Fun with Probability!
The Probable Pen in the Cereal Box
Comments from Participating Teachers
This page contains comments received on the submission forms of the various teachers. Thanks for providing comments!!!! I have included both comments which came with the data as well as selected comments from the survey. I have included all types of comments, with responses where appropriate. They are roughly in reverse chronological order, so start reading at the top until you see something you've already read -- at that point you've read them all.
My students really enjoyed this project. I thought the worksheets and web site were very well
done. I teach seventh graders and wanted to have them collect more that the data for one try,
so I gave each of them a class worksheet and had them fill it in. This gave them a chance to
compare not only their data to the rest of the class, but also to see how under the same
conditions they could get different data.
One thing I liked about the project was that it was set-up in such a way that children of various levels could participate. I just have one suggestion - for teachers that need to post data for more than one class is it possible to have the standard data remain so that you don't have to keep typing it in? I have a feeling that the answer is no, but I had to ask.
- Eileen Bendixsen (Hazlet, NJ)
Actually, not impossible at all. In fact, that's quite a good idea. Thanks for the suggestion -- I'll definitely use it in the future. <Mike>
This was a really nice project - A really good way to show people the potential of the Internet
for use to enhance the curriculum directly in the class room. Nice job in showing that there's
more to the Web than surfing pages randomly and finding only fluff along the way. I believe
this interaction shows the real power and future of the Internet and Web.
- Ben Lesch (New York, NY)
Great job! Can we have more like this? As a math facilitator, I didn't actually conduct the
experiments but passed this project on to the teachers. We only had 4 teachers participate;
but this was not a convenient time of the year to do this. I think if this had been at another time
we would have had more participation. The tech facilitator and I are interested in developing a
project similar to this within our campus and possible into the district. Thanks again for the
- Charlotte Flowers (Cedar Park, TX)
The project was very well organised. I especially appreciated the ready made forms that
could be downloaded. We did have problems in submitting our results via the web. Overall,
an excellent project that helped meet my curricular objectives.
- Tom Wilson (Lethbridge, Canada)
And you were wondering who rolled 95 times???
I am the student who had to "purchase" 95 boxes of cereal to get one of each color of pen. I would like to know if I am the only one in the entire simulation that had to buy 95 boxes? Thanks!
Carrie (Columbia, MO)
Yes Carrie, you get the record at 95. The next highest were 50, 52, 53, 62 and 71. You may have noticed that the graph doesn't show any of these values. That's because it would have made the bars so tiny that we couldn't have seen them. Either that, or I would have had to have made the graph bigger than the screen!!!! Hope you didn't get a stomach ache from all that cereal!!! Thanks for being a part of the project. <Mike>
Thank you for your hard work in this endeavor! I've done something like this before although
not on such as large basis. The only suggestion I can think of for improving is modifying the
student worksheet so that the number on the dice corresponds with the color. I ended up
downloading a worksheet, then cutting it apart and pasting and xeroxing to "fix" it. Thanks
again. P.S. If this was for a class, I think you deserve an "A". (You can tell your professor I
- Rhonda Moore (Columbia, MO)
Great activity for first graders!
- Nancy Cale (Snow Hill, NC)
This probability study was simple, beautifully set up, and so much fun. My second graders
were amazed at how very expensive it would have been to accumulate all six colors of pens!
They were able to tie ideas into our Economics unit in social studies. We've enjoyed being
part of this very much.
- Katie Sucato
I prefer projects with more of an interactive nature...perhaps classes could have needed to
contact each other to solve a problem. Each would have parts to the solution and need each
other to put them together and solve the problem. Just researching and submitting outcome is
not too stimulating for the kids.
- Joan Berger (Roslyn, NY)
An excellent point! I will look for that type of activity when I do my next project. Thanks for the feedback. -Mike
I intend to start my Probability unit each year with each class using your "Probable Pen in the
Cereal Box" activity. Of course, I will give you full credit each time I introduce it. My students
are still talking about the activity. I did start off with an empty cereal box. The students
watched me put six different colored pens in the box. I walked around the classroom asking
each student to pull out a pen. The entire class was captivated with keeping a mental track of
which colors were pulled out and how many boxes it took to complete the set. I could see
that each student hoped to pull out a color that had not already been taken out. There was
some disappointment when it was the same color over and over again. But a lot of joy when
finally the last color appeared. All the students agreed that it was a GREAT way to start the
unit. I would most definitely participate again and again, and would try any other activity you
might want to send my way. Good luck in your work. Do let me know what grade you get for
this project. I give you an "A"! Thanks again for a wonderful activity.
- Lynn Rakatansky (East Providence , RI)
The kids really enjoyed this activity. They thought it would be cheaper just to go buy
everyone a set of pens. It was a good basis for a disussion on advertising and how they
appeal to our sense of winning. Thanks for the opportunity to take part.
- Milburn/Soldan (Forest, Ontario Canada)
This was a great activity for the kids to do. The follow up activities were great as well. One
question that still has me confused, is the one about the expected value. The reciprocal of the
probabilities did not make sense to me. Could you please clarify this for me. Thank you for
your efforts and "wonderful ideas."
- Chris Stamer (Clarence, NY)
Good question. Perhaps an example would suffice. In a perfect world of coin flips, how many flips would we "expect" to make before getting one of each type? Answer: 2 (One Tail and one Head). How many rolls to get one side of each die exactly once? Answer 6. Each of these values is the reciprical of the probability of any of the equally likely events occurring. Of course, as we saw in the experiment, the expected value never actually occurs, but it serves as a target. Hope this helps. - Mike
We can tell you're in college - are you dreaming? I've been teaching for almost 20 years and
have never had a class size under 23!!! Results would have been easier to calculate if
recording sheet allowed for 25 students. Good job - Fun for the students - not the teacher.
- Anne Pizzi (Norfolk, MA)
You're right, Anne. I almost did put more lines on the page, but then I ran out of room for the instructions too. In the future, I think I'll put the instructions on a separate page and leave as much room for calculations as possible. - Mike
All five of my classes really enjoyed doing this project. Your timing could not have been
better, since I had planned to start my unit on Probability when I learned of your work. Thank
you. In our discussions some of my students noted that they would have to eat a lot of cereal
in order to get a complete set of pens. They were surprised at the expense. One student
suggested just buying the pens separately, but another noted that the toys included in the
boxes usually are exclusive to that cereal and could not be bought elsewhere. It was such fun
to see them really thinking about this. One of my objectives each year is to get the students to
see if their work is reasonable and answer why they think what they do. The "why" is
sometimes so very difficult for them usually since it is the first time ever that they have been
asked such a question in a math class. I followed your pen activity with determining if certain
games are fair or unfair. They first guess, giving both an answer and a reason, and then they
play the game to verify their predicitons. Thank you for providing such a great introduction to
my probability unit. I would be most interested in any other activities you might have. Of
course, long after you have recovered from all the recording of the results. My students have
enjoyed seeing your graphs. I am excited to show them your latest one, with each pen being
equally likely to be found. Again thanks for such fun stuff! Lynn
- Lynn Rakatansky (East Providence, RI)
Great introduction to probability for the kids! Could use a little more theoretical support for
the teacher (on expected values as reciprocals of probabilities)
- Diana Stiefbold (Sharon, MA)
I did this activity with two mulitage classes of first and second graders. I had them predict the
total number of boxes of cereal and then do the actual activity. Even after discussing the
importance of collecting accurate data, I found that some were trying to get their results to
match their predictions like it was a contest. With the second group I had one child roll the die
while another child recorded the results, and then switch places. Interestingly enough both
groups collected very similar data!
- Kathy Busick (Plaistow, NH)
My class enjoyed this project very much. We included this project with several other activities
and projects over the topic of probability. The students seem to have a good understanding of
this topic now. Thank you for your creative ideas. Also thank you for making this project easy
to do and clear for teachers and students alike to understand. Bravo!!!
- Sharon Barnes (Greenwood, MO)
Project has been a lot of fun for students. The worksheets have been of tremendous use. The
web site is easy to maneuver around.
- Olivia Brohammer (Stone Mountain, GA)
It is not often an anecdote such as the following arrives. I feel compelled to share it. (I hope the students of Room 31 don't mind). <Mike>
The reply full of giggles with arms dramatically wrapped around their stomaches was: "Look at how many yellow pens you have? Do you know how many boxes of that cereal you'd have to eat to get the rest of the set?" When I shared with the kids the price of an average box of cereal they quickly figured out that the same amount money could be used to purchase not only a super deluxe set of pens but also a brand new bicycle!
Kind of puts it all in perspective, doesn't it? <Mike>
Mrs. Johnson's class would like to know why you wanted to do this.
- Mrs. Johnson (Cincinnati, OH)
This actually started as a class project (see the main Fun with Probability! page for a link to the class), but it has now taken on a life of it's own. I really enjoy communicating with classrooms all around the world. I hope to do more of these projects in the future!
The timing was perfect. We were just starting probability the day this came over the Internet.
My students designed Snowflake Cereal Boxes to go along with the project.
- Kathleen A. Sullivan (Norfolk, MA)
I thought that this was a wonderful activity for the students, a very good simulation of a real
life situation. We had a lot of fun with it and the students enjoy going to the home page to see
the results from other classes come in.
-Tom Wilson (Lethbridge, Canada)
A super activity and so "user friendly". Kids really enjoyed it.
-Lynn Gatchell (Athens, GA)
This was a great way to introduce probability to the class. The children loved the activity.
They also learned an important lesson about advertising too!
- Harriet Stolzenberg (Brooklyn, NY)
The students enjoyed this activity very much.
- Louisa Allen (Champaign, IL)
Fun project! Can't wait to see the results!
- Sandra Harthan (Gaylord, MN)
This activity was conducted with a combined class of first and second graders. We did a
whole class warm-up activity where each child predicted the number of rolls it would take for
each of the six numbers (colors) to appear. Some of their predictions, at this point, were
considerable to say the least. When they saw the reality of how many rolls it took during our
"practice," many modified their predictions for the actual activity.
- John Waldman (Urbana, IL)
The class found that this was fun to do, and they would like to do something like it in the
future. We are anxious to see our results.
- Mrs. McDaniel (Cincinatti, OH)
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