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12-1 Activity: An Array of Math ProblemsOrganizing Data Using Matrices

In this activity you will work with a partner to understand addition of matrices. You will each build your own matrix and then add them together.

A. Building a Matrix

Color will be used to represent the rows of your matrix. Th at is, everything in the same row of your matrix must be the same color. Th e fi rst row will be red, the second row green, and the third row blue. Similarly, shapes will be used to represent the columns of your matrix. So everything in the same column must have the same shape. For now we will build a matrix with only three columns.

On a separate piece of paper, draw a matrix by placing a square in each row of the fi rst column, a circle in each row of the second, and a triangle in each row of the third (do not forget to change colors with rows).

1. In which row would you fi nd a blue triangle?

2. In which column would you fi nd a blue triangle?

3. Would a green circle be out of place in the second row, third column?

4. Where would you put a red square?

Now draw a number of shapes in each matrix position using the color/row, shape/column convention. For instance, you might draw two green circles in the second row and second column. Your partner might draw four green circles in the same position.

B. Adding Matrices

5. In the space below, write the number of objects you put in each position. Th e position of the number you write down should correspond to the position of the objects in your matrix.

6. Write down your partner’s numbers.

7. Add the objects in your partner’s matrix to your own, being careful not to mix colors or shapes. Count the number of items in each position and write them to the right.

Your matrix Partner’s matrix

Check students’ work.

third

third

yes

fi rst row, fi rst column

All of the graphs below are rational functions. Match each function on the left to its graph on the right. Write your answers in the circle below. If the letters of your answers spell a word in both directions around the circle, then your answers are correct!

11-7 Puzzle: Circular ReasoningGraphing Rational Functions

1. y 53

x 2 2 2 1

2. y 51x

3. y 52

x 2 1

4. y 524x

5. y 521

x 2 1 2 2

6. y 523

x 1 1

A.

E.

P.

D.

I.

R.

xO

y

42

4

2

4

224

xO

y

42

4

2

4

224

xO

y

42

4

2

4

224

xO

y

42

4

2

4

224

xO

y

42

4

2

4

224

xO

y

4

4

2

4

224

D6.

R1.

I5.

E2.

A4.

P3.

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Th is game is for two players.

Cut out the squares below. Mix them up and turn them face down on a table or desk. Label the unprinted sides with the numbers 1 through 30. Place the squares in six columns and fi ve rows, with the number labels facing up.

Draw two squares at a time. Each square has a value of x and y on it. A coordinate pair such as (2, 3) means that x 5 2 and y 5 3. For both squares, fi nd the

constant of variation k in the inverse variation y 5kx

. Multiply x and y to fi nd the

value of k for both of your squares. Your teacher will tell you whether you should use mental math or a calculator. If the two squares show inverse variations that have the same value of k, then keep the squares and take another turn. If the values of k do not match, then turn the squares face down and give your opponent a turn.

Th e player with the most pairs is the winner.

11-6 Game: You’ve Met Your Match!Inverse Variation

x 3y 8

x 3y 3

x 1y 5

x 3y 1

x 0.1y 100

x 2y 2

x 1y 6

x 4y 3(2, 3)

(5, 2) (9, 1)

(8, 1) (1, 3)

(6, 4)

(2, 8)

(1, 2)

(4, 4)

(1, 4)

(1, 0.3) (6, 2)

x 4

y 12

k 19

k 19

x 3

y 110

y 3

x 127

x 5

y 12

x 13

y 13

x 2

y 12

25, 15

5, 15

16, 12

25, 110

k 24

k 1

k 9

k 2

k 1

k 8

k 10

k 16

k 0.3

k 0.3

k 2

k 4

k 3

k 10

k 3

k 24

k 2.5

k 12

k 9

k 12

k 16

k 4

k 6

k 2.5

k 6

k 5

k 5

k 8

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Work in small groups for this activity.

Each group is hiring two workers to mow a golf course. Roll a number cube to determine the number of hours h that one worker would take to mow the course. Th e expression 12 2 h is the number of hours it takes the other worker to mow the course. Th e sum of h and 12 2 h equals 12. Th en compute how long it will take the two workers to mow the course together.

1. After each group has made its computations, complete the table below. Make a table of results for diff erent h-values. If the time for any h from 1 to 6 has not been computed, the class should compute this.

2. Which value of h gives the two workers the fastest time?

3. Go back into small groups to fi nd a formula for the time t using h. What expression do you get for t? What type of expression is it?

4. Use your graphing calculator to graph the formula you found in Exercise 3. In the graph, what occurs when the value of h equals 6?

5. Discuss your results to Exercises 124 as a class. What would happen if the sum of the two workers’ times was a number other than 12?

11-5 Activity: Together or Alone?Solving Rational Equations

h 5 1

t 5 112(12h 2 h2); quadratic expression

The vertex of the graph is located at h 5 6.

53

94

83

1112

3512

h 12 h Time

1 11

10

9

8

7

6 3

2

3

4

5

6

Answers will vary. Sample: The vertex of the parabola will not have an h-value of 6.

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12-5 Activity: A Classroom SamplerSamples and Surveys

Work in small groups for this activity. You will investigate whether a stratifi ed sample, which divides a population into groups, gives results better than a random sample.

Your class will be a sample of the population of all students at your school taking Algebra 1. Th e survey question is “How many hours per week do you spend on the Internet?” As a class, write all the responses to the questions on the board. In addition, group the responses by male students and female students.

1. What is the average number of hours per week spent on the Internet?

2. What is the average number of hours per week spent on the Internet for male students?

3. What is the average number of hours per week spent on the Internet for female students?

4. What is the average of the two numbers in Questions 2 and 3? How does that compare to your answer in Question 1?

5. How does the number of male and female students in your class compare? Do you think that this is representative of all students taking Algebra 1 at your school? Explain.

6. If the number of male and female students taking Algebra 1 at your school is about equal, then the number found in Question 4 would be a good refl ection of the number of hours spent on the Internet. Explain why this is so.

7. What additional research would you need to do in order to fi nd a more precise average using your answers from Questions 2 and 3?

Check students’ work.

12-4 Game: Show and TellBox-and-Whisker Plots

Th is is a game for two teams of two students each. You will need several sheets of scrap paper.

In the rectangles below, there are 16 mathematical terms that you have learned so far in this chapter. Cut out the rectangles and lay them face down.

Pick up any four rectangles. Look at the terms on each rectangle, but do not reveal them to your partner.

In this game, your partner will have a total of two minutes to fi gure out which four terms you have. Th e only clues that you may give are pictures or calculations on the pieces of scrap paper. For instance, to describe the term “scalar multiplication,” you write the following.

But, if you say or write any words used to defi ne the term, then your team cannot get credit for that term. (Th e other team will act as referees.)

Th e four players will play four rounds. Players 1 and 2 form Team A and Players 3 and 4 form Team B. In each round four terms are drawn without replacement.

• Team A plays Round 1. (Player 1 gives clues to Player 2.)

• Team B plays Round 2. (Player 3 gives clues to Player 4.)

• Team A plays Round 3. (Player 2 gives clues to Player 1.)

• Team B plays Round 4. (Player 4 gives clues to Player 3.)

Th e team that fi gures out the most terms wins!

−1 −3

2 4

3

63

12

9=

element(of a matrix)

interval(of a histogram, and so on)

mean

box-and-whisker plot quartile

median

frequency table

matrix scalar histogram

symmetry(of a histogram, and so on)

range

outlier

cumulativefrequency table

mode

interquartile range

Check students’ work.

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12-3 Puzzle: One Mean PuzzleMeasures of Central Tendency and Dispersion

Match the solutions to the problems below. Write the letters of your answers in the blank spaces toward the bottom of the page. Your answers will spell out the names of the two mathematicians who are credited with the founding of probability theory.

Use the following data sets.

Data Set 1: 7, 11, 5, 9, 7, 19, 8, 13, 2

Data Set 2: 84, 78, 66, 93, 68, 72, 96, 88, 96, 89

1. the mean of Data Set 1 A. 7

2. the median of Data Set 1 C. 86

3. the mode of Data Set 1 E. 96

4. the maximum of Data Set 1 F. 30

5. the range of Data Set 1 L. 8

6. the mean of Data Set 2 M. 83

7. the median of Data Set 2 P. 19

8. the mode of Data Set 2 R. 9

9. the minimum of Data Set 2 S. 17

10. the range of Data Set 2 T. 66

and

4 3 5 7 3 2 10 8 1 6 3 9

P

R

L

A

P

S

M

C

E

T

F

A S C A L F E R M A T

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12-2 Puzzle: Order in the Court!Frequency and Histograms

A list of points scored by a basketball team is shown below.

97, 85, 91, 80, 108, 96, 104, 90, 111, 102, 97, 87, 105, 91

Match each exercise with the correct letter. Write the letters next to the exercise numbers on the basketball court below. Th en follow the direction of the arrows to complete the sentence underneath.

1. the frequency of points from 100 to 109 N. 3

2. the cumulative frequency of points from 100 to 109 S. 4

3. the frequency of points from 90 to 99 K. 6

4. the cumulative frequency of points from 110 to 119 T. 14

5. the minimum number of points A. 111

6. the frequency of points from 80 to 89 H. 9

7. the maximum number of points B. 80

8. the cumulative frequency of points from 90 to 99 O. 13

bank shotA occurs when the basketball bounces off the backboard and into the basket.

6. N

3. K

1. S

4. T

8. H

2. O

7. A

5. B

Prentice Hall Algebra 1 • Activities, Games, and PuzzlesCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

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Find and circle the following words in the puzzle below. Words appear vertically, horizontally, or diagonally. Words may read either forward or backward.

bias combination event factorial

frequency histogram independent matrix

median mode odds outlier

percentile population probability qualitative

quantitative quartile range sample

12-8 Puzzle: Hide-and-SeekProbability of Compound Events

I D J I B S N K O M L V Z P H R

S V R S E L I T R A U Q M M C G

W F E V I T A T I T N A U Q G X

V W B V R M A R G O T S I H L Q

I M H O I P O N I R Y N S J Y I

K D E H B T V T I C T Y E W C F

D V M O G E F N T E A F Y B E G

M O D S P M E U W L B U B K R X

C O E E D C O G U P O Q Q G F M

B L D Y R D U P N M R Q P B T V

W N U E B L O L W A P S K G W U

I E P G C P O R J S R G Y F E T

S V S D C E A X V N I E R V N P

H O M A I N N T E C L E T O E O

R T F W I A F D I I I Y I M U A

T T J B Z B N J T L B T R M Q F

12-7 Activity: Probability and AreaTheoretical and Experimental Probability

In this activity, you will use experimental probability to estimate area.

Th e grid at the right has 36 squares for a total area of 36 square units. Each square has a dot inside it. Th e coordinates of each dot are expressed by the ordered pair (column number, row number). For example, (5, 1) is the dot in the 5th column and 1st row of the grid. By rolling a number cube twice, you can randomly generate the coordinates of a dot.

1. Suppose you roll a number cube 18 times to generate the coordinates of nine dots: (1, 1), (2, 1), (2, 6), (3, 3), (3, 5),(4, 3), (5, 2), (5, 5), (6, 1). What is the experimental probability that a dot will be on or inside the circle?

2. To estimate the area of the circle, use the following formula.

estimated area 5 total area 3 experimental probability

What is the estimated area of the circle?

Roll a number cube 20 times until you generate the 10 coordinates of 10 diff erent dots. (Coordinates may appear more than once.) Estimate the area of each fi gure below by using the experimental probability that a dot is on or inside the fi gure. (To save time, use the same 10 ordered pairs for all exercises.) Th en select 10 more dots in each fi gure and estimate each area again. Compare your results with the actual area. Discuss your results with classmates.

3. 4.

5. 6.

6

5

1

1 65432

2

3

4

6

5

1

1 65432

2

3

4

6

5

1

1 65432

2

3

4

5

1

1 65432

2

3

4

5

1

1 65432

2

3

4

79

28 units2

Answers may vary.

Sample: 14.4 units2

Sample: 7.2 units2

Sample: 14.4 units2

Sample: 10.8 units2

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Th is is a game for three students. One student is the host, and two students are the players. Your teacher will provide the host with a separate sheet of questions and answers. Th e players use the gameboard below to play the game.

Rules • Decide who goes fi rst. One player is X and the other player is O. Players

alternate turns.

• Th e object of the game is to be the fi rst player to write four marks (X or O) in consecutive boxes horizontally, vertically, or diagonally.

• During your turn, select a number from the table. Th en the host asks a combination or permutation question corresponding to the number selected. (Note that the numbers do not refl ect the level of diffi culty of the questions.)

• Give an answer in a reasonable amount of time determined by your teacher. Th e answer must be given as a number. For example, if the answer is found by computing C4 2, you must give the number 6.

• If you answer correctly, write your mark (X or O) on the selected number.

• If you answer incorrectly, the other player has an opportunity to answer the question and write his or her mark on the number. If the other player also answers incorrectly, then the number is out of play and crossed out.

• If no player writes four marks consecutively, then the player with the most marks on the gameboard wins. Otherwise, the game ends in a tie.

12-6 Game: A Winning CombinationPermutations and Combinations

1 2 3 4 5

6

11

21

7 8 9 10

12 13 14 15

16 17 18 19 20

22 23 24 25

See Teacher Instructions page.

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12-6 Game: A Winning CombinationPermutations and Combinations

Provide the host with the following questions and answers.

1. How many positive three-digit numbers are possible by using each digit once? (Allow 0 as a fi rst digit.)

2. How many types of confetti can a party store make by selecting from 3 of 7 colors?

3. How many basketball teams of 5 diff erent positions are possible from 10 eligible players?

4. How many arrangements of 3 diff erent numbers are possible on a lock that uses 36 numbers?

5. In how many ways can you answer 6 out of 10 questions on a test? 6. How many triangles are possible by selecting any 3 points of a hexagon? 7. In how many ways can you rank 5 favorite TV shows from a sample of 10 shows?

8. In how many ways can you invite 3 of your 6 friends to dinner? 9. In how many ways can the judges of a contest award 3 prizes to 6 eligible contestants?

10. In how many ways can you put 4 party invitations into 4 envelopes? 11. How many four-letter computer passwords are possible from the letters A–Z and the

digits 0–9 without repeating any characters? 12. In how many ways can a sailboat captain choose 4 fl ags from 10 to hoist on a mast?

13. In how many ways can a boating club form a crew of 8 diff erent positions from 12 eligible club members?

14. How many schedules of 5 class subjects can you make from a selection of 12 subjects?

15. In how many ways can you arrange the letters of the word DISCOVERY? 16. How many varieties of pizza with two toppings can you make from eight toppings?

17. In how many ways can 4 students take their places in 6 seats on a bus? 18. How many musical arrangements of 3 notes can you play from 12 notes? 19. How many school committees of 3 persons (president, treasurer, and secretary) can your

teacher form from 8 eligible persons? 20. In how many ways can a teacher assign eight tutors to eight classes? 21. In how many ways can you choose 3 songs from a list of the top 10 songs? 22. In how many ways can you choose 5 friends from a group of 10 to wait in line at a movie

theater? 23. How many seven-digit cell phone numbers are possible with no repeated digits? (Allow

0 for a fi rst digit.) 24. In how many ways can 3 of your friends have diff erent birthdays? (Assume that there are

365 days in a year.) 25. How many relay teams of 4 persons can you make from a group of 10 runners if the order

is not important?

Answer: 720

Answer: 35

Answer: 30,240

Answer: 42,840Answer: 210

Answer: 20

Answer: 30,240Answer: 20

Answer: 120Answer: 24

Answer: 1,413,720

Answer: 5040

Answer: 19,958,400

Answer: 95,040Answer: 362,880

Answer: 28Answer: 360

Answer: 1320

Answer: 336Answer: 40,320

Answer: 120

Answer: 30,240

Answer: 604,800

Answer: 48,228,180

Answer: 210