COIN DROP
Performance Standard 10C.F
Calculate theoretical and empirical probability by dropping coins on a grid and recording data, and compare the
theoretical to the empirical probability.
• Mathematical knowledge: Set up a simulation, calculate theoretical probability, record probabilities as
fractions, decimals, and percents, demonstrate that the sum of the probabilities equals one;
• Strategic knowledge: Conduct an experiment to collect empirical data and compare it to the theoretical data;
• Explanation: Explain completely what was done and why it was done.
Procedures
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In order to determine, describe, and apply the probabilities of events (10C), students should experience
sufficient learning opportunities to develop the following:
• Record probabilities as fractions, decimals, or percents.
• Demonstrate that the sum of all probabilities is equal to one.
• Set up a simulation to model the probability of a single event.
• Discuss the effect of the sample size on the empirical probability compared to the theoretical probability.
Provide each student with a “Drop of the Coin” packet.
The student needs to read through the entire packet before s/he begins. It helps to know where the entire
assessment is going before s/he begins.
The student needs to color the 100-square grid according to directions.
The student then makes predictions, writing them on the sheet provided.
Using the grid and directions for coloring, the student fills in the chart with the theoretical probability. If the
coin landed perfectly as it should every time it is dropped, it should land on green how many times out of 100?
(10 out of 100 times.)
The number of times the coin should land on a certain color is put over 100 to form a fraction, the fraction is
written as a decimal, and the decimal is written as a percent.
The student should do the coin drop experiment with a partner following the directions given.
The student then fills in the chart for 50 drops of the coin using his/her tally chart as completed by his/her
partner. (The student should know that the numerator and denominator could be doubled to make a fraction that
is easily expressed as a decimal. The student can also divide the numerator by the denominator to get the
decimal.)
The teacher then collects the data from 20 students and records it on the board or overhead so each student can
copy it.
The student must find the sum of each color of the 20 samples and record each sum on the chart under the color
indicated. The fraction is made by making the sum the numerator and 1000 the denominator. The fraction must
then be expressed as a decimal and then as a percent.
The student then discusses the influence of sample size (his/her 50 drops and the class’ 1000 drops) when
comparing the empirical probability with the theoretical probability of the events.
The teacher needs to circulate and talk to each student about his/her strategy in coloring the grid. A student may
think that putting all of one color in one sector of the grid will increase the chances of the coin landing on it.
Another student may think a certain pattern has an influence. In theoretical probability, the placement of the
colors should have no impact on the outcome.
The students should correctly predict that white is the color the coin will most likely land on because 30 out of
the 100 will be white. That is the highest number of squares for any color.
The student should correctly predict that black is the least likely because on 2 out 100 are colored black. That is
the smallest number of any color.
ASSESSMENT 10C.F
16. The theoretical probability chart should be filled out as follows:
Conditions
Green
Blue
Red
Yellow
Purple
Black
White
Number of Squares
10
5
25
8
20
2
30
Fraction of time coin
should land on this
color.
Change the fraction to a
decimal.
10/100
= 1/10
5/100 =
1/20
0.1
0.05
0.25
0.08
0.2
0.02
0.3
1.0
Percent of time coin
should land on this
color.
10%
5%
25%
8%
20%
2%
30%
100%
25/100
= 1/4
8/100 =
2/25
20/100
= 1/5
2/100 =
1/50
30/100
= 3/10
Sum of
each row
100
100/100
=1
17. The student should keep an accurate tally of the number of drops. The tally marks should add up to 50.
18. The student should double the numerator and the denominator to get a fraction that is easily expressed as a
decimal. The student could also divide the numerator by the denominator to get the decimal. Either method is
acceptable.
19. The percent is expressed by moving the decimal point 2 places to the right.
20. When looking at the “1000 Drops of the Coin” grid, the denominator of each fraction will be 1000. The student
should divide the numerator and the denominator by 10. If the denominator becomes a decimal, the student
should round it to the nearest whole number. The denominator will be 100 and the fraction can be expressed as
a decimal.
21. In the student’s writing, s/he should discuss how much closer the theoretical probability is to the data from 1000
drops than it is to the data from 50 drops. S/he should also state that the larger the sample is, the more likely it is
to come closer to matching the theoretical probability of the event.
Examples of Student Work follow
Time Requirements
• Two class periods
Resources
• “Drop of the Coin” packet
• Colored pencils or crayons
• A penny or dime for each pair of students
• Pencil
ASSESSMENT 10C.F
NAME _______________________________________________ DATE _______________________________
DROP OF A COIN
ASSESSMENT 10C.F
Directions: The squares may colored any way you want-in a pattern or randomly.
1. Color any 10 squares green.
2. Color any 5 squares blue.
3. Color any 25 squares red.
4. Color any 8 squares yellow.
5. Color any 20 squares purple.
6. Color 2 squares black.
7. Leave the rest white.
Predictions:
On which color is the coin most likely to land? ___________________________________________________
Why? ____________________________________________________________________________________
On which color is it least likely to land? ________________________________________________________
Why? ____________________________________________________________________________________
Theoretical Probability:
Record the theoretical probability of each event on the table below.
Conditions
Green
Blue
Red
Yellow
Purple
Black
White
Sum of
each
Number of Squares
Fraction of time coin
should land on this color.
Change the fraction to a
decimal.
Percent of time coin
should land on this color.
Conduct an experiment:
Work with a partner. You drop the coin 50 times on to your grid and your partner will keep a tally of the times the
coin lands on each color. If the coin does not land on the grid, try again. Only those times that the coin lands on the
grid should be counted. If the coin lands on two colors, pick the color that is covered the most by the coin. Then
your partner will drop the coin onto his/her own grid and you will keep a tally of how many times it lands on each
color.
Your Tally
Green
Purple
Blue
Black
Red
White
Yellow
ASSESSMENT 10C.F
Results:
On the first chart below record the results of your 50 drops of the coin. Convert the numbers into fractions, decimals,
and percents. On the second chart, your teacher will help you and the rest of the class compile the results of 20
students or 1000 drops of the coin. After you have written the number of times the coin landed on each color,
convert to a fraction, decimal, and percent.
50 Drops of the Coin
Event
Green
Blue
Red
Yellow
Purple
Black
White
Sum of
each
Green
Blue
Red
Yellow
Purple
Black
White
Sum of
each
Number of times coin
landed on each color
Fraction of time coin
landed on each color.
Change the fraction to a
decimal.
Percent of time coin
landed on each color.
1000 Drops of the Coin
Event
Number of times coin
landed on each color
Fraction of time coin
landed on each color.
Change the fraction to a
decimal.
Percent of time coin
landed on each color.
In writing, discuss how closely the results of 50 drops compared to the theoretical probability. Then discuss how
closely the results of 1000 drops compared to the theoretical probability. Explain how the sample size affects the
empirical probability in relation to the theoretical probability. Please use this page and the back of this page for your
writing.
* Adapted from Everyday Mathematics, The University of Chicago School Mathematics Project
ASSESSMENT 10C.F
"Meets" (page 1)
"Meets" (page 2)
"Meets" (page 3)
"Meets" (page 4)
"Exceeds" (page 1)
"Exceeds" (page 2)
"Exceeds" (page 3)
"Exceeds" (page 4)