The Probability Tour
This is a web based lesson on probability, designed to
review the topics recently covered in class.
You are going to travel to different locations on the internet and do
some activities while you are at each site.
As you proceed through the lesson, you will be asked to follow all
directions in both the "instructional strategies" section and those on
the worksheet handouts. Please show
all of your work on the worksheet handouts.
At the ãintroduction siteä you will read about
theoretical probability and see some demonstrations.
You will also visit sites about certain and and impossible events and
independent events. After that you
can choose to do a crossword puzzle or a word search about probability.
At the "birthday" site, you will simulate
several lists of birthdays, record the data and answer related questions.
This will be an example of experimental probability.
At the "probable pen" site, you will read about an
experiment conducted on the internet with several students from the United
States and other countries, and then try the experiment yourself.
You will then compare your results to those recorded duing the internet
experiment. This is another example
of experimental probability. At the
"darts" site, you will manipulate the size of a circle and a
rectangle to explore the probability that a dart thrown will land in the circle.
Two activities are provided at this site. This is another example of
experimental probability.
These sites are "LIVE". As you go through the activities, come back here to click on
the site for the activity you wish to do. The
"live" sites below can also be found below the directions for each
activity.
Everyone will do the ãintroduction site.ä
You will then be assigned an additional site, either the ãbirthdayä
site or the ãprobable penä site or the ãdartsä site for your assessment.
SITES FOR ACTIVITIES
Introduction,
exercises and puzzles
http://www.mathgoodies.com/lessons/toc_vol6.shtm
Experimental probability problem. (birthday)
http://www.mste.uiuc.edu/reese/birthday/intro.html
Experimental Probability. (probable pen)
http://lrs.ed.uiuc.edu/students/mcornell/cerealbox/probability.html
Experimental probability. (darts) (needs shockwave program)
http://exploremath.com/activities/activity_list.cfm?categoryID=13
INSTRUCTIONAL STRATEGIES
First stop ------ the
"introduction"site.
While at this
site you will:
- Click
on ãIntroduction to Probabilityä and read about theoretical probability,
do the demonstrations and try the exercises.
- Click
on ãCertain and Impossible Eventsä, read and do the demonstrations and
try the exercises.
- Click
on ãIndependent Eventsä, read and do the demonstrations and try the
exercises.
- Do
either the crossword puzzle or the word search or both if you wish. (print
out available)
Examples of
theoretical probability:
http://www.mathgoodies.com/lessons/toc_vol6.shtm
Second stop -----
the "birthday" problem.
Before you go to the ãbirthdayä site below, please read these
directions.
1. Read the entire introduction.
2. Do the birthday simulation activity at the site. ( See
hand out for directions.)
3. Scroll to top of web page and click on
"EXPLANATION."
4. Read entire explanation and examine the graph.
5. Write a conclusion about the probability of two people
in the same room having the same birthday, based on the data you found and what
you see happening in the graph
Example of experimental probability: (birthday problem)
http://www.mste.uiuc.edu/reese/birthday/intro.html
Third stop -----
the "probable pen in the cereal box" problem.
Before you go to the ãprobable penä site below, please read these
directions.
1. Read the entire introduction. Don't click on anything yet.
( Note that the experiment done by these students is the same as the
activity you will do on your handout.)
2. Do the activity on your handout to find out how many
boxes of cereal you may have to buy to collect all 6 pens.
3. Click on the cereal box to get to the ãFun with
Probability page. Find the words
"final results" and click there.
4. Read the results and examine the histogram.
5. Answer the questions on your handout about the
histogram.
6. Write a paragraph about how your results compared to
results in the histogram.
7. To view more graphs about this experiment, click on
ãMean and Standard Deviation.ä
Example of experimental probability: (probable pen )
http://www.bigchalk.com/cgi-bin/WebObjects/WOPortal.woa/3/wa/HWCDA/file?flt=GA&fileid=170815
Fourth stop ----- the
"darts" problem. Before
you go to the ãdartsä site below, please read these directions.
Activity 1:
-
Using
the original settings for the width and height of the rectangle and the
radius of the circle, try the darts game at least 10 times, using 100 darts
each time. Keep track of your data in a table (trial #, #of darts that hit
the circle.)
-
Average the number of darts that hit the circle.
-
Click
on the boxes labeled: area of the circle, area of the rectangle, and the
area ratio and then record that data..
-
Write a paragraph comparing the average you found to the
area ratio.
Activity 2:
-
Play the darts game 10 times, using 100 darts each time,
but change the size of you width and height of your rectangle and the radius
of your circle for each trial.
-
Record all data:
w,h,r,A(circle),A(rectangle), A(ratio),# of darts that hit the
circle, and the % of darts that hit the circle into a table.
-
Make
a scatter plot using the axes: Area
ratio vs. # of darts that hit the circle.
-
Write
a paragraph about the data you collected and your resulting scatter plot.
Example of experimental probability. (darts)
Note: Needs the program "shockwave" to run.
This program can be downloaded from the internet.
http://exploremath.com/activities/activity_list.cfm?categoryID=13
| 