Coin Tossing: Teacher-Led Lesson Plan
Subject/Strand/Topic: Math – Data Management &
Probability
Key Concepts:
Grade(s) / Course(s):
7
Ontario Expectations:
7m85, 7m86
probability of tossing a coin
Link: http://nlvm.usu.edu/en/nav/frames_asid_305_g_3_t_5.html
Required Materials: Pre-Assessment/Answer Key, Teacher-Led Handout, Teacher-Led Handout Answer Key,
Post-Assessment/Answer Key, calculators, pencils
Before Starting: sign out the data projector and ensure you have an internet connection in the classroom;
students should be familiar with probabilities
Introduction (~ 10 minutes including pre-assessment)
1.
2.
3.
4.
Introduce topic (determining probability of flipping heads or tails on a coin)
Distribute pre-assessment; allow 5-7 min. for students to complete
Using a coin, quickly have students predict whether or not you’ll toss a heads or tails
Introduce activity to students (looking at experimental and theoretical probabilities of flipping heads or tails for a
certain number of trials)
Use of Learning Object with Handout (~ 20 - 40 minutes)
1.
2.
3.
4.
5.
6.
7.
8.
9.
Distribute handout for each student to complete; briefly go over the structure of the handout
Open above link and have displayed on data projector
Discuss the format of the experiment (teacher-led, student participation)
Go through the meaning of each subtitle on the screen before beginning the experiment (e.g. probability of
heads, number of tosses, number of heads, etc. – ignore longest runs and chance error)
You will perform the four coin toss/three free throw experiments as a class and then individual students may
come to the front and enter in their own coin toss/free throw values for the last row in their tables
Make sure students make their predictions BEFORE you run each experiment! Give them 10 seconds to
fill in the prediction part of their tables
Press “Clear” after each set of coin tosses/free throws
Students may answer the questions with a partner
Ask the following questions throughout the experiments:
a. Could we use this learning object to calculate the probability of rolling a 3 on a die? Why or
why not? (no, because there are 5 other possibilities when rolling a die, whereas there are only
two options for flipping a coin or sinking a free throw)
b. Coby Bryant sinks 60% of his three point shots in a basketball game. Why do you think this
probability lower than him sinking free throws? (there is nothing between Coby and the basket,
all other players are still and away from him, he has more concentration, he doesn’t have to dribble
around players, a free throw is set up, etc.)
Consolidation (~ 10 minutes including post-assessment)
1. Ask students the following questions:
a. What do you expect to happen as you increase the number of trials? (the experimental
probabilities get closer to the theoretical probabilities – flipping a heads or tails gets closer to 50%)
b. What are some other real-life applications of probabilities? (hockey pools - teams winning or
losing, weather – rain or shine, stock market, probability of flaws in manufactured goods on an
assembly line, etc.)
2. Distribute post-assessment; allow 5-7 min. for students to complete
3. Take up answers from questions on handout as a class if need be
© 2007 University of Ontario Institute of Technology (UOIT) ~ Permission to Copy
Teacher-Created Resources: Teacher-Led Lesson Plan
Page 1 of 1
Coin Tossing
Teacher-Led Lesson Pre-Assessment
Name: ___________________________
Birthday: ____________________________
Instructions: Answer the following questions to the best of your ability. You may use a calculator. Good luck!
1. Out of 10 coin tosses, 2 showed up as heads and 8 showed up as tails.
a) What is the theoretical probability of flipping tails in a single coin toss? (3 marks)
b) What was the experimental probability of flipping tails? (3 marks)
c) How many tails should have been flipped, based on the theoretical probability? (2 marks)
2. Brian just purchased a lottery ticket. The odds of him winning are 1 out of 1,310.
a) What is the probability of Brian winning the lottery? Express your answer as a percentage. (3 marks)
b) What is the probability of Brian losing the lottery? Express your answer as a percentage. (2 marks)
© 2007 University of Ontario Institute of Technology (UOIT) ~ Permission to Copy
Teacher-Created Resources: Teacher-Led Lesson Pre-Assessment
13
Coin Tossing
Teacher-Led Lesson Pre-Assessment
Answer Key
Name: ___________________________
Birthday: ____________________________
13
Instructions: Answer the following questions to the best of your ability. You may use a calculator. Good luck!
1. Out of 10 coin tosses, 2 showed up as heads and 8 showed up as tails.
a) What is the theoretical probability of flipping tails in a single coin toss? (3 marks)
In one flip, the chance of flipping a head is equal to that of flipping a tail. So, in one flip,
there is the chance of two outcomes:
1/2 = 1 ÷ 2 9
= 0.500 9
0.500 x 100% = 50% 9
b) What was the experimental probability of flipping tails? (3 marks)
8/10 = 8 ÷ 10 9
= 0.80 9
0.80 x 100% = 80% 9
c) How many tails should have been flipped, based on the theoretical probability? (2 marks)
50% x 10 flips
= 0.50 x 10 flips 9
= 5 flips 9
2. Brian just purchased a lottery ticket. The odds of him winning are 1 out of 1,310.
a) What is the probability of Brian winning the lottery? Express your answer as a percentage. (3 marks)
1/1310 = 1 ÷ 1310 9
= 0.00076 9
0.00076 x 100% = 0.076% 9
b) What is the probability of Brian losing the lottery? Express your answer as a percentage. (2 marks)
Probability of losing = 100% - Probability of winning
= 100% - 0.076% 9
= 99.924 9
© 2007 University of Ontario Institute of Technology (UOIT) ~ Permission to Copy
Teacher-Created Resources: Teacher-Led Lesson Pre-Assessment
Coin Tossing
Teacher-Led Lesson Handout
Name: _____________________________
Date: ______________________________
50
Link: http://nlvm.usu.edu/en/nav/frames_asid_305_g_3_t_5.html
Instructions: Please follow through this handout as your teacher goes through the learning object titled “Coin
Tossing.”
PART A - Coin Tossing Experiment
•
As a class, your task is to compute the experimental and theoretical probabilities of flipping heads or tails in a
virtual coin toss experiment.
EXPERIMENTAL RESULTS
•
Please fill in the following table as you perform several coin tossing experiments as a class. Make sure to record
your predictions before each trial of coin tosses! (8 marks)
PREDICTION
COIN TOSSES
# of Heads
ACTUAL OUTCOME
# of Tails
# of Heads
# of Tails
10
20
50
100
•
For the last column in the table above, choose a number of coin tosses that is between 100 and 1000 and enter it
into the learning object. Record your results in the table above. (2 marks)
•
Record the experimental probabilities for heads in each trial from the results on the projector screen (beside
“Percentage of Heads”) in the table below. Use the experimental probabilities for heads to find those for tails. (10
marks)
COIN TOSSES
Experimental Probability (Heads)
Experimental Probability (Tails)
10
20
50
100
© 2007 University of Ontario Institute of Technology (UOIT) ~ Permission to Copy
Teacher-Created Resources: Teacher-Led Lesson Handout
Page 1 of 3
Coin Tossing
Name: _____________________________
Date: ______________________________
Teacher-Led Lesson Handout
QUESTIONS
•
What is the theoretical probability of flipping tails in a single coin toss? Express your answer as a percentage. (3
marks)
•
What do you notice about the experimental probabilities as you increase the number of coin tosses? (1 mark)
•
How do you think the probabilities would change if a coin had three sides (heads/tails/toes)? (1 mark)
PART 2: Applications
•
Coby Bryant can sink 80% of his free throws. As a class, you will compute the experimental
probability of Coby sinking a free throw shot in a basketball game.
EXPERIMENTAL RESULTS
•
Please fill in the following table as you perform several “free throw” experiments as a class. Make sure to record
your predictions before each trial of free throws! (6 marks)
PREDICTION
FREE THROWS
# of Baskets
# of Misses
ACTUAL OUTCOME
# of Baskets
# of Misses
10
20
40
•
For the last column in the table above, choose a number of free throws that is between 40 and 100 and enter it
into the learning object. Record your results in the table above. (2 marks)
© 2007 University of Ontario Institute of Technology (UOIT) ~ Permission to Copy
Teacher-Created Resources: Teacher-Led Lesson Handout
Page 2 of 3
Coin Tossing
Teacher-Led Lesson Handout
•
Name: _____________________________
Date: ______________________________
Record the experimental probabilities for baskets (i.e. heads on the screen) in each trial from the results on the
projector screen (beside “Percentage of Heads”) in the table below. Use the experimental probabilities for sunken
baskets to find those for missed baskets. (8 marks)
FREE THROWS
Experimental Probability (Baskets)
Experimental Probability (Misses)
10
20
40
QUESTIONS
•
What is the theoretical probability of Coby missing the basket? Express your answer as a percentage. (3 marks)
•
What do you notice about the experimental probabilities as you increase the number of free throws? (1 mark)
•
List some variables that could affect Coby’s free-throwing capabilities. (3 marks)
•
Why do you think the experimental probabilities usually differ from the theoretical probabilities? (2 marks)
© 2007 University of Ontario Institute of Technology (UOIT) ~ Permission to Copy
Teacher-Created Resources: Teacher-Led Lesson Handout
Page 3 of 3
Coin Tossing
Name: Answer Key for Teacher
Teacher-Led Lesson Handout Answer Key
50
Link: http://nlvm.usu.edu/en/nav/frames_asid_305_g_3_t_5.html
Instructions: Please follow through this handout as your teacher goes through the learning object titled “Coin
Tossing.”
PART A - Coin Tossing Experiment
•
As a class, your task is to compute the experimental and theoretical probabilities of flipping heads or tails in a
virtual coin toss experiment.
EXPERIMENTAL RESULTS
•
Please fill in the following table as you perform several coin tossing experiments as a class. Make sure to record
your predictions before each trial of coin tosses! (8 marks) – sample answer
PREDICTION
ACTUAL OUTCOME
COIN TOSSES
# of Heads
# of Tails
# of Heads
# of Tails
10
3
7
8
2
20
14
6
9
11
50
20
30
17
33
100
50
50
52
48
200
101
99
98
102
•
For the last column in the table above, choose a number of coin tosses that is between 100 and 1000 and enter it
into the learning object. Record your results in the table above. (2 marks)
•
Record the experimental probabilities for heads in each trial from the results on the projector screen (beside
“Percentage of Heads”) in the table below. Use the experimental probabilities for heads to find those for tails. (10
marks)
COIN TOSSES
Experimental Probability (Heads)
Experimental Probability (Tails)
10
80%
20%
20
45%
55%
50
34%
66%
100
52%
48%
200
49%
51%
© 2007 University of Ontario Institute of Technology (UOIT) ~ Permission to Copy
Teacher-Created Resources: Teacher-Led Lesson Handout Answer Key
Page 1 of 3
Coin Tossing
Name: Answer Key for Teacher
Teacher-Led Lesson Handout Answer Key
QUESTIONS
•
What is the theoretical probability of flipping tails in a single coin toss? Express your answer as a percentage. (3
marks)
Probability of flipping heads = 0.5
0.5 x 100% = 50%9 Æ Probability of flipping a tails = 100% - 50% 9
= 50% 9
•
What do you notice about the experimental probabilities as you increase the number of coin tosses? (1 mark)
As the number of coin tosses increases, the experimental probabilities get closer to the theoretical
probabilities.
•
How do you think the probabilities would change if a coin had three sides (heads/tails/toes)? (1 mark)
The probabilities would decrease for heads and tails and each would be 33.3% (100% ÷ 3 = 33.3%)
PART 2: Applications
•
Coby Bryant can sink 80% of his free throws. As a class, you will compute the experimental
probability of Coby sinking a free throw shot in a basketball game.
EXPERIMENTAL RESULTS
•
Please fill in the following table as you perform several “free throw” experiments as a class. Make sure to record
your predictions before each trial of free throws! (6 marks) – sample answers
PREDICTION
•
ACTUAL OUTCOME
FREE THROWS
# of Baskets
# of Misses
# of Baskets
# of Misses
10
8
2
10
0
20
18
2
15
5
40
30
10
32
8
100
80
20
83
17
For the last column in the table above, choose a number of free throws that is between 40 and 100 and enter it
into the learning object. Record your results in the table above. (2 marks)
© 2007 University of Ontario Institute of Technology (UOIT) ~ Permission to Copy
Teacher-Created Resources: Teacher-Led Lesson Handout Answer Key
Page 2 of 3
Coin Tossing
Name: Answer Key for Teacher
Teacher-Led Lesson Handout Answer Key
•
Record the experimental probabilities for baskets (i.e. heads on the screen) in each trial from the results on the
projector screen (beside “Percentage of Heads”) in the table below. Use the experimental probabilities for sunken
baskets to find those for missed baskets. (8 marks)
FREE THROWS
Experimental Probability (Baskets)
Experimental Probability (Misses)
10
100%
0%
20
75%
25%
40
80%
20%
100
83%
17%
QUESTIONS
•
What is the theoretical probability of Coby missing the basket? Express your answer as a percentage. (3 marks)
Probability of sinking a free throw = 0.8
0.8 x 100% = 80%9 Æ Probability of missing = 100% - 80% 9
= 20% 9
•
What do you notice about the experimental probabilities as you increase the number of free throws? (1 mark)
As the number of free throws increases, the experimental probabilities get closer to the theoretical
probabilities.
•
List some variables that could affect Coby’s free-throwing capabilities. (3 marks)
3 of any of the following:
-
•
Coby’s health that game (injuries, illnesses, etc.)
Distractions from other players or fans
Distance from basket
Condition of basketball
Why do you think the experimental probabilities usually differ from the theoretical probabilities? (2 marks)
The theoretical probability is only the likelihood that a certain event will occur (i.e. It represents what should
happen, but not necessarily what DOES happen).
© 2007 University of Ontario Institute of Technology (UOIT) ~ Permission to Copy
Teacher-Created Resources: Teacher-Led Lesson Handout Answer Key
Page 3 of 3
Coin Tossing
Teacher-Led Lesson Post-Assessment
Name: ___________________________
Birthday: ____________________________
Instructions: Answer the following questions to the best of your ability. You may use a calculator. Good luck!
1. Out of 20 coin tosses, 13 showed up as heads and 7 showed up as tails.
a) What is the theoretical probability of flipping tails in a single coin toss? (3 marks)
b) What was the experimental probability of flipping tails? (3 marks)
c) How many tails should have been flipped, based on the theoretical probability? (2 marks)
2. Brian just purchased a lottery ticket. The odds of him winning are 1 out of 235.
a) What is the probability of Brian winning the lottery? Express your answer as a percentage. (3 marks)
b) What is the probability of Brian losing the lottery? Express your answer as a percentage. (2 marks)
© 2007 University of Ontario Institute of Technology (UOIT) ~ Permission to Copy
Teacher-Created Resources: Teacher-Led Lesson Post-Assessment
13
Coin Tossing
Teacher-Led Lesson Post-Assessment
Answer Key
Name: ___________________________
Birthday: ____________________________
13
Instructions: Answer the following questions to the best of your ability. You may use a calculator. Good luck!
1. Out of 20 coin tosses, 13 showed up as heads and 7 showed up as tails.
a) What is the theoretical probability of flipping tails in a single coin toss? (3 marks)
In one flip, the chance of flipping a head is equal to that of flipping a tail. So, in one flip,
there is the chance of two outcomes:
1/2 = 1 ÷ 2 9
= 0.500 9
0.500 x 100% = 50% 9
b) What was the experimental probability of flipping tails? (3 marks)
7/20 = 7 ÷ 20 9
= 0.35 9
0.35 x 100% = 35% 9
c) How many tails should have been flipped, based on the theoretical probability? (2 marks)
50% x 10 flips
= 0.50 x 20 flips 9
= 10 flips 9
2. Brian just purchased a lottery ticket. The odds of him winning are 1 out of 235.
a) What is the probability of Brian winning the lottery? Express your answer as a percentage. (3 marks)
1/235 = 1 ÷ 235 9
= 0.0043 9
0.0043 x 100% = 0.43% 9
b) What is the probability of Brian losing the lottery? Express your answer as a percentage. (2 marks)
Probability of losing = 100% - Probability of winning
= 100% - 0.43% 9
= 99.57 9
© 2007 University of Ontario Institute of Technology (UOIT) ~ Permission to Copy
Teacher-Created Resources: Teacher-Led Lesson Post-Assessment