Introduction                 

Guess what?  Mrs. Hash is out for 3 days due to injuries sustained when failing off a horse.  It is up to you to learn Geometric Probability on your own and to assist your classmates.  
Essential question:what is the formula for probability and what are the 3 types of problems addressed in geometric probability.
 
 

Day 1:  Learn the formula for geometric probability and the 3 types of problems.  Practice solving problems and viewing lots of information.
Day 2:  Use Geometer's Sketchpad to create your own problems, including a dart board and provide answers on the back.
Day 3:  Using the collection of problems, carousel around the room working the other students problems.

P(_______) =  # of __________  /  #of total outcomes.

Inside the parenthesis would go the event you were asking about, for example rolling a 6, or hitting the bull's eye. 

Click on the target to read more about the history and formula.  Make sure you pick Geometric Probability by Art Johnson.

 
 
 
 
 

Since we are only spending 3 days on Probability I am compacting it into 3 types of problems.  The first is dealing with length.  The second is making a list or counting and the third is dealing with area. 

Type 1
Let's look at length first.  If you had the following segment and were ask, what is the probability of randomly landing on a certain part, this is how you would do it.

                                                B

Lets use the example of landing on AD.
P(AD)=6/14, because AD is 6 units long and that number goes on top.  That is the length of the segment ask about.  14 goes on the bottom because that is the total length of the segment.  Now this could be converted to a % by taking 6 and dividing it by 14 and then multiplying by 100.  So this could be expressed as 42.9% and you could express the answer as 6 out of 14 or reduce it to 3 out of 7.

How about P(CD)?  You try first!  Did you get 3/14 or 21.4%?

How about P(AC U EF)?  The U means or.  So the question is what is the probability of landing on AC or EF.  Well how long is AC? 3 How long is EF? 5 Now take those numbers and Add them.  So 8 goes on top of the formula and 14 is still the bottom.  The answer if 8/14 or 4/7 or57.1%.

How about P(CD U DE)?  You try first!  Did you get 6/14 or 3/7 or 42.9%?

Now here is your list (245), (246), (256), and (456).  Do you noticed the pattern I used?  Which ones make a triangle?  They all do except (246). 2+4=6 and that will not make a triangle.  So the answer is 3/4.  There are 3 that do make a triangle out of 4 possible sets. The probability is 3/4 or 75%.  The answer is basically derived by counting. 

Look at the picture below.  What it the probability of hitting the shaded area on the dart board? Since it is divided equally all you have to do is count.  How many total squares?  How many are shaded?

Answer 1/9 or 11.1%

What if you had a circle like the one below and were ask the probability of hitting one section.  Well it would be 1/4, because they are evenly divided.  If you had a circle and the section you were asking about only covered lets say 60 degrees, then it would be 60/360.  Why 360 degrees?  That's how many degrees in the total circle.  Then you could reduce to 1/6 or 16.6 %

Type 3

Regular Polygons!  If you need to review finding the area of regular polygons, click on the picture.

 

Click here to see a Dart board with circles.

Now you can use any shape you like as long as you can find its area and you can even put them on a grid.  Take a look at this!  Click on the picture.

Look at this site and make sure you do the adjustable Spinner Worksheet!

Day 3:  The teacher will place the problems around the room and working individually you are to rotate until you have done all the problems.  Then they will be graded by the teacher.

Describe to the learners how their performance will be evaluated. Specify whether there will be a common grade for group work vs. individual grades.

	Beginning 1	Developing 2	Accomplished 3	Exemplary 4	Score
Problems turned in to be worked by other students	The problems were turned in late and were not very appropriate to the three types and the solutions were not provided.	The problems were turned in on time but were not of the three types and there were more than one piece of information incorrect.	The problems were turned in on time but were  slightly inappropriate, whether it was in difficult level or the information or the solution. The problems were not done on the computer.	Problems covered were the appropriate types.  The problems were easy, medium, and hard.  The solutions were correct.  All information was presented neatly and correctly.
Problems you worked that were provided by your classmates.	worked 60-70% correctly	worked 70-80% correctly	worked 80-90% correctly	worked 90-100% correctly
Your attitude, team work, on task etc.	Very poor attitude, contributed little to the team and was a real discipline problem, but still participated.	Had to be called on more than twice and had a poor attitude.	Had to be called on once or twice.  Knew how to do it, but couldn't work as a team.	No problems existed.

Now you should have a good knowledge base for probability.  This certainly does not cover the topic.  There are whole classes devoted to probability.  This was only an introduction.  Go to this site to see more problems that will extend your knowledge 

and go to this site to practice standardized test.  You can do any of them, but remember chapter 10 lesson 6 is probability.

Thanks to the people who created all the pages I used.