MATH 7 QUARTER 4 NOTEBOOK 2014 - 2015

Name: _________________________ Teacher: _________________ Block: ______

Table of Contents  Warm – Ups

page 2

 Unit 12 – Probability    

The Fundamental Counting Principle Theoretical Probability Independent & Dependent Events Experimental Probability

page 4 page 7 page 10 page 14

 Unit 13 – Histograms    

Intro to Histograms Comparing Two Sets of Data Practice 1 Practice 2

 SOL Review Packet

page 17 page 20 page 21 page 22

page 24

1

Warm Ups

2

Warm Ups

3

Tree Diagrams and The Fundamental Counting Principle

Learning Target: SOL 7.10 The student, will determine the probability of compound events, using the Fundamental (Basic) Counting Principal.

The pizza place around the corner allows you to choose hand tossed, thin & crispy, or stuffed crust. You can also order pepperoni, meat lovers, supreme, or cheese pizza.

1. How many different combinations of crust and pizza can your order?

A TREE DIAGRAM can be used to represent the possible outcomes.

2. Mindy is getting ready for school. Her school has uniforms. She can wear a khaki skirt or kaki pants. She can wear a blue, yellow, or white blouse, and she can wear brown or black dress shoes. How many different outfits can Mindy put together for school?

3. Tim is ordering a new car from the dealership. His options are listed in the table below. Transmission Manual Automatic

Exterior Color White Silver Red

Interior Color Black Grey Tan

Is there another way to determine how many combinations are possible without creating a tree diagram? 4

The FUNDAMENTAL COUNTING PRINCIPLE relates the number of outcomes to the number of choices. If event M can occur in ______ ways and is followed by event N that can occur in _______ ways, then the event M followed by N can occur in _____________ways.

Use the Fundamental Counting Principle to answer the following questions. 1. A coin is tossed three times. How many possible outcomes are there?

2. Flo has seven skirts and five blouses. How many outfits are possible?

3. Julie can choose wings or potato skins for an appetizer; water, pop, or lemonade for a beverage; and chicken, steak, or pasta for an entrée. How many different dinner combinations can she choose from?

4. Two number cubes are rolled and two coins are tossed. Find the number of possible outcomes.

5. A quiz has 10 true-false questions. How many answer keys are possible?

6. A store sells three brands of gel pens. Each brand comes in four different ink colors: blue, pink, purple, and green. Kerry buys one of each brand and ink color. How many pens does Kerry buy?

7. Shira is going to the movies. She can choose to watch The Hunger Games or The Avengers; she can buy Sour Patch, M & M’s or popcorn; and she can drink any one of seven different soft drink flavors. How many possible combinations are there for her night at the theater? 6

Theoretical Probability Vocabulary:

Learning Target: SOL 7.9 The student, will investigate the difference between the experimental probability and theoretical probability of an event.



The PROBABILITY of an event is the _______________________________.



We often express probability as a _______________ and as a ___________________.



The _______________________________ is the set of all possible outcomes.

Example 1: Mrs. Neterer has red, green, and purple M & M’s left in the bag.   

The probability that the next M&M she eats will be red is 31%. The probability that the next M & M she eats will be green is 2/5. The probability that the next M & M she eats will be purple is .29 a) What color is she most likely to eat next?

b) If there were 100 M & M’s in the bag, how many of them are that color?

Example 2: Find the theoretical probability of rolling an even number when you roll a die containing the numbers 1-6.

Fraction

Decimal

Percent

P(even number)

Challenge: Using the same six-sided number cube, can you think of a situation that would have a 0% probability of happening? 7



______________________________ is the probability that an event will occur when all events are assumed to be ___________________________.

THE SKITTLES SNACK BAG: a. If I select one Skittle from the snack bag at the front of the room, which color am I most likely to grab? How do you know?

b. If one Skittle is selected at random, what is the probability that it is orange?

c. What is the probability that it is NOT purple?

d. If one skittle is picked at random, which color do you have a 10% chance of picking?

You Try It #1 Practice Question: There are five green, six brown, three red, and four yellow M & M’s in a bag. a. What is the probability that a randomly selected M & M will be brown?

b. What is the probability that a randomly selected M & M will not be yellow?

c. Which color do you have a 1/6 chance of selecting? 8

Practice Question: Charlie bought a roll of Mentos. If he has 100% chance of getting a mint flavored candy, what does that tell you about his roll of Mentos?

Directions: You have a spinner that goes from 1 to 12. Find the odds for spinning each of the following. 1. P(6)

2. P(Not13)

3. P (prime number)

4. P (4, 8, or 12)

5. P (Not an odd number)

6. P(7 or 9)

7. P (odd number less than 7)

8. P (A number greater than 12.)

9

Independent and Dependent Probability 1. Jerry’s sandwich shop offers customers the following choices.

Sandwiches PB & J Roast Beef Turkey Chicken Salad

Menu Chips Sun Chips BBQ Potato Chips Fritos

Beverages Lemonade Ice Tea Water

What is the probability that Jerry orders a roast beef sandwich with sun chips and ice tea?

2. Terri is trying to decide what to wear to the fair. She can wear blue jeans, overalls, or a black skirt. She can wear one of eight different color T-shirts. She can wear tennis shoes or cowboy boots. What is the probability that she decides to wear her black skirt with a green t-shirt and a pair of cowboy boots?

TWO INDEPENDENT EVENTS: The probability of two independent events is found by multiplying the probability of the first event by the probability of the second event. THE SPINNER: a. You are spinning to win a candy bar, what is the probability that you win a Kit Kat? b. You have won the right to spin twice. What is the probability that you will win a Kit Kat two times in a row?

Three Musketeers

Kit Kat

Snickers Milky Way

c. What is the probability that you will win a Three Musketeers OR a Milky Way on the first spin, and a Kit Kat on the second spin?

10

You Try It #2 – Calculating the Probability of Independent Events Practice Question: A quarter is flipped. a. What is the probability that the quarter will land heads up?

b. What is the probability that the quarter will land heads up two times in a row?

Directions: There are 5 yellow marbles, 1 purple marble, 3 green marbles, and 3 red marbles in a bag. Once a marble is drawn, it is replaced. Find the probability of each outcome: 5. P(purple then red)

6. P(red then green)

7. P(NOT green, NOT green)

8. P(two yellow marbles in a row)

9. P(purple then yellow)

10. P(red then yellow)

TWO DEPENDENT EVENTS: If the probability of two events, A and B, are dependent, then the probability of both events occurring is the product of the probability of A and the probability of B after A occurs. Directions: Decide if each set of events is independent or dependent. Explain. a. A student spins a spinner and rolls a number cube. b. A student picks a raffle ticket from a box and then picks a second raffle ticket without replacing the first raffle ticket. 11

Tess had a bag of dinner mints sitting on her plate at her sister’s wedding reception. There are 3 green mints, 2 pink mints, 4 white mints, and 1 yellow mint in the bag. She is going to eat three of them before dinner. a.

What is the probability that the first mint is green, the second mint is pink, and the third mint is white?

b. What is the probability that all three of the mints are green?

c. What is the probability that the first two mints are white and the last mint is yellow?

THE DECK OF CARDS: a. A card is drawn from a standard deck of cards. What is the probability that the card is a face card?

b. A card is drawn from a standard deck of cards. It is NOT REPLACED and a second card is drawn. What is the probability that the first card was clubs and the second card was hearts?

c. A card is drawn from a standard deck of cards. It is NOT REPLACED and a second card is drawn. What is the probability that both the first and second cards where red face cards?

12

You Try It #3 – Calculating the Probability of Dependent Events Directions: There are 4 yellow marbles, 3 purple marbles, 1 green marble, and 1 white marble in a bag. Once a marble is drawn, it is not replaced. Find the probability of each outcome. 1. P(purple, white)

2. P (white, green)

3. P (purple, purple)

4. Two yellow marbles in a row

5. a yellow then a purple marble

6. A green then a white marble

Directions: Determine if each set of events is independent or dependent. 1. Drawing a two from a deck of cards, setting it aside, then drawing a king. 2. Choosing an appetizer and an entrée from the dinner menu at Ruby Tuesdays. 3. Laura has 8 pairs of shorts: 2 white, 3 denim, 1 red, 2 khaki. Laura is packing for a trip and she randomly chooses two pair of shorts without replacement. 4. Michael records the number of times his dog barks and spins a spinner. 13

Experimental Probability 8.

Review of Theoretical Probability 1. What is theoretical probability?

Learning Target: SOL 7.9 The student, will investigate the difference between the experimental probability and theoretical probability of an event.

2. You are given a 6 sided dice. What is the theoretical probability of each of the following? a. P (6)

b. P (even)

c. P(less than 3)

d. P (0)

What is Experimental Probability?

EXPERIMENT: Roll a six-sided number cube 20 times. Record your results on the table below.

Number rolled 1 2 3 4 5 6

Tally

Frequencies

Use the results to find the following: 1. P (6)

2. P(even)

3. P(odd)

14

How could we make our experimental probability more accurate? 4. P(4 or 5)

5. P(less than 3)

6.P(0)

The more trials run, the __________ the ________________probability will get to the _______________ probability. Example 1: The gumball machine at a video arcade contains an equal number of orange, red, and green gumballs. 1. What is the theoretical probability that the next customer who buys a gumball will get a green gumball?

2. Alli bought 20 gumballs from the machine. She had four green gumballs, six red gumballs, and ten orange gumballs. Based on Alli’s data, what is the probability that the next customer will get a green gumball? What kind of probability is this? How do you know?

Example 2: A survey was conducted to find out how students get to school. The results of the survey are shown in the table below.

Bus 85

Car 65

Bike Walk 25 45

a) What is the probability a student walks to school? b) What is the probability the student rides to school in a car or in a bus? c) What is the probability a student does not bike to school?

d) Are your results to the questions above based on experimental or theoretical

probability? How do you know? 15

Unit 12 Scratch Paper

16

Histograms Vocabulary

Learning Target:SOL 7.11a,c The student, given data for a practical situation, will construct and analyze histograms; and compare and contrast histograms with other types of graphs presenting information from the same data set.

Definition

Example

Histogram Interval Frequency Frequency Table Example 1: 1. Use the histogram on the right to fill in the frequency table below.

2. How many restaurants sell chicken sandwiches that cost under $3?

3. How many restaurants were surveyed?

Cost of Chicken Sandwiches Interval Frequency

4. What percent of the restaurants surveyed sell chicken sandwiches that cost between $2.00 and $2.49?

17

Example 2: Create a histogram that illustrates the number of counties in each state using the data below. http://www.tommcmahon.net/2008/12/number-of-counties-in-each-state.html (Updated 12/09/2008)

• 254 – Texas

• 87 – Minnesota

• 58 – California

• 21 – New Jersey

• 159 – Georgia

• 83 – Michigan

• 56 – Montana

• 17 – Nevada

• 134 – Virginia

• 82 – Mississippi

• 55 – West Virginia

• 16 – Maine

• 120 – Kentucky

• 77 – Oklahoma

• 53 – North Dakota

• 15 – Arizona

• 115 – Missouri

• 75 – Arkansas

• 14 – Vermont

• 105 – Kansas

• 72 – Wisconsin

• 46 – South Carolina

• 102 – Illinois • 100 – North Carolina • 99 – Iowa

• 67 – Pennsylvania • 67 – Florida • 67 – Alabama

• 44 – Idaho

• 14 – Massachusetts

• 39 – Washington

• 10 – New Hampshire

• 36 – Oregon

• 8 – Connecticut

• 33 – New Mexico

• 5 – Rhode Island

• 29 – Utah

• 5 – Hawaii • 3 – Delaware

• 95 – Tennessee

• 66 – South Dakota

• 93 – Nebraska

• 64 – Louisiana

• 27 – Alaska

• 92 – Indiana

• 64 – Colorado

• 24 – Maryland

• 88 – Ohio

• 62 – New York

• 23 – Wyoming

THINGS TO REMEMBER:  There is no space between bars.  Because the intervals are equal, all of the bars have the same width.  Intervals with a frequency of 0 have no bar. Number of Counties in Each State Counties Tally Frequency 1 – 25 26 – 50 51 – 75 76 – 100 101 – 125 126 – 150 151 – 175 176 – 200 201 – 225 226 – 250 251 – 275

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Using Different Intervals

DIRECTIONS: Spin your spinner 50 times. Record your results in the frequency table given below. Then, use the frequency table to create three different histograms with the given intervals.

Using an Interval of 1

# Spun 1 2 3 4 5 6 7 8

Tally

Frequency

Using an Interval of 2

Using an Interval of 4

19

COMPARING TWO SETS OF DATA The histogram below describes winning times for Women’s Olympic Swimming. 1. Which event has the slowest winning time? 2. How many women in both events finished between 60 and 70 seconds? 3. Which event has the fastest winning time? 4. Which event has more winning times less than 1 minute?

The histogram below describes U.S. National Parks and Monuments 5. Why is there a JAGGED LINE in the vertical axis?

6. Are there more states with two or more national parks or two or more national monuments?

7. How many more states have either one or no national parks than either one or no national monuments?

20

Practice with Histograms 1 Directions: The data below describes the number of books read by 20 participants in the library’s summer reading program. 

Use the data below to fill in the frequency table and create a histogram with INTERVALS OF TEN.



Don’t forget to TITLE your histogram and LABEL your HORIZONTAL and VERTICAL AXIS. 8

28

12

9

1

14

42

40

25

16

5

23

26

55

28

32

12

7

20

33

Number of Books Read in the Summer Reading Program # of Books

Tally

Frequency

21

Practice with Histograms 2 Directions:The data below describes how many pieces of candy thirty different trick– or–treaters collected last Halloween. 

Use the data below to fill in the frequency table and create a histogram with INTERVALS OF TEN.



Don’t forget to TITLE your histogram and LABEL your HORIZONTAL& VERTICAL AXIS. 24

28

33

40

56

44

29

50

62

54

32

39

26

55

28

37

42

40

61

20

21

35

45

54

65

56

50

61

54

73

Pieces of Candy Collected on Halloween # of Pieces

Tally

Frequency

22

Unit 13 Scratch Paper

23

SOL REVIEW PACKET Comparing Numbers, Perfect Squares, Absolute Value, Scientific Notation and Powers of Ten (7.1a-e) 1. What is the difference between converting them to standard form.

and

2. Complete the table:

? Explain how the process differs when

Fraction

10

Decimal

-2

10-3 10-4

3. Circle ALL of the numbers below that are perfect squares. 14

9

1

4. What two numbers does √

-100

0

169

fall between?

5. The fraction is equivalent to _________. A)

125%

B)

12.5%

C)

1.25%

D) .125%

6. Which number is the greatest? A) 3.5 x 103

B) 3.8 x 10-3

C) 3

D) 35% 24

7. Which number is less than 500%? A) 5

B)

C)√

D) 5.3

8. Which list is ordered from greatest to least? A)

B)

C)

D)

9. Write the following numbers from least to greatest. 6.25 x 106

0.625

_______________

______________

______________

6.25%

_____________

10. What is the definition of absolute value?

Evaluate the following: 11. |

|

12. |

|

13. | |

|

14. |

| |

25

Arithmetic and Geometric Sequences (7.2) Directions: A. State whether the sequence is arithmetic, geometric, or neither. B. If the sequence is arithmetic or geometric, find thecommon difference or ratio. A) 2, 5, 8,11,…

B) 2, 4, 8, 16,…

C) 2, 5, 15, 18,…

D) 62, 60, 58, 56,…

E) 5, -15, 45, -135,…

F) 27, 9, 3, …

Variable Expressions: 1. The expression n – 2 could be used to find the next term in which of the sequences above?

2. The expression could be used to find the next term in which of the sequences above?

3. The expression 2n could be used to find the next term in which of the sequences above?

26

Integer Operations (7.3a,b) 1. When you are adding a positive and a negative number, find the ______________________ and keep the sign of the ____________________________. 2. What does K.C.C. stand for? _____________________________________ 3. Write the addition problem that is being modeled by the picture on the right:

KEY = Negative = Positive

4. Model the equation 5 – 8 in the box at the right. Hint: You may need to use K.C.C.

Evaluate each of the following: 5. -18 + (-10)

8. -20 ÷ (-4)

11. 11 – (-4)

6. -7 •3

9. 0 – 14

12. -5 • (-8)

7. -8 – 10

10. -5 + 13

13. -20 – (-2)

14. Use order of operations to simplify: 7 + (6 x 52 + 10) ÷ -4

Solve the problems below. SHOW ALL OF YOUR WORK! 15. Seth has $100 in his checking account. He writes a check for $45, and then deposits $30. How many dollars does Seth have in his account?

16. The temperature in northern Michigan on January 17th is -180F. The temperature in Austin, Texas on the same day is 430F. What is the difference between the temperature in Michigan and the temperature in Texas?

27

Proportional Reasoning (7.4) 1. How do you solve a proportion? 2. Which of the following is NOT a proportion? (1 point) A.

B.

C.

D.

Directions: Set up the Proportion and Solve. SHOW YOUR WORK! 3. Goofy can hike five miles in two hours. At this rate, how long will it take Goofy to hike 12 miles?

4. Yogi Bear steals five picnic baskets for every 9 people that enter Jellystone Park. If Yogi Bear managed to a make off with 80 picnic baskets over the 4th of July, how many people must have visited the park?

5. Trey wants to use a scale of 1 inch = 37 feet to build a scale model of the Washington Monument. If the actual height of the Washington Monument is 555 feet, how tall will his model be?

6. On a map, the scale is 1 inch = 2.5 miles. Find the dimensions of a school district that is 4 inches by 9 inches on the map. (5 points)

28

The Percent Proportion (7.4) Directions: Complete the table below. NO CALCULATOR! Original Value

10%

15%

20%

25%

440

26

Directions: Answer each question below. Show all of your work. 1. Tommy wants to buy a new pair of running shoes. The pair he wants is $150 and the sales tax is 15%. What is the total price of the shoes?

2. 86% of the questions on Sam’s math test were correct. If there were 50 questions on the test, how many were correct?

3. The Andersons went to dinner at the Olive Garden. If their dinner cost $42.95 and they left a 18% tip for their server, how much did they pay altogether?

4. There are 250 students that attended the Mercer Madness Basketball Tournament. If 64% of these students are female, how many male students attend the Mercer Madness?

5. Justin went to the movies. If he bought popcorn for $4.25 and a soda for $2.25, what was his total bill after adding 6.25% sales tax?

29

Volume and Surface Area (7.5a,b,c) 1. What is the difference between the radius and the diameter of a circle?

DIRECTIONS: Find the volume and surface area of each figure below. 1.

2.

8 cm

8 ft 7 ft 15 ft 6 cm

DIRECTIONS: Decide which shape represents the given situation. Then, determine which formula is needed to answer each question. SHOW ALL OF YOUR WORK! 3) On a cold day, Bridget is trying to find out how much hot cocoa she can bring along with her on a hike. If her thermos is 9 inches tall and 4 inches wide, how much hot cocoa can she bring with her?

4) Sear’s is having a sale on all refrigerators. The biggest refrigerator is 4 feet long and 4 feet wide and has 112 cubic feet of space inside. a. How tall is the refrigerator? b. If Sear’s were to double the width of the refrigerator, how would it affect the volume?

5) A cylindrical hay bale needs to be wrapped in netting to keep it together during the storm. If the hay bale is 4 feet in diameter and 7 feet long, how much netting is required?

30

Similar Figures (7.6) Determine whether each pair of figures is similar. 7.

8.

9. Explain how you can use cross-products to determine if two figures are similar?

Directions for Problems 18 & 19: Find the missing value. Assume each pair of geometric figures is a pair of similar figures. SHOW YOUR WORK!

32.5 cm

10.

26 cm

5 cm

11.

x cm

4 cm 3 cm

31

Quadrilaterals (7.7) 1. Consider the figure at the right. Circle all that apply:

quadrilateral, parallelogram, square, rectangle, rhombus, trapezoid.

True or False: _______ 2. The figure at the right is a trapezoid. ________ 3. All squares are parallelograms. ________ 4. All rectangles are squares. ________ 5. All squares are rhombuses. ________ 6. The figure at the right is a parallelogram.

7. What is the difference between a rectangle and a rhombus?

8.

Why are all rectangles not considered squares?

9.

What is the difference between a trapezoid and a rectangle?

32

Transformations (7.8) Directions: Identify each of the transformations below as a reflection, translation, rotation, or dilation. The figure in bold is the pre-image and the dotted figure is the image. 1.

2.

3.

4. One of the transformations above was a rotation. Tell me how many degrees the figure was rotated (900 or 1800) and in what direction (clockwise or counterclockwise).

5. Plot ABC on the grid on the right. A (0, 3)

B(2, -1)

C(-3, -3)

6. Plot the image of ABC after a size transformation (dilation) of 3. List the coordinates of A’B’C’.

Use triangle ABC below to answer questions 7 and 8. C

A

7. What would the coordinates of A’ be if triangle ABC was reflected over the x axis?

8. What would the coordinates of A’ be if triangle ABC was translated -4 units vertically? 33

Functions (7.12) 1. What is the definition of a function?

2. What is the difference between the domain and range of a function?

Directions for #3 - 5: Identify the domain and range of each relation. Then, determine if the relation is a function. x y 8 0 3. {(4, 3), (6, 2), (4, -3), (8, 1)}4. {(8, 7), (7, 7), (6, 7), (5, 7)} 5. 9 -1 10 -2 11 -3 12 -4 11 -5

Directions: Create a table of values for each of the given equations. Use your table to graph the function. 14. y = -x + 1 Use the domain {-2, -1, 0, 1, 2}.

15. y = -2x + 4 Choose any four domain values.

34

Translating Expressions & Order of Operations (7.13a,b) 1. What is the difference between “eight less a number x” and “eight less than a number x?”

Directions: Complete the table below. Verbal Phrase The product of seven and a number x is thirty-five.

Mathematical Symbols

2 x+4 3 The quotient of a number x and fifteen is two. 4 A number b increased by ten is twenty-five. 5 6

y-8

7

x–7=9

8

Five more than the product of six and a number.

9

The difference between twice a number and six is ten.

10 Three times the sum of a number and twelve.

11. What does PEMDAS stand for?

12. Evaluate 6x2 + 4 when x = 10.

13. Evaluate (5 + x • 3) + 18 ÷ y whenx = 4 and y = 6.

35

Solving Equations (7.14a,b) Solve each of the equations below: 1.

4.

5.

2. y – (-12) = 15

6. 2x + 10 = -6 3. 7x + 9 = 37

Using the key on the right, write an equation for each of the models below. Then, solve the equation. 1.

2.

KEY = Negative = Positive

3.

Directions: Write an equation to represent each situation below. Then, solve your equation. Your equations must contain a variable.

1. The last football game Shelly went to was extremely cold. She bought 4 cups of hot chocolate and one hand warmer at the concession stand. The hand warmer cost $4. If she spent a total of $12, how much was each cup of hot chocolate?

2. The toy store down the street is having a huge sale. Victor buys several board games for $10 each and one train set for $35. If Victor spent a total of $95 (before taxes), how many board games did he buy? 36

Inequalities (7.15a,b) Directions for #1-6: Write an inequality to represent the given situation. 1. A number is at least nine.

2. Seven is less than a number.

3. Negative four is greater than a number.

4. A number is greater than or equal to six.

5. A number is at most seventy.

6. A number is no more than 200.

7. When you are solving an inequality, when do you have to flip the sign?

8. Is 8 a solution to x + 4 > 12? How do you know?

Directions: Solve the following inequalities. Then, graph the solution on the number line provided. 9.

10. x - 3 ≤ -12

11. -6x ≤ -18

12. -80 < -8x

37

The Properties of Real Numbers (7.16a-e) Complete the table below: Property Commutative Property of Addition

Example 9•0=0

Inverse Property of Multiplication 9 + (6 + 8) + 4 = 9 + 6 + (8 + 4)

8 + (-8) = 0

Multiplicative Identity Property

Associative Property of Multiplication

0 + 12 = 12 9 • (4 • 6) = 9 • (6 • 4)

Distributive Property

Section F Directions: Each of the expressions below has been partially simplified. Identify the property that was used to simplify them: 1) 4 + 5 ∙ 0 – 3 4+0–3

2) 3 + 4∙ 1 + 2 3+4+2

3) 4(20 + 1) 80 + 4

4) 4 + (6 + -5) (4 + 6) + -5

38

SOL Review Scratch Paper

39