numbers 1-16 are review from 6th grade Common Core State Standards.



WARM-UP NUMBER

CCSS TOPIC ✓

17-207.NS.1A7.NS.1B7.NS.3

describe situations that make zeroadd rational numbers on a number linesolve real-world problems with rational numbers

21-247.NS.1C7.NS.1D7.NS.3

subtract rational numbers on a number lineapply properties to add/subtract numberssolve real-world problems with rational numbers

25-28 7.NS.27.NS.3

multiply and divide rational numberssolve real world problems with rational numbers

29-32 7.EE.17.EE.2

expand linear expressions with rational coefficientsrewrite expressions

33-36 7.RP.17.RP.3

compute unit rates with fraction ratiossolve multistep ratio and percent problems

37-40

7.RP.2A7.RP.2B7.RP.2C7.RP.3

determine proportionalityidentify the constant of proportionalityrepresent proportional relationships in equationssolve multistep ratio and percent problems

41-44 7.RP.2D7.RP.3

interpret a coordinate point on a graphsolve multistep ratio and percent problems

45-48 7.EE.3 solve multistep real-world problems

49-52 7.EE.4 use variables to solve equations and inequalities (prerequisite)

53-56 7.EE.4 use variables to construct equations and inequalities

57-60 7.G.1 scale drawings of geometric figures

61-64 7.G.27.G.3

draw geometric shapesdescribe a 2-D shape as a slice of a 3-D shape

65-68 7.G.47.G.5

solve area and circumference problemsfind unknown angles in a figure

69-72 7.G.6 area and surface area of 2-D objects

73-76 7.G.6 volume of 3-D objects

77-80 spiral all geometry concepts



WARM-UP NUMBER

CCSS TOPIC ✓

81-84 7.SP.17.SP.2

examine sample populations make valid inferences using data

85-88 7.SP.37.SP.4

compare two numerical data distributionsdraw informal inferences about two populations

89-92 7.SP.57.SP.6

understand the probability of an eventapproximate the probability of an event

93-96 7.SP.7 find probability of simple events

97-100 7.SP.8 find probability of compound events

1017.NS.1A7.NS.1B7.NS.3

describe situations that make zeroadd rational numbers on a number linesolve real-world problems with rational numbers

1027.NS.1C7.NS.1D7.NS.3

subtract rational numbers on a number lineapply properties to add/subtract numberssolve real-world problems with rational numbers

103 7.NS.27.NS.3

multiply and divide rational numberssolve real-world problems with rational numbers

104 7.EE.17.EE.2

expand linear expressions with rational coefficientsrewrite expressions

105 7.RP.17.RP.3

compute unit rates with fraction ratiossolve multistep ratio and percent problems

106

7.RP.2A7.RP.2B7.RP.2C7.RP.3

determine proportionalityidentify constant of proportionalityrepresent proportional relationships in equationssolve multistep ratio and percent problems

107 7.RP.2D7.RP.3

interpret a coordinate point on a graphsolve multistep ratio and percent problems

108 7.EE.3 solve multistep, real-world problems

109 7.EE.4 use variables to solve equations and inequalities (prerequisite)

110 7.EE.4 see variables to construct equations and inequalities

*Warm-up numbers 101-120 are a spiral review of all 7th grade standards.



WARM-UP NUMBER

CCSS TOPIC ✓

111 7.G.1 scale drawings of geometric figures

112 7.G.27.G.3

draw geometric shapesdescribe a 2-D shape as a slice of a 3-D shape

113 7.G.47.G.5

solve area and circumference problemsfind unknown angles in a figure

114 7.G.6 area and surface area of 2-D objects

115 7.G.6 volume of 3-D objects

116 7.SP.17.SP.2

examine sample populations make valid inferences using data

117 7.SP.37.SP.4

compare two numerical data distributionsdraw informal inferences about two populations

118 7.SP.57.SP.6

understand the probability of an eventapproximate the probability of an event

119 7.SP.7 find probability of simple events

120 7.SP.8 find probability of compound events

*Warm-up numbers 101-120 are a spiral review of all 7th grade standards.

1. Solve the following:

a. b.

2. Solve the following:

a. b. 3.4 358.7

3. Cathy is purchasing a DVD player and a TV at the local electronic store. The DVD player costs $49.36, and the TV costs $705.20. If she plans to pay for them in 12 equal payments, then what is her monthly cost?

1. Find the GCF:

a. 24 and 72

b. 16 and 80

2. Find the LCM:

a. 6 and 14

b. 3 and 8

3. The ratio of cats to dogs at a pet store is 4:5, which means…

4. The price for five pounds of candy is $8, which is a rate of ______ per pound.

Name ___________________________________ Date _______________________ Pd ____1

Name ___________________________________ Date _______________________ Pd ____2



81.94+ 27.39

64.07- 13.67

18.3x 1.5

1. Label each table below as to whether or not theratio is equivalent.

a. ______ b. ______

c. ______ d. ______

2. It takes 6 hours to travel 372 miles. How longwill it take to travel 279 miles?

3. A student gets 13 out of 20 questions correct on a test. What percent of questions did the student get correct?

x y

2 4

3 6

6 12

x y

1 5

2 10

5 25

x y

0 0

3 3

6 6

x y

2 1

6 2

8 4

1. Evaluate the expression below: 2. Evaluate the expression below:

3. Write a numerical expression below:

a. add 14 and x

b. the product of 6 and y

4. Using the formula below, solve when, s = 3

Name ___________________________________ Date _______________________ Pd ____3

Name ___________________________________ Date _______________________ Pd ____4



32 + 5(8 – 3) – 10 17 – 3(16 ÷ 4) + 23

A = 6s2

1. Simplify the expression below: 2. Simplify the expression below:

3. Combine like terms: 4. Match the equivalent expressions below:

1. Solve the following. Answer in reduced form:

a.

b.

2. Write an integer to describe each situation:

a. a town sits 380 feet below sea level

b. $98 is deposited into a checking account

3. How many 14

cup servings are in a 12-cup container?

Name ___________________________________ Date _______________________ Pd ____5

Name ___________________________________ Date _______________________ Pd ____6



56÷ 1

8=

34÷ 1

6=

2(3x – 5y) 3(7.1y + 4x)

x + x – x + y + y + y – z + z – z

2(x – 2y)

x + x + y + y – x

x + x + y + y + x

2x – 4y

x + 2y

2y + 3x

1. Use the coordinate plane to answer the questions:

a. The point (-6,-2) is located in quadrant _____.

b. If the point (2, -4) is reflected over the x-axis, thenit will be in quadrant _____.

c. Label point A at (5, -1) and point B at (-7, -4).

d. How is (5, 9) different than (-5, 9)?

2. Use the number line below to find the value:

a. point A _____ b. point C is the opposite of point _____ c. point _____ is at -2

d. two opposite points are _____ and _____ e. the opposite of point B is _____

1. Match each phrase with the appropriate inequality. Use the number line to help.

_____ -7 is located to the right of -10 a. 6

_____ the absolute value of 6 b. 6 ≥ -3

_____ -3 is greater than -8 c. -7 > -10

_____ -3 is located to the left of 6 d. -3 > -8

_____ |-8| e. -3 < 6

_____ 6 is greater than or equal to -3 f. 8

_____ this number is located 6 units to the left of 0 g. -6

Name ___________________________________ Date _______________________ Pd ____7

Name ___________________________________ Date _______________________ Pd ____8



B EC F AD

● ●●●●●

1. Write an equation to represent the situation:

Brand A costs $46.29, and brand B costs$42.89. What is the difference in the cost of brand A and B?

2. Solve the following equation:

3. Solve and graph the following inequality: 4. Write an inequality to represent the situation:

A theater rents their space for $300 per night. If the company charges $9 per ticket, then what is the least number of tickets that must be sold in order to make a profit?

1. Determine if the equation is true if x=4. 2. Determine if the inequality is true if x=4.

3. Write an equation to represent the situation:

The total cost of five equally priced DVDs is$55. How much does each DVD cost?

4. Solve the following equation:

Name ___________________________________ Date _______________________ Pd ____9

Name ___________________________________ Date _______________________ Pd ____10



2 +6x = 28 x + 13 < 41

x + 8 = 23

17x = 102

x – 15 ≥ 8

1. A grown man will burn roughly 120 calories foreach mile run. How many calories will be burned when a grown man runs 6.5 miles?

a. What is the independent quantity?

b. What is the dependent quantity?

c. Write an equation to describe the problem.

d. Solve the equation.

2. Find the area of the shape below. Break the larger shape into smaller pieces if needed.

1. Complete the shape to make a rectangle that has an area of 35 units squared.

a. What is the location of point C? D?

b. What is the perimeter of the rectangle?

2. Find the volume of the package below.

A

B

Name ___________________________________ Date _______________________ Pd ____11

Name ___________________________________ Date _______________________ Pd ____12



12 in5.8 in

3 in

8.4 m

11.4 m

4 m

8 m

1. Huey reviews his progress report andnotices the following grades:

65, 92, 84, 76, 84, 94Find the mean of his grades.

2. Use the data in question 1 to find the median ofhis grades.

3. Label each statistical question with an S.

a. Do students prefer pancakes or waffles? ____

b. How many parents are in the PTA? ____

c. How much does a movie ticket cost? ____

d. How many households in the neighborhood recycle? ____

1. Find the surface area of the prism below: 2. Find the surface area of the square pyramid:

Name ___________________________________ Date _______________________ Pd ____13

Name ___________________________________ Date _______________________ Pd ____14



h = 9 in

7 in

3 in

5.5 in

11 in

1. Create a line plot below, using the followingnumbers:

15, 22, 18, 30, 18, 21, 18, 26, 26, 18, 22

2. Create a stem-and-leaf plot using the datafrom question 1.

1. Use the following box-and-whisker plot toanswer the questions below.

a. Q1 ______

b. Median ______

c. Range ______

d. Interquartile range ______

e. Q3 ______

2. Mercedes would like to have an average of 88 in her math class. There are five assignments with the following grades: 85, 100, 88, 80, 95. What grade will Mercedes need to make on the last assignment to meet her goal?

10 13 20 26 31

Name ___________________________________ Date _______________________ Pd ____15

Name ___________________________________ Date _______________________ Pd ____16



1. Noah has mixed up the stat sheet from the football game Friday. Match the different situations sothat they all result in zero.

_____ a loss of 6 yards A. two quick passes that gained 4 yards each

_____ a gain of 9 yards B. a loss of 10 yards

_____ two runs for 5 yards each C. the ball is run 6 yards

_____ quarterback is sacked for 8 yards D. a fumble for a loss of 9 yards

2. Label the number line with the appropriateequation.

3. Use the number line to model the problem below:

1. The temperature was -10o Fahrenheit at 8:00PM one day in Denver. A cold front lowered the temperature over the next hour by 3 degrees. What was the new temperature at 9:00 PM?

2. Angelina overdrew her account by $35. She then quickly deposited her babysitting money of $25. What is the current balance on the account?



Name ___________________________________ Date _______________________ Pd ____17

Name ___________________________________ Date _______________________ Pd ____18



-5 + 3 = -2

4 + -7 = -3

1. Westmoreland, CA is 157 feet below sea level.Dallas, TX is 430 feet above seal level. What is the difference in the two cities’ altitudes?

2. Solve:

a. -18 + 7 =

b. 45 + (-13) =

c. -9 + (-27) =

d. − 14

+ 34

=



1. A credit card customer owes $325.60. Theyare only able to make a payment of $120. How much money does the customer still owe?

2. Solve:

a. -124 + 56 =

b. 32 + (-40) =

c. -18 + (-12) =

d. 13.5 + (-20) =



Name ___________________________________ Date _______________________ Pd ____19

Name ___________________________________ Date _______________________ Pd ____20



-4 + -1 = -5

-3 + -1 = -4

1. In Anchorage, AL the temperature is -13oF. A cold front is scheduled to come in and drop the temperature 14 degrees. What will the temperature be after the cold front?

2. Solve:

a. -13 - 9 =

b. 45 – 60 =

c. -9 – (-18) =

d. − 14– 3

4=



1. A credit card customer owes $325.60. Theycharge another purchase of $45.20. How much money does the customer owe?

2. Solve:

a. -230 – 65 =

b. 68 – (-23) =

c. -10.75 – 5.25 =

d. −23– 2

3=



Name ___________________________________ Date _______________________ Pd ____21

Name ___________________________________ Date _______________________ Pd ____22



3 – 8 = -5

-1 – 4 = -5

1. Christina borrowed $8 from her brother and $13 from her sister. How much money has Christina borrowed?

2. Solve:

a. -19 – 32 =

b. 28 – 63 =

c. -17 - (-14) =

d. − 18– 5

8=



1. A customer purchases a new computer and awarranty to protect it. The computer is priced at $1486.25, and the warranty is $199.99. If the customer would like to pay this over a period of 18 months, then how much will each payment be?

2. Solve:

a. -164 – 24 =

b. 39 – (-12) =

c. -7.55 – 3.25 =

d.35– 4

5=



Name ___________________________________ Date _______________________ Pd ____23

Name ___________________________________ Date _______________________ Pd ____24



-5 – (-2) = -3

-3 – 2 = -5

1. Solve:

a. 4(-6) =

b. -9(5) =

c. -1.5(-7) =

d. − 14• 3

8=

2. Solve:

a. −125 ÷ 5 =

b. −22 ÷ (−4) =

c. 72 ÷ (−8) =

d. − 14

÷ −38

=

3. Mrs. Hermann plans to exercise in order to lose 4 pounds per month. How many pounds will she lose over a period of 6 months?

4. An oven’s temperature rises 273 degrees in 7 minutes. What is the rate at which the temperature rises?

1. Solve:

a. 8(-3.2)=

b. -11(-11) =

c. -10(9) =

d.12• −2

3=

2. Solve:

a. −100 ÷ −8 =

b. 64 ÷ (−4) =

c. 2 ÷ (−4) =

d.25÷ −4

3=

3. Mr. Mullen owes $288.40 on his credit card.He would like to make 4 equal payments. How much will each payment be?

4. Cocoa owes three of her friends $5.60 each. How much money does Cocoa owe in total?

Name ___________________________________ Date _______________________ Pd ____25

Name ___________________________________ Date _______________________ Pd ____26



1. Solve:

a. -9(-9)=

b. -7(13)=

c. 2.5(-4)=

d. − 34• 3

5=

2. Solve:

a. 90 ÷ (-3) =

b. -18 ÷ (-4) =

c. 144 ÷ (-12) =

d. −23÷ 1

3=

3. Cleo and Jandi are having a Halloween

party. They have 312

pounds of candy to divide

into 14 goodie bags. How much candy will be in

each bag?

4. At the grocery store, almonds are on sale for $2.88 per pound. What is the price of 3.5 pounds?

1. Solve:

a. -6(5.7)=

b. -13(-9) =

c. 15(7) =

d.16• − 6

7=

2. Solve:

a. -200 ÷ (-40) =

b. 88 ÷ (-11) =

c. 49 ÷ (-7) =

d. − 35÷ 1

3=

3. The average high temperature on Mars is70oF. The average low temperature is -225oF. What is the difference between the high and the low?

4. New York City has an elevation of 410 feet above sea level. Omaha, Nebraska is about three times as high. What is the approximate elevation of Omaha?

Name ___________________________________ Date _______________________ Pd ____27

Name ___________________________________ Date _______________________ Pd ____28



1. Combine like terms:

a. 4x – 3y + 2x + y

b. -2x + 3y – 4y + 5y

2. Simplify:

a. 2(4x + 5y)

b. -3(2x + 4y)

3. Factor out the common terms:

2x + 4y

4. Write an expression to find the perimeter ofthe rectangle below:


a. -6m + 7p – 3m + p

b. 3p – 3m – 3m + 3p

2. Simplify:

a. 4(3m – 8p)

b. -3(7m – 3p)


6m – 21p


Name ___________________________________ Date _______________________ Pd ____29

Name ___________________________________ Date _______________________ Pd ____30



2x

3x – 4

4x

2– x


a. -6s – 11t – 5s – 3t

b. -12t + 2t + 3s – 7s

2. Simplify:

a. -5(-3x – 2y + 1)

b. 6(x + 3y – 5)


8x – 12y + 16



a. 10a + 7b – 13a – 4b

b. -5a – 8a + 2b – b

2. Simplify:

-7(3x) + 2(3x – 2)


24a + 12b – 40c


Name ___________________________________ Date _______________________ Pd ____31

Name ___________________________________ Date _______________________ Pd ____32



3x – 1

2x – 3y

x – 2

6x

1. If a person walks 12

of a mile in 14

of an hour,

what is the rate per hour at which they walk?

a. Write an expression to represent the problem:

b. Solve the problem:

2. An cell phone is on sale for $180. It originallycost $200. What percent off is the sale offering?

1. A marathon runner runs 1012

miles in 2

hours. What is her hourly rate?



2. At East Middle School, 28% of the students arein the band. If 168 students are in the band, then how many students go to East Middle School?

Name ___________________________________ Date _______________________ Pd ____33

Name ___________________________________ Date _______________________ Pd ____34



1. The average third grade student can read 60words in 5 minutes. What is the average reading rate per minute?



2. If a car travels at a rate of 64 miles per hour,then how long will it take the car to travel 224 miles?

1. Elizabeth pumps 312

gallons of gas in 14

of a

tank. How many gallons does a full tank hold?



2. On a soccer team, 40% of the goals arescored by the star player on the team. If 70 goals are scored all season, then how many are scored by the rest of the team?

Name ___________________________________ Date _______________________ Pd ____35

Name ___________________________________ Date _______________________ Pd ____36



1. At a back to school sale, backpacks are marked down 15%. If the original price was $34, then what is the sale price?

3. Plot the points and then answer the questions:(3, 6) (-2, -4) (1, 2)

a. Is this a proportional relationship?

b. What is the constant of proportionality?

2. On a recent field trip, students paid $15 for each ticket. If $675 is the total cost, then how many tickets were purchased?

a. Write an equation:


1. In Mr. B’s classroom, there are 20 students. Twelve students got a B, one student got a C, and the rest received an A. What percent of the class received an A?

3. Plot the points and then answer the questions:(1, -3) (-3, 9) (2, -6)



2. A cup of coffee costs $2.50. If the total costis $17.50, then how many cups of coffee were purchased?



Name ___________________________________ Date _______________________ Pd ____37

Name ___________________________________ Date _______________________ Pd ____38



1. At dinner Rodrigo and his friend spent $24. They left a 20% tip and then split the cost. How much did each person pay?

3. Use the table below to answer the questions:



2. In a fundraiser, Mrs. Diego pledges $1 for each mile walked. If Sam walks 20 miles, then how much will Mrs. Diego donate?



1. A new product price is increased from $5 to $6. What is the percent of change?



a. What is the constant of proportionality?

2. A cup of coffee costs $2. If the total cost is$18, then how many cups of coffee were purchased?



x y

4 2

7 3.5

8 4

x y

-2 8

-1 5

0 2

Name ___________________________________ Date _______________________ Pd ____39

Name ___________________________________ Date _______________________ Pd ____40



1. In a science experiment, Judson is tracking the height of a small tree. At the beginning, the tree measures 32 inches. Six weeks later the tree measures 36 inches. Find the percent increase of the tree.

2. Use the graph to answer the questions:

a. What does (3, 36) represent?

b. What ordered pair describes the unit rate?

Dozen

Coo

kies

1 2 3 4 5 9 8 7 6 10

12 24

84 72 60 48 36

96 108 120

1. Emerson is starting a new business. Product A costs her $26.50. She decides to mark the product up 30%. How will Emerson charge for Product A?




Number of Days

Deg

rees

Cel

sius

1 2 3 4 5 9 8 7 6 10

2

4

14 12 10 8 6

16 18 20

Name ___________________________________ Date _______________________ Pd ____41

Name ___________________________________ Date _______________________ Pd ____42



1. If Vernie eats 12 cookies, which represents 25% of the bag, then how many cookies are in the bag?




1. The kicker on the football team made 8 out of 9 of his field goals. About what percent of field goals did the kicker miss?




Number of Days

Inch

es o

f Sn

ow

1 2 3 4 5 9 8 7 6 10

24

14 12 10 8 6

16 18 20

Number of Weeks

$ E

arne

d B

abys

ittin

g

1 2 3 4 5 9 8 7 6 10

20 40

140 120 100

80 60

160 180 200

Name ___________________________________ Date _______________________ Pd ____43

Name ___________________________________ Date _______________________ Pd ____44



1. Mr. Ferris is hanging pictures on the wall. He would like the picture to be in the center of the wall.

The picture measures 2212

inches wide. The wall measures 6 feet wide. How many inches should be on

either side of the picture?

a. Convert the width of the wall to inches.

b. Subtract the width of the picture from the width of the wall.

c. Divide the difference by two, since the picture is to be centered.

1. At a after Thanksgiving Day sale, jeans are 15

off. Manual will purchase two shirts for $18.95 each

and a pair of jeans originally priced at $50. How much will Manual spend before tax?

a. Convert 15

to a percent.

b. Find the price of the jeans on sale.

c. Find the total price of the jeans and two shirts.

Name ___________________________________ Date _______________________ Pd ____45

Name ___________________________________ Date _______________________ Pd ____46



1. Taylor runs a smoothie shop and is placing his order for the week. Each week he needs to have 2gallons of pineapple juice and 4 gallons of orange juice on hand. If he already has 3 quarts of pineapple juice and 5 quarts of orange juice, then how many ounces of each should he order?

a. Convert the gallons of juice needed to ounces.

b. Convert the quarts of juice on hand to ounces.

c. Find the number of ounces he should order.

1. A local clothing shop is marking down all of its summer clothes by 75%. Teisha would like topurchase a swimsuit that is originally priced at $50. When she gets to the register, she signs up for a loyalty card that saves her an additional 10%. How much did she spend on the swimsuit after both discounts?

a. Find the markdown price of the swimsuit.

b. Then, find the markdown of the loyalty card.

c. Subtract to find the final price.

Name ___________________________________ Date _______________________ Pd ____47

Name ___________________________________ Date _______________________ Pd ____48



1. Solve for x: 2. Solve for x:




Name ___________________________________ Date _______________________ Pd ____49

Name ___________________________________ Date _______________________ Pd ____50



16x + 8 = 88 1.5x + 5 = 32

3x + 9 < 27 2x – 10 ≥ 5

2.5x – 4 = 41 4x – 16 = -20

5x – 7 > 63 12x + 4 ≤ 10





Name ___________________________________ Date _______________________ Pd ____51

Name ___________________________________ Date _______________________ Pd ____52



-2x – 12 = 32 1.5x – 8 = -0.5

-12x + 20 < -52

2(3x – 3) = -18

14x – 3

4≥ 4

12(4x + 8) = -40

5.5x – 10.5 > 33.5 -4x + 24.6 ≤ -18.2

1. Write an equation and solve.

In order to attend the carnival, students must pay a $5 admission fee plus $0.75 per ride ticket. How many tickets are purchased if a student spends $11?

2. Write an inequality and solve.

A computer salesperson is paid a base amount of $100 for the month. For each computer he sells, he receives $15. This month he would like to make at least $450.


A taxi ride from the airport to the hotel is $15.50. If the taxi charges a flat fee of $3.50 and $0.75 per mile, then how many miles is the hotel from the airport?


A theater rents their space for $650 per night. The renters are willing to contribute $200 but need to make the rest in ticket sales. If the renters charge $8 per ticket, then what is the least number of tickets that must be sold in order to make a profit?

Name ___________________________________ Date _______________________ Pd ____53

Name ___________________________________ Date _______________________ Pd ____54




Beau was shopping for his girlfriend’s Valentine’s Day present. He bought her a box of chocolate for $12.49 and six balloons. In total Beau spent $19.63 for the chocolate and balloons. How much did each balloon cost?


Elsie saved the money from her summer job. In August her savings account had $1,250. Each month she must pay her cell phone bill of $65. After how many months will Elsie have less than $800 in her account?


Two different companies offer online gaming subscriptions. Company A charges $45 upfront and then $10 per month. Company B does not charge an upfront fee but charges $25 per month. After how many months will the two companies charge the same amount?


The setup fee for a photo book is $35. The paper is an additional charge of $0.80 per page. What is the greatest number of pages that a book can have if the total bill is to be less than $50?

Name ___________________________________ Date _______________________ Pd ____55

Name ___________________________________ Date _______________________ Pd ____56



1. Find the missing side, x, in the similar figures below.

2. Use the scale factor of 1:3 to create a newfigure.

1. Determine the scale factor of these similar figures.

2. Rectangle A and B are similar figures, where A is the original figure and B is the new figure. Find the area of rectangle B.

Name ___________________________________ Date _______________________ Pd ____57

Name ___________________________________ Date _______________________ Pd ____58



4 in

3 in

10 in5 in

x

3.5 in

3.5 in

2.5 in15 in

21 in

9 ft

15 ft 5 ft

xA B

1. A triangle is shown below. If the image is dilated by a scale factor of 1.5, then what is the perimeter of the new triangle?

2. Mr. Scobey is going to place a layer of mulchin his garden. His blueprint shows the garden below:

If the blueprint has a scale factor of 1 cm:1.5 feet, then how many square feet of mulch does Mr. Scobey need?

1. Rectangle R and S are similar figures. Find the perimeter of rectangle R.

2. Rectangle D and E are similar figures. Find the perimeter of rectangle E.

Name ___________________________________ Date _______________________ Pd ____59

Name ___________________________________ Date _______________________ Pd ____60



4 m5 m

3 m

5 cm

10 cm

8 cm

10 in

16 inx in

2.5 in 4.5 ft

9 ft 31.5 ft

xSR D E

1. Construct and label an equilateral triangle. 2. A rectangular pyramid is sliced horizontally. What 2-D figure describes the shape?

3. Name the shape below:

1. Construct or draw an isosceles triangle with one angle measure of 70o. Label all of the angle measures.

2. A 3-D figure is sliced to form a rectangle. Name 2 possible names of the 3-D figure.


32˚

100˚

Name ___________________________________ Date _______________________ Pd ____61

Name ___________________________________ Date _______________________ Pd ____62



1. Construct and label an obtuse scalene triangle. 2. A cylinder is sliced vertically. Draw the 2-D shape that represents the slice.


1. Construct and label an acute isosceles triangle. 2. A cylinder is sliced horizontally. Draw the 2-D shape that represents the slice.


28˚126˚

26˚

Name ___________________________________ Date _______________________ Pd ____63

Name ___________________________________ Date _______________________ Pd ____64



1. Find the area of a circle with a radius of 3cm. Use 3.1 for π.

2. Angle A measures 65o. What is itscomplementary angle measure?

3. If the circumference of a circle is 43.4 cm,then what is the diameter? Use 3.1 for π.

4. Triangle ABC has two 40o angles. What is themeasure of the third angle?

1. Betsy’s Bakery sells world famous cherry pies.Each pie is measured by its diameter. What is the distance around a 10-inch pie? Use 3.1 for π.

2. Find the missing angle.

3. A shipping company places circular labels on allof their products. Each label measures a 2-inch radius. If the company orders 20 labels, then how many square inches are needed?


Name ___________________________________ Date _______________________ Pd ____65

Name ___________________________________ Date _______________________ Pd ____66



120o

xo

xo

60o

90o

1. The area of a circle is 49.6 squarecentimeters. What is the diameter? Use 3.1 for π.


3. Find the area of the shaded region. Use 3.1 for π.

4. Triangle ABC is a right isosceles triangle.What are the measures of the three angles?

1. A sprinkler sprays the lawn in a rotating circle.If the sprinkler shoots water 10 feet, then what area of the lawn is getting watered? Use 3.1 for π.


3. Find the distance around the race track. Use3.1 for π.

4. Triangle MLN is an isosceles triangle with angleL measuring 30o. What are the measures of angles M and N?

Name ___________________________________ Date _______________________ Pd ____67

Name ___________________________________ Date _______________________ Pd ____68



40o

65o

xo

xo36o

100 m

30 m

L

M N

12 m

6 m

1. Find the area of the shape below: 2. Find the total area of the figure below. Break the larger shape into smaller pieces if needed.

3. Matt is carpeting his bedroom. The room measures 12 feet by 14 feet. If carpet costs $2.29 per square foot, then how much will Matt spend to carpet his bedroom?

1. Find the area of the shape below: 2. Find the total area of the square pyramid below. Break the larger figure into smaller pieces if needed.

3. Damien is placing tile in a small rectangular room. The room measures 8 feet long by 5.5 feet wide. If one square foot tiles are sold in packages of 12, then how many packages will he need?

Name ___________________________________ Date _______________________ Pd ____69

Name ___________________________________ Date _______________________ Pd ____70



8 ft

10 in

4.3 in

234

ft

7.2 in

4 in

3 in

h = 5 in

4.1 in

1. Find the area of the shape below: 2. Find the total area of the figure below. Break the larger shape into smaller pieces if needed.

3. A new homeowner is mulching a rectangular flower bed in his backyard. The flower bed is 9 feet long and 3.5 feet wide. How many square feet will need to be covered in mulch?

1. Find the area of the shape below: 2. Find the total area of the cube below. Break the larger shape into smaller pieces if needed.

3. Marie is redecorating her bedroom and decides to paint 3 of the walls. Each of the walls measures 12 feet by 10 feet. How many square feet will she need to paint?

Name ___________________________________ Date _______________________ Pd ____71

Name ___________________________________ Date _______________________ Pd ____72



7 in

11 in

8 in

5 in

10 in

4 in

8 in

h = 3.5 in

4 in

2.1 in

1. A rectangular prism has the followingmeasurements:

How many 12

inch cubes will fill the prism above?

2. Find the volume of the package below.

1. A rectangular prism has the followingmeasurements:

How many 12

inch cubes will fill the base of the

prism?

2. A pool has a depth of 10 feet and a width of 14feet. If it holds 1,120 cubic feet of water, then what is the length of the pool? (Draw a picture to help.)

Name ___________________________________ Date _______________________ Pd ____73

Name ___________________________________ Date _______________________ Pd ____74



5 in

5 in10 in

3 in

6.2 in14 in

2 in

2 in

4 in

1. Mr. Switzer’s class collected tissue boxes. Theclass brought in a total of 20 boxes. If the tissue box dimensions are listed below, then how much space will Mr. Switzer need?

2. A refrigerator box measures 9 feet by 5 feetby 5 feet. Sam decides to fill up the box halfway with trash. How much space will the trash take up? (Draw a picture to help.)

1. A sandbox is being built at a nearby elementaryschool. The sandbox will be filled to the brim with sand.

If each bag of sand holds 10 cubic feet of sand, then how many bags are necessary?

2. A game cube has a side length of 4 inches.What is the volume of the cube? (Draw a picture to help.)

Name ___________________________________ Date _______________________ Pd ____75

Name ___________________________________ Date _______________________ Pd ____76



4 in

3 in7 in

215

ft6 ft

3 ft

1. The two rectangles below are similar figures. Use the information given to determine themissing side, x.

2. Use the scale factor of 23

to create a new

figure.

1. Pete’s Pizza prices their pizza per squareinch. A large pizza costs $16.74 and has a radius of 6 inches. Approximate the cost per square inch of a large pizza. Use 3 for π.

2. Angle A measures 113o. What is itssupplementary angle measure?

3. A shipping company places circular labels on allof their products. Each label measures a 4-inch radius. If the company orders 10 labels, then how many square inches are needed? Use 3.1 for π.

4. Angle C and angle D are adjacent angles. Ifangle C measures 39o, then what is the measure of angle D?

Name ___________________________________ Date _______________________ Pd ____77

Name ___________________________________ Date _______________________ Pd ____78



6 in

7.5 in

x

5 in

4 in

D

C

2.5 in

1. Find the area of the shape below: 2. Find the area of the shape below. Break the larger shape into smaller pieces if needed.

3. Matt is carpeting his bedroom. The room measures 12 feet by 14 feet. If carpet costs $1.90 per square foot, then how much will Matt spend to carpet his bedroom?

1. A swimming pool is constructed to thedimensions below. How much water will the swimming pool hold?

2. A game cube has a side length of 6 inches.What is the volume of the cube? (Draw a picture to help.)

Name ___________________________________ Date _______________________ Pd ____79

Name ___________________________________ Date _______________________ Pd ____80



413

ft

12 ft

12 ft

6 ft

5.5 ft

6.8 in

3 in

2 in

1. A new mall in town wants to include a food court. They would like to know what fast food restaurantspeople would prefer. The city council is debating the different ways that they can collect the town’s vote. Which of the ways below would be a random sample and why?

a. Have a questionnaire for every high school student to complete.

b. Have people at the city council meetings vote.

c. Poll every tenth person in the phone book.

2. The results of the survey are listed below. Make two inferences about the data.

1. The Student Council at school would like to hold an end-of-the-school-year event for the eighth gradestudents. They would like to know what students would enjoy doing but do not have time to poll everyone. Provide a suggestion for them to implement that would be unbiased.

2. The results of the survey are listed below. Make two inferences about the data.

EVENT FIELD DAYSCHOOL DANCE

TALENT SHOW

VOTES 18 42 2

Name ___________________________________ Date _______________________ Pd ____81

Name ___________________________________ Date _______________________ Pd ____82



RESTAURANTBURGER

YUMTACO TASTE

PIZZA PIE

CHOOSEY CHICKEN

VOTES 904 1352 632 128

1. A company that produces TVs would like to know why their sales have dropped. They decide to callevery fifth customer who has made a purchase in the past year to ask for suggestions. Is this a random sample? If not, what would you suggest?

2. Based on the data below, mark each statement as valid or invalid.

a. About seven times as many people liked Burger Yum as liked Choosey Chicken.

b. Taco Taste had 23

as many votes as Burger Yum.

1. A cell phone company is marketing their new package to teenagers. They would like to know what anappropriate price would be, so they decide to survey a random sample of teenagers. What would need to be adjusted in this sample for it to be more valid?

2. Based on the data below, mark each statement as valid or invalid.

a. The talent show would be a very unsuccessful event.

b. The field day would be the most attended event.

EVENT FIELD DAYSCHOOL DANCE

TALENT SHOW

VOTES 18 42 2

Name ___________________________________ Date _______________________ Pd ____83

Name ___________________________________ Date _______________________ Pd ____84



RESTAURANTBURGER

YUMTACO TASTE

PIZZA PIE

CHOOSEY CHICKEN

VOTES 904 1352 632 128

1. Mrs. McKinney is comparing the grades from her 1st and 5th period classes. She has the data below:

Create a box-and-whisker plot. Then, compare the two sets of data. Describe the variability between her two classes.

1. Coach Smith has to choose the next starter for the basketball team. She compares their pointsbelow:

Create a box-and-whisker plot. Which player has the higher average? Which player would you suggest that Coach Smith choose?

1st Period 75, 82, 88, 60, 75, 90, 82, 92

5th Period 84, 93, 100, 100, 88, 90, 94

Player A 12, 0, 16, 15, 2, 8

Player B 9, 12, 6, 6, 7, 11

Name ___________________________________ Date _______________________ Pd ____85

Name ___________________________________ Date _______________________ Pd ____86



1. Jada and her sister are always complaining about who gets to choose the TV show. They kept trackof the number of minutes they spent watching below:

Make a parallel box plot to compare. Is one sister getting to choose the show more often? How much more time are they getting to watch?

1. Mr. Berkley took a poll of his 14 students. He asked students how many books they read over thesummer.

Create a box-and-whisker plot. Which group of students had the higher average? Do AP students read more?

Jada 30, 15, 45, 60, 60, 30, 15

Sister 15, 15, 90, 30, 15, 30, 15

AP Students 3, 9, 0, 4, 6, 10, 2

On Level Students 3, 4, 2, 2, 6, 1, 2

Name ___________________________________ Date _______________________ Pd ____87

Name ___________________________________ Date _______________________ Pd ____88



1. Label each situation below as impossible,unlikely, or likely.

a. rolling a one on a number cube

b. rolling a number less than five

c. rolling a number greater than six

d. rolling a number less than two

2. Tanner spins the spinner, and it lands on B. If he spends the spinner 32 more times, then how many times can he expect it to land on B?

A

B C

D

1. Label each situation below as impossible,unlikely, or likely.

a. choosing an ace in a deck of cards

b. choosing a heart, a spade, or a diamond card in a deck of cards

c. going swimming in January

d. pizza for lunch in the cafeteria this month

2. What is the probability of spinning a A or C if the spinner is spun 400 times?

B

BC

AD

B

AB

Name ___________________________________ Date _______________________ Pd ____89

Name ___________________________________ Date _______________________ Pd ____90



1. Assign a number (0 to 1) to the likelihood of theevents below:

a. someone younger than 16 can drive legally

b. it will be sunny in Florida

c. a kindergartner is learning to read

d. a grocery store sells apples

2. If the spinner below is spun 160 times, then how many times can you expect to land on C?


a. your math teacher is older than you

b. it will snow in Denver in the winter

c. flipping tails on a coin

d. using a vowel in a word

2. If the spinner below is spun 500 times, then how many times can you expect to land on B?

B

B

C

A

DB

AB

B

B

C

A

DB

AB

Name ___________________________________ Date _______________________ Pd ____91

Name ___________________________________ Date _______________________ Pd ____92



1. A number cube is rolled 20 times. Use theresults below to answer the questions:

a. experimental probability of rolling a 1

b. experimental probability of rolling a 5

c. theoretical probability of rolling a 6

2. In a drawer, there are 10 white socks, 8 blacksocks, and 7 blue socks. What is the probability of randomly selecting a white sock?

3. A gumball machine with 200 gumballs has 40 red gumballs, 30 yellow gumballs, 55 blue gumballs, and the rest are green. What is the probability of randomly selecting a green gumball?

Number Times Rolled

1 0

2 4

3 3

4 6

5 5

6 2


a. experimental probability of rolling a 0

b. experimental probability of rolling a 3

c. theoretical probability of rolling a 5

2. A deck of game cards each have a differentshape on them. Twelve have a diamond, 8 have a square, and 5 have a circle. What is the probability of drawing a square or a circle?

3. The word “Mississippi” is spelled in Scrabble tiles. If one letter is chosen at random, what is the probability that it is an “s”?

Number Times Rolled

1 1

2 5

3 5

4 2

5 3

6 4

Name ___________________________________ Date _______________________ Pd ____93

Name ___________________________________ Date _______________________ Pd ____94




a. experimental probability of rolling a 1 or a 4

b. experimental probability of rolling a 5 or a 3

c. theoretical probability of rolling an even number

2. What is the probability of rolling a 2 or a 5 on asix-sided number cube?

3. What is the probability of drawing a face card in a 52-card deck of playing cards?

Number Times Rolled

1 0

2 4

3 3

4 6

5 5

6 2




c. theoretical probability of rolling a number greater than 4

2. A sewing bag contains 9 gold buttons and 8black buttons. How many gold buttons need to be added to the sewing bag so that there are 60% gold buttons?

3. The word “school” is spelled in Scrabble tiles. If one letter is chosen at random, what is the probability that it is an “o”?

Number Times Rolled

1 3

2 3

3 5

4 2

5 3

6 4

Name ___________________________________ Date _______________________ Pd ____95

Name ___________________________________ Date _______________________ Pd ____96



1. For breakfast, Joellen can choose fromoatmeal or scrambled eggs. She can drink milk, orange juice, apple juice, or hot chocolate. Make a list, a table, or a tree diagram to represent the sample space.

2. What is the probability of rolling an evennumber on a six-sided number cube?

3. What is the probability of drawing a 3, a 5, or a 7 in a 52-card deck of playing cards?

1. The spinner is spun twice. What is theprobability of spinning a 7 and then landing on stripes?

2. A deck of game cards each have a differentshape on them. Twelve have a diamond, 8 have a square, and 5 have a circle. What is the probability of drawing a circle, replacing it, and drawing a diamond?

3. The letters of the word “classroom” are placed in a bag. What is the probability of randomly drawing an “m” on the first draw, replacing it, and then randomly drawing an “s” on the second draw?

10 12

3

9

8

7

6

4

5

Name ___________________________________ Date _______________________ Pd ____97

Name ___________________________________ Date _______________________ Pd ____98



1. In a game, they toss a coin that can land either on heads or tails and spin a spinner that can land on any of 5 equal regions. If a coin is tossed and the spinner is spun, make a list, a table, or a tree diagram to represent the sample space.

2. Nicole played a handheld game. There were 15questions, of which she answered 6 incorrectly. At this rate, how many questions should Nicole expect to answer incorrectly if she answers a total of 135 questions?

3. In a deck of playing cards, what is the probability of drawing a heart, replacing it, and then drawing an ace?

1. The spinner is spun twice. What is theprobability of spinning an odd number and then landing on dots?

2. For Valentine’s Day, the student council isselling roses and carnations. They also offer a choice of a balloon, a bear, or chocolate. If a flower and a gift are chosen, make a list, a table, or a tree diagram that represents the different options.

Name ___________________________________ Date _______________________ Pd ____99

Name ___________________________________ Date _______________________ Pd ____100



10 12

3

9

8

7

6

4

5

1. Death Valley, CA is 282 feet below sea level.Black Mountain, KY is 750 feet above seal level. How many more feet above sea level is Black Mountain than Death Valley?

2. Solve:

a. -32 + 17 =

b. 86 + (-27) =

c. -12 + (-37) =

d. − 16

+ 56

=


4. Use the number line to solve the problem below:

1. A credit card customer owes $523.85. Theyare only able to make a payment of $184.50. How much money does the customer still owe?

2. Solve:

a. -108 – 23 =

b. 49 – (-62) =

c. -9.5 – 2.5 =

d. 25– 4

5=


4. Use the number line to solve the problem below:

Name ___________________________________ Date _______________________ Pd ____101

Name ___________________________________ Date _______________________ Pd ____102



-4 + 6 = 2

-1 – 4 = -5

1. Solve:

a. -7(-9)=

b. -5(15)=

c. 3.3(-6)=

d. − 35• 2

9=

2. Solve:

a. 140 ÷ −7 =

b. -36 ÷ −4 =

c. 192 ÷ −12 =

d. −23÷ 5

6=

3. Caleb and Sarah are having a Halloween party.

They have 625

pounds of candy to divide into 16

goodie bags. How much candy will be in each

bag?

4. At the grocery store, almonds are on sale for $3.79 per pound. What is the price of 4.5 pounds?


a. 7a + 7b – 13a – 11b

b. -5a – 12a + 2b – 3b

2. Simplify:

-5(4x) + 6(3x – 2)

3. Factor out the like terms:

24a + 72b – 40c

4. Write an expression to find the perimeter ofthe rectangle below.

Name ___________________________________ Date _______________________ Pd ____103

Name ___________________________________ Date _______________________ Pd ____104



6x

3x – 5

1. The average third grade student can read 80words in 5 minutes. What is the average reading rate per minute?



2. If a car travels at a rate of 74 miles per hour,then how long will it take the car to travel 481 miles?

1. A new product price is increased from $7 to $11. What is the percent of change? Round to the nearest whole number.




2. A cup of coffee costs $2.50. If the total costis $22.50, then how many cups of coffee were purchased?



x y

-1 -3

1 1

3 5

Name ___________________________________ Date _______________________ Pd ____105

Name ___________________________________ Date _______________________ Pd ____106



1. If Tyrone eats 18 cookies, which represents 30% of the bag, then how many cookies are in the bag?




Number of Lawns Mowed

$ E

arne

d

1 2 3 4 5 9 8 7 6 10

20 40

140 120 100

80 60

160 180 200

1. A local clothing shop is marking down all of its summer clothes by 75%. Rona would like topurchase a swimsuit that is originally priced at $80. When she gets to the register, she signs up for a loyalty card that saves her an additional 15%. How much did she spend on the swimsuit after both discounts?

a. Find the markdown price of the swimsuit.

b. Then, find the markdown of the loyalty card.

a. Subtract to find the final price.

Name ___________________________________ Date _______________________ Pd ____107

Name ___________________________________ Date _______________________ Pd ____108






Two different companies offer online gaming subscriptions. Company A charges $75 upfront and then $20 per month. Company B does not charge an upfront fee but charges $35 per month. After how many months will the two companies charge the same amount?


The setup fee for a photo book is $15. The paper is an additional charge of $0.17 per page. What is the greatest number of pages that a book can have if the total bill is to be less than $40?

Name ___________________________________ Date _______________________ Pd ____109

Name ___________________________________ Date _______________________ Pd ____110



-4x – 18 = 22 1.5x – 6 = 7.5

-11x + 32.5 < 8234x – 3

4≥ -6

1. A triangle is shown below. If the image is dilated by a scale factor of 3.5, then what is the perimeter of the new triangle?

2. Mr. Jackson is going to place a layer of mulchin his garden. His blueprint shows the garden below:

If the blueprint has a scale factor of 1 cm:2.5 feet, then how many square feet of mulch does Mr. Jackson need?

1. Construct and label an acute isosceles triangle. 2. A cylinder is sliced horizontally. Draw the 2-D shape that represents the slice.


29˚131˚

20˚

Name ___________________________________ Date _______________________ Pd ____111

Name ___________________________________ Date _______________________ Pd ____112



4 m

3 m

5 m

5 cm

3 cm

7 cm

1. The area of a circle is 111.6 squarecentimeters. What is the diameter? Use 3.1 for π.


3. Find the area of the shaded region. Use 3.1 forπ.

4. Triangle ABC is a right isosceles triangle. What are the measures of the three angles?

1. Find the area of the shape below: 2. Find the surface area of the cube below:

3. Marya is redecorating her bedroom and decides to paint 3 of the walls. Each of the walls measures 12 feet by 10 feet. If a quart of paint will cover 90 square feet, then how many quarts does she need?

Name ___________________________________ Date _______________________ Pd ____113

Name ___________________________________ Date _______________________ Pd ____114



10 m

6 m

12 in

6.2 in

62o

37o xo

4.7 in

1. Mr. Jones’s class collected tissue boxes. Theclass brought in a total of 30 boxes. If the tissue box dimensions are listed below, then how much space will Mr. Jones need?

2. A refrigerator box measures 11 feet by 6feet by 6 feet. Sam decides to fill up the box three-fourths with trash. How much space will the trash take up? (Draw a picture to help.)

1. A television broadcasting company would like to produce a new comedy show. They would like theshow to target young families and teens. Provide a suggestion for them to poll their potential viewers that would be unbiased.

2. Below is data collected in two random samples regarding student sport preference. Make two inferences based on the information.

SPORT VOLLEYBALL SOCCER FOOTBALL

VOTES 24 18 58

Name ___________________________________ Date _______________________ Pd ____115

Name ___________________________________ Date _______________________ Pd ____116



4 in

3 in 7 in


a. You will go to school on a Monday.

b. A new baby will be a girl.

c. It will be 100 degrees in Antarctica.

d. Kids like cookies.

2. If the spinner below is spun 500 times, then how many times could you expect to spin a D?

B

B

C

A

DB

AB

1. Mr. Gaver took a poll of his 20 students. He asked their hourly pay rate.

Create a box-and-whisker plot. Which group of students had the higher hourly pay rate? Do seniors make more money?

Seniors 10, 9.50, 8, 11, 12, 10, 15, 7.50, 9, 9

Sophomores 7.50, 8, 10, 7.50, 8, 8, 9, 8.5, 7.50, 10

Name ___________________________________ Date _______________________ Pd ____117

Name ___________________________________ Date _______________________ Pd ____118



1. In a closet, there are 4 different colored tops: red, green, purple, and black. There are also shorts, jeans, and a skirt. If a top and a bottom are chosen, make a list, a table, or a tree diagram to represent the sample space.

2. Jamila played a handheld game. There were 15questions, of which she answered 8 incorrectly. At this rate, how many questions should Jamila expect to answer correctly if she answers a total of 135 questions?

3. In a deck of playing cards, what is the probability of drawing a red card, replacing it, and then drawing a queen?




c. theoretical probability of rolling a number greater than 4

2. A sewing bag contains 3 gold buttons and 4black buttons. How many buttons need to be added to the sewing bag so that there are 30% gold buttons?

3. The word “science” is spelled in Scrabble tiles. If one letter is chosen at random, what is the probability that it is a “c”?

Number Times Rolled

1 2

2 2

3 4

4 5

5 3

6 4

Name ___________________________________ Date _______________________ Pd ____119

Name ___________________________________ Date _______________________ Pd ____120



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