Download Think-Tac-Toe: Probability

This document is used with the author’s permission. It is limited to classroom use in CCS.
Think-Tac-Toe: Probability
Overview: These Think-Tac-Toe options allow students to choose their own ways of
showing what they have come to know and understand about probability and its
applications in the real world. The tasks are structured to address student interest and
personal choice. Students may choose any three options going across, down or diagonally
within the grid. This Think-Tac-Toe can be used as one of the culminating activities for a
unit on probability and can be combined with other formal assessments to evaluate
student learning.
Standards:
 Analyze problem situations and make predictions, using knowledge of probability
 Use a sample space to determine the probability of an event
 Conduct experiments involving simple and compound events
 Design and conduct experiments to solve problems
 Investigate and describe the difference between the probability of an event found
through simulation versus the theoretical probability of that same event
Objectives:
The students will KNOW
 Conducting a probability experiment can simulate theoretical results.
 Probability can be expressed as a fraction or a percentage.
 Probability is inherent in the natural and man-made world.
The students will UNDERSTAND THAT
 The actual probability of an event does not always equal the theoretical
probability of an event.
 Data can be used to estimate the probability of future events.
 The larger the number of samples in a simulated experiment, the more likely the
chance that the result approximates the theoretical probability.
The students will BE ABLE TO
 Conduct a probability experiment.
 Predict the probability of future events.
 Determine and compare experimental and theoretical probabilities for simple and
compound events.
 Design a probability experiment and conduct it to solve a problem.
Basis for Differentiation: Student interest and personal choice
Note to the teacher: The answer to the last problem in the grid concerning the lottery is
1/1,906,884. Each time a numbered ball is drawn, it reduces the number of balls that pop up.
The solution is reached by multiplying 5/49 x 4/48 x 3/47 x 2/46 x1/45, and reducing the
answer. For students unfamiliar with how lottery numbers are picked, you may need to
explain the process for this activity to be correctly analyzed.
© 2008 Pieces of Learning
from Demystifying Differentiation in Middle School
This document is used with the author’s permission. It is limited to classroom use in CCS.
Think-Tac-Toe: Probability
Select a novel of your choice and
turn to a random page. Tally the
number of times each letter of
the alphabet appears on the
page, designing a chart to record
the data. Add up the totals for
each letter and the grand total of
letters on the page. Use a
calculator to determine the
percentage probability of finding
each letter. Record all data on
your chart. Report to the class
the top ten letters that occurred
and the bottom five letters. If you
were a player on “Wheel of
Fortune” what advice does this
survey give you?
Theoretically, tossing a coin gives
you a 1/2 chance of tossing a head
or a tail. Test this probability. Toss
a coin 100 times and record
whether you tossed a head or a tail.
Determine the probability of your
experiment. How close were you to
the theoretical probability? Would a
larger number of tosses have
gotten you closer? Why or why not?
Conduct a survey of 75 people,
recording their birthdays. Design
a chart to collect and record the
data. The people you survey can
be students, teachers, family
members, neighbors, etc. Using
your data, what is the probability
that: 2 people have the same
birthday? a person has the same
birthday as yours? Using your
data, estimate the probability of
child being born in May during the
up-coming year.
A rider is participating in a
moun-tain biking race whose
route crosses a variety of terrain.
The path comes to a fork, with
one choice being significantly
shorter than the other. However,
the rider has a 4/1 chance of
blowing a tire on the shorter
route than on the longer route.
Create a picture of both routes,
indicating why the one has a 4/1
probability of popping a tire over
the other. Which route should the
rider choose and why? Include
this written response with your
picture.
Use a pair of regular dice. Roll the
dice 100 times and record how
many times you roll a double 1, a
double 2, a double 3, a double 4, a
double 5, and a double 6. Do not
record any of the throws that don’t
produce doubles. Express the
probability of rolling each of the six
possibilities of producing a double
throw as fractions. What is the
probability of rolling any set of
doubles? How would you predict
board game makers would use this
information when designing the
rules of their games?
Using a deck of playing cards,
what is the probability of drawing
a face card (Jack, Queen, or
King) from the deck? Conduct an
experiment to determine how
close you come to this theoretical
probability. Shuffle the cards 50
different times and have a partner
or yourself draw one card after
each shuffle. Record the number
of times a face card is drawn and
calculate your actual probability.
How close were you to the
theoretical probability?
Based on your observation
alone, predict the probability a
student in your school wears
glasses or contacts. Conduct a
survey of 50 students in your
school to determine how many
do or do not wear contacts
/glasses. Calculate the
probability of wearing
contacts/glasses and not wearing
them. Express the results as a
fraction and a
percentage. You may use a
calculator. Would you
recommend that an eye doctor
move into your school’s
attendance zone? Why or why
not?
The probability of being struck by
lightning is 1/600,000. We are
bombarded with probabilities such
as this from many different walks of
life. Using your search engine and
the Internet, research at least six
other interesting probabilities that
apply to our lives. Share these with
the rest of your class, along with a
paragraph that describes what, if
any, effects these probabilities have
on your life.
Many states have a lottery today
to raise money for important
causes. Much of this money is
given to education within the
state. The most popular game
has a player pick five numbers
from the sequence 1-49. If the
player’s numbers match the five
drawn in any order, then the
player wins a great deal of
money. Design a method to
determine what the probability is
of winning this type of lottery.
(Hint: multiplication is involved)
© 2008 Pieces of Learning
from Demystifying Differentiation in Middle School