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Easy Money - Is it so Easy by rps19132

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									                                                    Easy Money – Is it
                                                        so Easy?


         Author                                    Jennifer Hoffman
Identified Grade/Course                                7th Grade
Mathematical Concepts                                 Probability
         of Focus
    PASS Objectives                          2.1b, 2.2b, 2.2c, 5.1, 5.2*, 5.3
   Lesson Summary       The lesson will reinforce concepts such as changing fractions to
                        decimals, changing decimals to percents, and rounding skills. This
                        is a good project for students to review data analysis and to
                        introduce probability. It could also be used as a cross-curriculum
                        lesson to stress the importance of budgeting. This lesson allows the
                        students to apply what they have learned to real life situations. The
                        students will be given background knowledge on the Pick 3 lotto
                        and have an understanding of how it is played. The students will
                        then be asked to do the following:
                        1. Determine probability of winning (with numbers in order)
                        2. Determine probability of winning (playing front 2 numbers)
                        3. Determine probability of winning (playing back 2 numbers)
                        4. Determine probability of winning (with numbers out of order)

 Placement within Unit     Review of data analysis and introductory to probability.
   Materials Needed        FAKE lottery tickets, Ping Pong balls (at least one set number 0 –
                           9), Container to put Ping Pong balls in
  Problem Situation      With the lottery being an up and coming form of entertainment and
    (for students)       a possible way to fortune it is very interesting to many people.
                         Suppose you were of age to buy a $1 ticket that could win you $500
                         or more. Would it be worth it? Would it be “easy money” or would
                         it be a risk you might not want to take. Below is a portion of a
                         pickslip that is similar to the Pick 3 lotto ticket. Use the ticket to
                         answer the following questions.

                                                           PANEL A

                                                 PICK 3              $1.00

                                                               PLAY TYPE

                                                0 0 0       STRAIGHT
                                                            (EXACT ORDER)
                                                 1 1   1

                                                2 2 2       BOX
                                                            (ANY ORDER)
                                                3 3 3

                                                4 4 4       FRONT PAIR
                                                            (EXACT ORDER)
                                                5 5 5

                                                6 6 6       BACK PAIR
                                                            (EXACT ORDER)
                                                7 7 7

                                                8 8 8       EASY PICK

                                                9 9 9       VOID



Questions for Students   1. What is the theoretical probability of matching the numbers you
                         choose in order. If you won you could win $500 (Example: You
                         choose 1 2 3 in the STRAIGHT box and those numbers are drawn
                         exactly.)

                         2. Based on the theoretical probability what is the probability of
                         someone in your class winning playing the STRAIGHT box?

                         3. Choose 3 numbers in the STRAIGHT box. You may choose the
                         same number more than once or you may choose 3 different
                         numbers. For you to win in this box you must match all 3 numbers.
                         You would win $500. Your teacher will now play the lottery with
                         you by randomly drawing numbers for each of the three boxes. Did
                         you win? Did any of your classmates win? What is the
                         experimental probability of winning?

                         4. Find the theoretical probability of winning if you were to choose
                         two numbers in the FRONT PAIR box. You would win $50.

                         5. Based on the theoretical probability what is the probability of
                         someone in your class winning playing the FRONT PAIR?
                   6. Choose 3 numbers in the FRONT PAIR box. You may choose
                   the same number more than once or you may choose 3 different
                   numbers. For you to win the FRONT PAIR you only have to match
                   the first two numbers. Your teacher will now play the lottery with
                   you by randomly drawing numbers for each of the three boxes. Did
                   you win?
                   Did any of your classmates win? What is the experimental
                   probability of winning?

                   7. Find the theoretical probability of winning if you were to choose
                   two numbers in the BACK PAIR box. You would win $50.

                   8. Based on the theoretical probability what is the probability of
                   someone in your class winning playing the BACK PAIR?

                   9. Choose 3 numbers in the BACK PAIR box. You may choose the
                   same number more than once or you may choose 3 different
                   numbers. For you to win the BACK PAIR you only have to match
                   the last two numbers. Your teacher will now play the lottery with
                   you by randomly drawing numbers for each of the three boxes. Did
                   you win?
                   Did any of your classmates win? What is the experimental
                   probability of winning?

                   10. Based on your findings with theoretical and experimental
                   probability of winning for the STRAIGHT, FRONT PAIR, and the
                   BACK PAIR would it be worth spending money on a ticket?

Sample Solutions         1 1 1    1   1
                   1.     ! ! = 3=       = .001 or .1%
                        10 10 10 10 1000

                       1
                   2.     ! # of students in class = number of students who would win
                     1000
                   Number of students who would win = % who should win
                   Number of students in classroom


                   3.      Number of students who win
                           Number of students in class

                            1 1   1  1
                   4.        ! = 2 =    = .01 or 1%
                           10 10 10 100
                             1
                         5.     ! # of students in class = number of students who would
                            100
                         win

                         Number of students who would win = % who should win
                          Number of students in classroom



                         6.    Number of students who win
                               Number of students in class

                               1 1   1  1
                         7.     ! = 2 =    = .01 or 1%
                              10 10 10 100

                             1
                         8.     ! # of students in class = number of students who would
                            100
                         win

                         Number of students who would win = % who should win
                         Number of students in classroom

                         9.             Number of students who win
                                        Number of students in class

                         10. Students should find that the odds are against them when buying
                         lottery tickets.
     Scaffolding             • What is theoretical probability?
(Supporting) Questions       • What is experimental probability?
                             • How do you find probability?
 Extension Questions     1. Compare and contrast the theoretical and experimental
                         probabilities. Why are the so different? What would make them
                         more alike?
                                  Theoretical probability is not based on a set number of
                         people whereas experimental is. In this situation theoretical
                         probability looks better than experimental. They might look more
                         alike if there were more students in the class.

                         2. On a complete Pick 3 ticket you are given 5 Panels to play off of.
                         This means that you could play the STRAIGHT 5 times as well as
                         the BOX, FRONT PAIR, and BACK PAIR. Each panel costs $1 to
                         play so you could possibly pay $5 to play all 5 panels.
                         Would this increase the theoretical probability of winning playing
                         the STRAIGHT? If yes, how?
                          Yes,
                      1    1     1   1    1    5
                        +      +   +   +    =     = .005 or .5%
                    1000 1000 1000 1000 1000 1000

                    3. The BOX option on the ticket means that you can play Box 3-
                    Way or Box 6-Way. If you play Box 6-Way the numbers can be
                    rearranged in any order to win. If you chose your three favorite
                    numbers, how many ways could they be arranged to win?

                    Six possible ways.

                    4. Find the theoretical probability of winning if you were to choose
                    your three favorite numbers in the BOX 6-Way.

                      6
                         = .006 or .6%
                    1000

                    5. Choose 3 numbers in the BOX (any order). You would win $80.
                    Your teacher will now play the lottery with you by randomly
                    drawing numbers for each of the three boxes. Did you win? Did
                    any of your classmates win? What is the experimental probability
                    of winning?

                           Number of students who win
                           Number of students in class


Other Information   References:
                    OK Lottery: http://www.lottery.ok.gov/pick3.htm

								
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