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Understand the concept of probability and solve problems
D.PR.06.01 Express probabilities as fractions, decimals, or percentages between 0 and 1; know
that 0 probability means an event will not occur and that probability 1 means an event will occur.
D.PR.06.02 Compute probabilities of events from simple experiments with equally likely
outcomes, e.g., tossing dice, flipping coins, spinning spinners, by listing all possibilities and
finding the fraction that meets given conditions.
D.PR.08.03 Compute relative frequencies from a table of experimental results for a repeated
event. Interpret the results using relationship of probability to relative frequency.
D.PR.08.04 Apply the Basic Counting Principle to find total number of outcomes possible for
independent and dependent events, and calculate the probabilities using organized lists or tree
diagrams.
D.PR.08.05 Find and/or compare the theoretical probability, the experimental probability, and/or
the relative frequency of a given event.
D.PR.08.06 Understand the difference between independent and dependent events, and
recognize common misconceptions involving probability, e.g., Alice rolls a 6 on a die three times
in a row; she is just as likely to roll a 6 on the fourth roll as she was on any previous roll.
Unwrapping the GLCE’s:
Concepts (what students need to know):
 Basic Vocabulary such as: probability, event, experiment, outcome,
sample space, experimental probability, list, tree diagram, fair sides die,
and compute. (6th)
 0 probability means event will not occur. (6th)
 1 probability means event will occur. (6th)
 Anything in between is represented as fractions, decimals or percentages.
(6th)
 Probabilities of simple events. (6th)
 Vocabulary: complement, relative frequencies, theoretical probability,
counting principal, independent and dependent events, tree diagrams, and
list. (8th)
 Relative frequencies (8th)
 Difference between Independent and Dependent events. (8th)
 Theoretical and Experimental probability. (8th)
 Equally likely outcomes. (8th)
 Basic Counting Principal. (8th)
Skills (what students need to be able to do):
 Express probabilities as fractions, decimals, or percentages between 0-1.
(6th)
 Compute probabilities from simple experiments. (6th)
 Compute relative frequencies. (8th)
 Compare theoretical and experimental probability of a given event. (8th)
 Understand difference between independent and dependent events. (8th)
Big Ideas:
1. Understand that patterns do exist in seemingly random events. (6th)
2. Probability is the study of the likelihood of something happening. (6th)
3. It can be expressed as a fraction or a decimal from 0 to 1. (6th)
4. Probabilities of events may or may not depend on each other. (8th)
5. Basic Counting Principal. (8th)
6. How the outcomes are organized as either lists or tree diagrams. (8th)
Essential Questions:
1. What is probability?
2. What is an outcome of an event?
3. What is difference between theoretical and experimental probability?
4. How do you find the relative frequency of an event?
5. What is the difference between independent and dependent events?
6. What are the common misconceptions involving probability?
Post Assessment Questions:
1.
What is the probability of a number less than 4 showing when a number cube is
rolled?
A.
B.
C.
D.
2.
An event with a probability of
______.
A. is not very likely to occur
B. is certain to occur
C. cannot occur
D. is very likely to occur
3.
From left to right on the number line, order the events based on
how likely they are to occur.
a. The event is certain to happen.
b. The event is just as likely to happen as not to happen.
c. The event has no chance of happening.
d. The event could happen but is unlikely.
e. The event is likely to happen.
A.
C.
a, e, b, d, c
d, c, b, e, a
B.
D.
c, d, b, e, a
d, c, b, a, e
4.
Find the correct tree diagram for the flip of two coins.
A.
B.
C.
D.
5. In a standard playing deck of cards, what is the probability of drawing a Jack?
6. Find the relative frequency for the quiz scores in the 20-22 range.
Score
23-25
Quiz Scores
Tally
/////
20-22
///// /
6
17-19
////
4
14-16
///
3
11-13
//
2
Frequency
5
7. The list below shows the ages of the first 24 presidents at the time of inauguration
57
61
57
57
58
57
61
54
68
51
49
64
50
48
65
52
56
46
54
49
50
47
55
55
Using the following intervals, find the relative frequency of the ages of the presidents from
56-58.
(46-48), (49-51), (52-55), (56-58), (59-61), (62-65), (66-68)
8. A family has two children. Draw a tree diagram to show the sample space of the children’s genders.
Then determine the probability of the family having two boys.
9. Complete the following table which contains the sums when two number cubes are added
together after being tossed.
A. What is the number of times each sum appears in the table?
That is, how many 2's are there, how many 3's, etc.
B. Which sum appears most frequently?
C. What is the ratio of the most frequent sum to the total number of sums?
10. Toss a 4-sided number cube and a penny, which part of this experiment would be considered
the outcome? Explain?
A. 4-sided cube
B. 6-sided cube
C. 2 sided penny
D. 8 possibilities
Explanation:
11.
Post Assessment Scoring Rubric:
1. Answer: A
What is the probability of a number less than 4 showing when a number cube is
rolled?
A.
B.
C.
D.
2. Answer : D
An event with a probability of
______.
A. is not very likely to occur
B. is certain to occur
C. cannot occur
D. is very likely to occur
3. Answer: B
From left to right on the number line, order the events based on
how likely they are to occur.
a. The event is certain to happen.
b. The event is just as likely to happen as not to happen.
c. The event has no chance of happening.
d. The event could happen but is unlikely.
e. The event is likely to happen.
A.
C.
a, e, b, d, c
d, c, b, e, a
B.
D.
c, d, b, e, a
d, c, b, a, e
4. Find the correct tree diagram for the flip of two coins.
Answer: A
A.
B.
C.
D.
5. In a standard playing deck of cards, what is the probability of drawing a Jack? Express the
answer as a fraction, decimal, and as a percent. Round the decimal to the thousandths place.
Answer:
4 1
=
.077; 7.7%
52 13
7. Find the relative frequency for the quiz scores in the 20-22 range.
Score
23-25
Quiz Scores
Tally
/////
20-22
///// /
6
17-19
////
4
14-16
///
3
11-13
//
2
Answer:
Frequency
5
6
3

20 10
7. The list below shows the ages of the first 24 presidents at the time of inauguration
57
61
57
57
58
57
61
54
68
51
49
64
50
48
65
52
56
46
54
49
50
47
55
55
Using the following intervals, find the relative frequency of the ages of the presidents from
56-58.
(46-48), (49-51), (52-55), (56-58), (59-61), (62-65), (66-68) Answer:
6
1

24 4
8. A family has two children. Draw a tree diagram to show the sample space of the children’s genders.
Then determine the probability of the family having two boys.
Child One: Boy or Girl = each ½
Child Two: Boy or Girl = each ½
Answer : ½ * ½ = ¼
9. Complete the following table which contains the sums when two number cubes are added
together after being tossed.
A. What is the number of times each sum appears in the table?
That is, how many 2's are there, how many 3's, etc.
2) 1, 3) 2, 4) 3, 5) 4, 6)5, 7)6, 8)5, 9)4, 10)3, 11)2, 12)1
B. Which sum appears most frequently? 7 appears most
C. What is the ratio of the most frequent sum to the total number of sums?
1
36
10. Toss a 4-sided number cube and a penny, which part of this experiment would be considered
the outcome? Explain?
A. 4-sided cube
B. 6-sided cube
C. 2 sided penny
D. 8 possibilities
Explanation: Answer D: There are 8 possibilities because 4 possibilities for the number
cube times 2 possibilities for a penny, gives us 8 outcomes.
11.
Answer: A. Maggie is not correct. The probability of pulling a green marble is 3/10. There
are 6 out of 20 marbles and simplifies to 3/10.
B. Red Marble. There are 5 out of 20 red marbles so that simplifies to ¼.
C. She would need to add 1 red marble, and 3 yellow marbles. This would
make the total 24 marbles, and each color having 6 marbles. 6 out of 24 is
¼. They would now all have the same probability.
Pre-Assessment Questions:
1. If a letter in the word MICHIGAN is randomly selected, what is the probability of the
letter be selected being an “I” or an “A”?
2
8
3
B.
8
A.
C.
3
5
5
8
Liz is going to roll a fair six-sided number cube where each face is labeled with a
D.
2.
different numeral. If the numbers are 1 through 6, what is the probability she will roll a 3 on
the first roll?
A.
1
2
B.
1
3
C.
1
5
D.
1
6
3. Toss a four sided number cube, and a penny. Make a list to show the number of outcomes.
4. A bag contains 7 blue, 5 purple, 12 red, and 6 orange marble. Find each probability if you
draw one marble at random from the bag. Write as a fraction in simplest form.
A. P(red or orange) =
7. Use spinner below to find each probability. Write as a fraction in simplest form.
A. P(Green)
B. P(Purple or Orange)
6. Colin rolls a number cube 20 times with the following results: 3, 5, 1, 2, 3, 6, 1, 2, 5, 3, 1, 5,
5, 6, 6, 1, 1, 4, 2, 2. What is the relative frequency of the number 5?
A.
B.
C.
D.
7. A vendor has 14 helium balloons for sale: 9 are yellow, 3 are red, and 2 are green. A balloon is
selected at random and sold. If the balloon sold is yellow, what is the probability that the next
balloon, selected at random, is also yellow?
A.
8
13
B.
9
13
C.
5
14
D.
8
14
E.
9
14
8. Suppose Brooke tosses three quarters. Find the probability that all three will show heads.
A.
B.
C.
D.
9. An ice cream sundae at Bliss Dairy is made from one flavor of ice cream and one topping. For
ice cream flavors, you can choose from chocolate, vanilla and strawberry. For toppings you can
have hot fudge, butterscotch or caramel. Find the number of different sundaes that are possible.
A.
B.
C.
D.
6
8
9
18
10. Hayleigh rolls two number cubes. She can move her game piece if a sum of 5 is shown on the
number cubes, or if a 5 is shown on at least one number cube. What is the probability that she
can move her game piece on one roll of the number cubes?
A.
B.
C.
D.
Pre-Assessment Scoring Rubric:
1. If a letter in the word MICHIGAN is randomly selected, what is the probability of the letter
be selected being an “I” or an “A”? Answer: B
2
8
3
B.
8
A.
C.
3
5
5
8
Liz is going to roll a fair six-sided number cube where each face is labeled with a
D.
2.
different numeral. If the numbers are 1 through 6, what is the probability she will roll a 3 on
the first roll? Answer: D
A.
1
2
B.
1
3
C.
1
5
D.
1
6
3. Toss a four sided number cube, and a penny. Make a list to show the number of outcomes.
Cube: #1- H #1-T; #2-H #2-T; #3-H, #3-T; #4-H, #4-T; #5-H #5-T #6-H, #6T
8 Outcomes.
4. A bag contains 7 blue, 5 purple, 12 red, and 6 orange marble. Find each probability if you
draw one marble at random from the bag. Write as a fraction in simplest form.
3
A. P(red or orange) =
5
5.Use spinner below to find each probability. Write as a fraction in simplest form.
1
A. P(Green)=
5
B. P(Purple or Orange)=
2
5
6. Colin rolls a number cube 20 times with the following results: 3, 5, 1, 2, 3, 6, 1, 2, 5, 3, 1, 5,
5, 6, 6, 1, 1, 4, 2, 2. What is the relative frequency of the number 5? Answer:B
A.
B.
C.
D.
7. A vendor has 14 helium balloons for sale: 9 are yellow, 3 are red, and 2 are green. A balloon is
selected at random and sold. If the balloon sold is yellow, what is the probability that the next
balloon, selected at random, is also yellow? Answer: A
A.
8
13
B.
9
13
C.
5
14
D.
8
14
E.
9
14
8. Suppose Brooke tosses three quarters. Find the probability that all three will show heads.
Answer:B
A.
B.
C.
D.
9. An ice cream sundae at Bliss Dairy is made from one flavor of ice cream and one topping. For
ice cream flavors, you can choose from chocolate, vanilla and strawberry. For toppings you can
have hot fudge, butterscotch or caramel. Find the number of different sundaes that are possible.
Answer: C
A.6
B. 8
C. 9
D. 18
10. Hayleigh rolls two number cubes. She can move her game piece if a sum of 5 is shown on the
number cubes, or if a 5 is shown on at least one number cube. What is the probability that she
can move her game piece on one roll of the number cubes? Answer: B
A.
B.
C.
D.
INSTRUCTIONAL LESSON AND ACTIVITIES:
Day One:
TITLE:
AUTHOR:
PROBABILITY:
The Study of Chance
Shirley LeMoine , Garfield Re-2 School District,
Rifle, Co.
GRADE LEVEL/SUBJECT: Appropriate for grades 5-12
Math , Integrated studies, science
OVERVIEW: The theory of probability is an important branch of
mathematics with many practical applications in the physical, medical,
biological and social sciences. An understanding of this theory is
essential to understand weather reports, medical findings, political
doings and the state lotteries. Students have many misconceptions about
probability situations.
PURPOSE: The purpose of this activity, is to begin the process of helping
students to learn the basic principles of probability.
OBJECTIVES: As a result of this activity the student will:
1. conduct an experiment
2. determine if a game is "fair"
3. collect data (table)
4. interpret data ( range, mode, median)
5. display data (line graph)
6. conduct analysis of game ( tree diagram)
7. state and apply the rule (definition)for probability
RESOURCES, MATERIALS:
pencils, paper.
overhead grid, overhead,
ACTIVITIES AND PROCEDURES:
1. introduce activity with a demonstration of game: rock, scissors, paper.
2. divide class into pairs (player A and player B) and have them play the
game 18 times.
3. use overhead graph grid to graph the wins of player A in red (how many
A players won one game, two games etc.) Do the same for all B players in
a different color.
4. Help students determine range, mode and mean for each set of data.
Compare the results.
5. Do a tree diagram to determine the possible outcomes.
6. Answer the following questions to determine if the game is fair.
a. How many outcomes does game have ? (9)
b. Label each possible outcome on tree diagram as to win for A, B or
c.
d.
e.
f.
g.
tie.
Count wins for A (3)
Find probability A will win in
Explain what probability means
outcomes
Count wins for B (3)
Find probability B will win in
Is game fair? Do both players
in any round? (yes)
any round (3/9=1/3)
favorable outcomes/ possible
any round (3/9)
have an equal probability of winning
7. Compare the mathematical model with what happened when the
students played the game.
TYING IT ALL TOGETHER:
1. Use this as an introduction to a unit on probability.
2.
Follow-up with discussion about how probability is used in world.
3.
Play game again using 3 students. Using the following rules:
1. A wins if all 3 hands are same.
2. B wins if all 3 hands are different.
3. C wins if 2 hands are same.
There will be 27 outcomes this time. 3 to the third
power. 3*3*3=27
Day Two:
Phenomenological Probability
Robert Foote
Disney Magnet School
4022 N. Monticello
ChicagoIL 60618
(312) 604-8825
4140 N. Marine Drive
Chicago IL 60613
(312) 534-5844
Objective:
Students will find the difference between theoretical and experimental
probability in three different experiments. This mini-teach is designed for
junior high students.
Materials Needed:
* A pair of dice for each student
* Ten or more colored marbles and a spinner (or bag)
* A standard deck of 52 cards.
Strategy:
Set up three stations with the materials mentioned above at each station.
Give students about twenty minutes for each activity. Blow a whistle or clap
between each activity and then have groups switch activities. The following
is a description of each activity:
1. Rolling Two Dice: Have each student roll two dice 20 times and record
each sum. When the experiment is completed, have each student come up with a
groupprobability by combining the individual experiments. Experimental
probability is the number of times a sum is rolled divided by the number of
rolls (20).
2. Marbles in a Spinner: For this experiment, I used a spinner that allowed
one marble to land in a space on the spinner. You may do the same experiment
without the spinner using a bag and having students pick a marble out of the
bag 20 times. Make sure you have different color marbles of different
amounts so you have different probabilities for each color. Compute
experimental probability by keeping track of how many of each color are
picked or land in the spinner. Experimental probability here is the number
of the color picked divided by the total marbles picked.
3. Card Trick: Have each student in the group pick a card from the deck,
shuffle the cards and pick another card five times. The student will pick a
total of five cards. To determine experimental probability, find the desired
outcome such as number of face cards, over the total numbers of cards drawn.
After all the experiments are performed and experimental probabilities are
found, compare them to the theoretical probabilities of each experiment. You
may determine how close the two are as fractions, decimals, and percents.
Performance Assessment:
An easy performance assessment of this lesson would be to use the same
experiments with slight modifications such as adding one die,more marbles,or
changing the card events. You can thus assess student understanding of
probability using the experiments and have them compute them on their own by
writing up their own calculations from the experiment and comparing them to
the theoretical probability.
Day Three:
Do some online activities to help students find probability.
Rock, Paper Scissors Game Interactive
http://www.howe-two.com/free/PaperStoneScissors/index.html
Adjustable spinner
http://www.shodor.org/interactivate/activities/AdjustableSpinner/
Coin toss
http://www.shodor.org/interactivate/activities/coin/
Interactive Web Site to demonstrate experimental and theoretical probability
http://www.shodor.org/interactivate/activities/CrazyChoicesGame/
Marble simulation (w/ replacement and w/o replacement)
http://www.shodor.org/interactivate/activities/Marbles/
Day Four:
Teacher Preparation
Website : http://www.shodor.org/interactivate/lessons/TreeDiagramsProb/
Students will need:


Access to a browser
Pencil and paper
Key Terms
compound
event
conditional
probability
Two or more events that happen simultaneously
Conditional probability is the probability of an event occurring given that
another event also occurs. It is expressed as P(A/B). It reads "Probability of
Event A on condition of Event B." P(A/B) = P(A and B)/P(B), where P(B) is the
probability of event B and P(A and B) is the joint probability of A and B
1. Focus and Review
Remind students what has been learned in previous lessons such as concepts of
probability. Possibly use the example of rolling a die and the chances of that die rolling a
specific number is 1/6. Ask students what the probability is of rolling a 1 or a 2. Mention
the difference between the experimental probability and the theoretical probability. You
can even have the students roll dice themselves, collect data for the class and figure the
experimental probability for the class.
2. Objectives
Let the students know what it is they will be doing and learning today. Say something
like this:
o
Today, class, we will be talking more about probability and how to determine the
probability of multiple events, known as compound events. We will learn how to
create tree diagrams to determine the probabilities related to compound events.
o
We are going to use the computers but please do not turn your computers on
until I ask you to. I want to show you a little about the program first.
3. Teacher Input
Lead the students in a short discussion on trees as data structures.
Explain to the students how to do the assignment. You should model or demonstrate it
for the students, especially if they are not familiar with how to use our computer applets.
o
Open your browser to Racing Game with One Die in order to demonstrate this
activity to the students.
o
Demonstrate some of the functionality yourself such as changing the length of
the race, changing the game to an unfair race, and demonstrating how the
multiple run panel works.
4. Guided Practice
Discuss and draw a tree diagram for a one-step and a two-step fair race. If you have a
white board it is helpful to use a red and a blue marker to represent the two different
colored cars.
Make the race an unfair race by making the blue car move on rolls of 1 and 2 and the
red car move on rolls of 3, 4, 5, and 6.
Draw a tree diagram for a one-step unfair race. Mention that the sum of the end
probabilities always equal one, which makes them complementary probabilities. Discuss
why this must be so.
Ask the students to go to their computers and create an unfair race as described above.
In the multiple-run panel change the number of runs to 50,000. Have students run this
configuration 5 or 6 times. Ask them to develop a hypothesis as to what the theoretical
probability of an unfair two-step is based on the experimental data using the applet.
5. Independent Practice
Have the students create a tree diagram for an unfair two-step race to determine the
theoretical probability.
Have them show, based on their diagrams, the sum of the final probabilities equal one
demonstrating they are complementary probabilities.
6. Closure
You may wish to bring the class back together for a discussion and verification of their
findings. Once the students have been allowed to share what they found, summarize the
results of the lesson.
Alternate Outlines
If there is only one available computer, place the students in groups of two or three. Run the
multiple races yourself and have them develop the hypothesis with their partners.
Day Five: Can be done again or just use the activities.
Website: http://www.shodor.org/interactivate/lessons/ConditionalProb/
Abstract
This lesson is based on several interesting problems. Each problem has a somewhat
unexpected answer; in fact, many people have a hard time accepting experimental results for
these problems, as the results may seem counterintuitive. This very difference in expectations
and actual results leads to a deeper consideration of the related mathematics and to acquiring
new tools for solving problems, namely the ideas and formulas connected with conditional
probability and probability of simultaneous events.
Objectives
Upon completion of this lesson, students will:


have taken a closer look at conditional probability
have learned the formula for probability of simultaneous independent events
Standards Addressed:
Student Prerequisites


Arithmetic: Student must be able to:
o use addition, subtraction, multiplication and division to solve probability formulas
o understand how tables can be used in multiplication
Technological: Students must be able to:
o perform basic mouse manipulations such as point, click and drag
o use a browser for experimenting with the activities
Teacher Preparation
Students will need:

Please select a standards alignment
Access to a browser


Pencil and paper
Copies of supplemental materials for the activities:
o For the Racing Game with One Die activity:
 one six-sided die
 Racing Game Worksheet
 The Racing Game Table to tally game results
o
For the Two Colors game:
 three identical containers (e.g., small boxes or opaque cups)
 six objects of two different colors (three of each color), such as marbles or
poker chips. (The objects have to fit in the containers and have to be
indistinguishable from each other by touch.)
 Two Colors Worksheet
 The Two Colors Table to tally the results
o
For the Monty Hall activity:
 Three identical index cards
 Monty Hall Worksheet
 The Table to tally the results
Key Terms
experimental
probability
The chances of something happening, based on repeated testing and
observing results. It is the ratio of the number of times an event occurred to
the number of times tested. For example, to find the experimental probability
of winning a game, one must play the game many times, then divide the
number of games won by the total number of games played
probability
The measure of how likely it is for an event to occur. The probability of an
event is always a number between zero and 100%. The meaning
(interpretation) of probability is the subject of theories of probability.
However, any rule for assigning probabilities to events has to satisfy the
axioms of probability
random
number
generators
A device used to produce a selection of numbers in a fair manner, in no
particular order and with no favor being given to any numbers. Examples
include dice, spinners, coins, and computer programs designed to randomly
pick numbers
theoretical
probability
The chances of events happening as determined by calculating results that
would occur under ideal circumstances. For example, the theoretical
probability of rolling a 4 on a four-sided die is 1/4 or 25%, because there is
one chance in four to roll a 4, and under ideal circumstances one out of every
four rolls would be a 4. Contrast with experimental probability
1. Focus and Review
Remind students what has been learned in previous lessons that will be pertinent to this
lesson and/or have them begin to think about the words and ideas of this lesson
o
o
o
o
If I bet you that we could play a game and that I could win every time, would you
believe me?
This game is a racing game in which we take turns rolling a six sided die and
advancing on the numbers that we each are assigned. I bet you I can assign us
an equal quantity of numbers that we move on and no matter how many times
we play I will always win.
Then tell them that the numbers that you assign yourself are 1, 2, 3, 4, 5, and 6,
while the numbers you assign the person who takes you up on your bet are 7, 8,
9, 10, 11, and 12. (If you are only playing with one die then it is impossible to roll
anything higher than a 6 so the person assigned 6 -12 will never move.)
Who thinks this game is fair?
2. Objectives
Let the students know what it is they will be doing and learning today. Say something
like this:
o
o
Today, class, we are going to begin learning about probability
We are going to use the computers to learn about probability, but please do not
turn your computers on until I ask you to. I want to show you a little about this
activity first.
3. Teacher Input
o
Begin by describing the Racing Game with one die Conditional Probability and
Probability of Simultaneous Events.
4. Guided Practice
o
o
o
o
Have groups of students play the Racing Game with one die either using the
software (preferably) or rolling a six-sided die and using the Table to tally the
results.
Players in the game should have unequal chances to take a step. Knowing the
probability of each player taking a step, students can try to predict the probability
of each player winning the game, and try multiple experiments in order to test the
prediction.
Lead a discussion about the Probability of Simultaneous Events to introduce the
formula for probability of simultaneous independent events.
This discussion is based on the results of the Racing Game with one die. Each
group of students can think about and discuss the following questions, later
discussing them with other groups and with their mentor:
1. The experimental probability of winning the game is not the same as the
probability of taking one step. Why?
2. What would happen to the probabilities if there were more than two steps
to the finish.
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Next, initiate a discussion based on Conditional Probability. This discussion
requires the active participation of the mentor. If there are students who want to
take on the role of mentors, they can read the discussion ahead of time in order
to prepare. This way discussions can happen in smaller groups.
5. Independent Practice
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Have the students use the Two Colors game to perform experiments that will
demonstrate conditional probability.
There are three closed boxes. One box contains two green balls, another one
contains two red balls and the last one has one red and one green ball. If
students use the software, the computer will shuffle the boxes. If students use
manipulatives, one of them should shuffle the boxes. A student chooses one box
and picks one ball from it (without looking). If the first ball is red, the game starts
over. If the first ball is green, the student wins if the second ball in the same box
is also green.
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Groups of students can play the game many times, first trying to predict or guess
their chances of winning, and keeping track of the results using the Table.
6. Closure
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You may wish to bring the class back together for a discussion of the findings.
Once the students have been allowed to share what they found, summarize the
results of the lesson.
Alternate Outlines
This lesson can be rearranged in several ways.
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Include the Monty Hall problem to further clarify conditional probability. Each student or
group of students can try to solve the problem and explain the solution. Then they can
run the experiments on computers or by hand (in the latter case, recording the results in
the Table), comparing experimental data with their solutions. Groups of students can
discuss why their theoretical answers agree or do not agree with the data.
Use the Think and Check! discussion to help students understand the explanation of the
Monty Hall problem and the Two Colors Game.
Combine this lesson with the Unexpected Answers lesson.
Or choose fewer of the activities to cover; for example, use only the Racing Game with
One Die and the Conditional Probability discussion and make the focus conditional
probability only. Use the Probability of Simultaneous Events discussion somewhere else
in the Probability unit.
Have students come up with their own version of the Two Colors game, and present
their game and probability results to the class.
Day Six: Can do more activities online. Here are some more websites.
Game of Skunk: http://illuminations.nctm.org/LessonDetail.aspx?ID=L248
Interactive Spinner: http://illuminations.nctm.org/ActivityDetail.aspx?id=79
Boxing Up: http://illuminations.nctm.org/ActivityDetail.aspx?id=67
INTERACTIVE RESOURCES:
Website for questions for probability
http://mathassessments.mscenters.org
Spinner downloadable
http://nlvm.usu.edu/en/nav/frames_asid_186_g_2_t_5.html?open=activities
Interactive Spinner
http://www.shodor.org/interactivate/activities/BasicSpinner/
Rock, Paper Scissors Game Interactive
http://www.howe-two.com/free/PaperStoneScissors/index.html
Adjustable spinner
http://www.shodor.org/interactivate/activities/AdjustableSpinner/
Coin toss
http://www.shodor.org/interactivate/activities/coin/
Interactive Web Site to demonstrate experimental and theoretical probability
http://www.shodor.org/interactivate/activities/CrazyChoicesGame/
Marble simulation (w/ replacement and w/o replacement)
http://www.shodor.org/interactivate/activities/Marbles/
“In All Probability” Investigations in Probability and Statistics Teacher’s Guide Grades 3-6
ISBN: 0-924886-03-X