Probability Activities/Resources on the Internet
Some web sites on teaching probability and how we would use them in our classrooms to
meet the above stated goals:
How Large is Pennsylvania?
Just the Facts
Cereal box problem using TI-83
Conditional Probability
Rock,Paper,Scissors
Proabability Experiments
Take a Chance Probability Project
The New "New" Math - Internet Style
Chance News
Tootsie Pop Pull
Cut-the-knot Probability Page
Do you want to Bet?
Going in circles
"Crazy Choices" Game
Pauling's Joke
Simpson's Paradox
Buffon's Needle
Return to Terry & Jeff's Probability Home Page
- How Large is
Pennsylvania? This site includes an activity which meets the fourth goal of the
probality curriculum at the 5-8 grade levels. Students will make predictions and be
asked to rethink their predictions based on new information. We would use this
activity at the beginning of class to create interest and discussion about what it means
for an event to be more likely than another. The new information in the activity
would be given intermittently, perhaps every 5 minutes. The students would discuss
the problem in small groups. Whole class discussion would follow at the end
regarding the relevance of the activity. To further increase the relevance of
this activity to the lives of students (meeting the first curricular feature standard) we
would change the activity to investigate the size of a familiar geographic area--for
example, Wisconsin, Eau Claire, or the school. The actual area would be provided at
the end of the class. The focus of the activity, however, is not on getting the
right answer but on the reasoning process involved. Back to top
- Cereal box problem using
TI-83 This site provides an activity which can meet all of the goals of
the probability curriculum at the 5-8 grade levels. It also integrates the use of
technology in problem solving and reasoning (meeting the fourth curricular feature
standard). Students will use the TI-83 to simulate a discrete random
distribution. The instructions on this page are clear enough to minimize
teacher and student frustration. The students would work in groups of two. One
student will run the simulation and the other will record the results. The students
will switch roles so they both have experience running a simulation with the
calculator. Day 1 would end after compiling the frequency table and the suggested
questions would be assigned as homework. After this part of the exercise, the
activity becomes too advanced for the 5-8 curricullum. Further work and
discussion can include creating a frequency histogram and using it to begin answering some
of the questions for further exploration. Students would also explore the
descriptive statistics and analyze the meaning of those statistics.
Back to top
- Rock,Paper,Scissors
As an introductory activity to fundamentals in probability, this web page and the lesson
contained within address the first four goals of the probability curriculum at the 5-8
grade levels. Objectives include introducing students to probability, having students
construct a theoretical tree diagram, and comparting their tree diagram to experimental
data. Discussion can also include "what constitutes a fair game?" The second
curricular feature standard pertaining to math as communication is addressed in this
activity as well. At first, we would split students into groups of two. Through playing
the "rock,paper,scissors" game and recording the outcomes, students obtain
experimental data. Data collection would follow; both individual group data and whole
class data. Discussion would include the possible outcomes, comparison of theoretical data
to experimental data--why are there differences?--what does it mean to have a "1 in
3" chance of winning? Real world discussion--contests with a "1 in 12"
chance of winnning--what does this mean? To create further discussion, rule changes are
provided for a game involving groups of 3. Again, we would instruct students to create
tree diagrams and then play the game to obtain additional experimental data. Discussion
would focus on how the rules affected the theoretical probabilities and experimental data. Back to top
- Take a Chance Probability
Project This site provides a lot of great materials that can be used to introduce
probability at the middle school level. Included is a lesson plan very similar to
the rock, paper, scissors activity described above. The bulk of this site includes a
number of printable worksheets that are helpful to introducing probability. Some of
these worksheets are simply tally sheets for penny tossing, die tossing, and spinner
activities.
Some of the other worksheets
contain activities with follow-up questions. These questions would be great to
assign as group work. They could also be assigned as homework and then discussed the
following day in class. The worksheets involve conducting experiments, predicting
outcomes, and finding theoretical probabilities. These worksheets help to meet the first
four goals of the 5-8 probability curricullum.
An activity titled Perry
Probability is a great activity that helps students see some possible uses of
probability in the real world, meeting the fifth goal of the 5-8 probability
curricullum. The worksheets for this activity could be printed, and a day spent on
reading and discussing the problem. The follow up questions could be used during group
work or as an assignment.
Towards the end of
the web page are some more difficult activities, like urn problems, that introduce the
concept of dependent and independent events. There is a lot of room for class
discussion in these activities involving mathematical reasoning, helping to meet the
second 5-8 curricular feature. An entire unit could be developed for a middle
level grade based on this site alone. The activities and worksheets progress as you
scroll down the page. This site would also be great to use for a source of
supplementary materials/worksheets for lessons already created. Back to top
- Tootsie Pop Pull This
is a short lesson plan that introduces the idea of sampling without replacement. It
is a fun activity where the class gets a treat! The lesson plan is well written,
just be prepared with the tootsie pops. This activity meets Standard 1-4 of the NCTM
5-8 Probability Standards. Back
to top
- Going in circles This
is a worksheet that requires students to match problems with the correct
probabilities. Try having the students get the answers experimentally first, then
theoretically. By doing this, you would meet Standard 1& 3 of the NCTM 5-8
Probability Standards. It could also be used as a review assignment. This activity
also meets Standard 2 of NCTM 5-8 Probability Standards. Back to top
- Do you want to Bet?
This worksheet is very similar to Going in Circles except it uses probabilities of
cards and dice, helping students develop an appreciation for probability. Thus, this
workheet can be used to meet Standards 1-5 of the NCTM 5-8 Probability Standards. Here is a
similar worksheet Back to top
- Conditional Probability This
site includes a worksheet that addresses a conditional probabilities using mostly
theory. This would be an effective group assignment to meet Standard 2 of the NCTM
5-8 Probability Standards. Back to top
- Proabability Experiments
Here are some ideas for experiments to run. These would be used effectively as group
projects during class time. This site is great at meeting Standards 1-4 of the NCTM
5-8 Probability Standards. This site includes a printable worksheet which contains
tables to write in predictions and actual results. Back to top
- Chance News This
site is part of the Chance homepage. This section includes lesson plans and articles
with discussion questions from the Chance magazine current issues and backissues.
This is a great source for supplementary material for teaching or introducing probability
at 5-12 levels. Some of the topics are more detailed and ready to go while others
need some work before being introduced in the classroom. This site is and excellent
source that will meet the fifth goal of the 5-8 probability curricullum as well as the
first three curricullar features. Materials would probably best be chosen from the
latest issue and be something that is pertenent to the lives of the students. The
information and questions will be used to provoke discussion about the topics and the
probability issues underlying in the topics. This site should be great in creating
students' interest. Back to top
- Cut-the-knot Probability Page This page has
numerous activities relating to probability like the Monte Hall problem. A
description of the problem is given, the theoretical answer, and an interactive simulation
for the solution as well. Any of the problems would be good for the 5-12
curricullum. Some work would need to be done before introducing these problems to
the class. One of the activities could be introduced to the class, they could work
on creating a simulation for the solution (or using the simulation provided in the website
if computers are available), and then some discussion question could be asked leading them
to finding the theoretical solutions. Then they could compare their theoretical
solutions to their simulated solutions and discuss differences. The activities
provided in this site could be adapted to meet any of the first four goals of the 5-8
probability curricullum. Some of the problems pertain to real-world situations,
meeting the fifth goal and first curricullar feature as well. These activities could
be easily used as supplements as the class is beginning to learn about probability.
A major objective of using these activities would be invoking mathematical
reasoning. Technology could also be implemented through the use of the simulations
if access is available. These are fun activities that help students begin to use
mathematical reasoning. Back to top
Available activities on the "Cut-the-knot" page:
Pauling's joke : This is
a good problem for 5-12 students. It helps to introduce the idea of dependent and
independent events. It would be a good question to pose at the beginning of a
section about dependenct to get students to begin thinking about such things. The
solution could be discussed with the whole class, then definitions of dependence could be
provided relating to the joke. Back
to top
Simpson's paradox :
This is an urn problem that has a counter-intuitive solution. It would be a good
exercise for practice on finding theoretical probabilities and could provoke some
good discussion on the solution. In order to recognize why the solution is
counter-intuitive, ask the students what they think the solution is before they attempt to
work through the problem by calculating the probabilities. Back to top
Buffon’s Needle Problem would
be good in a geometry class to include some probability. Begin by asking if students
had ever tried avoiding stepping on the cracks in sidewalks or discussing a penny toss
game that might be found at a carnival. Once the idea of the problem is introduced,
it might be better to start by solving the simpler problem of the coin landing between two
lines rather than inside a square. Then you could advance to solving the original
problem. Be sure to discuss the notion of "geometric probabilty" and how
this problem relates to both geometry and probability. Also discuss how the
probability in this problem differs (compares measurements) from other types of
probabilites (like die rolling). It is probably only reasonable to use the first
part of this problem since it gets a little too advanced towards the middle and end of the
page. Back to top
- The New "New" Math - Internet
Style An extensive resource of internet materials for all areas of math
education. An essential "bookmark" for any mathematics educator interested
in using the internet for teaching and learning mathematics. Activities to meet all
of the standards for grades 5-12 can be found here. Back to top
- "Crazy
Choices" Game This is an excellent resource for interactive games,
proposed lesson outlines incorporating these games, and sample teacher-student
discussions. A java-capable browser is
required to run the games. However, the games can be adapted to a classroom without
this technology; the only drawback would be the speed of the simulation, quality of the
simulation, and the ability to run large numbers of trials. Back to top
Return to Terry & Jeff's Probability Home Page
NCTM 5-8 Probability Standards
NCTM 9-12 Probality Standards
