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Posted Sun Feb 20 13:08:23 PST 2005 by Tammy Mize (tammymize@charter.net).

Gettys Middle School, Easley, S.C. U.S.A.

Materials Required: Media and Materials to be used in the lesson: Media and Materials to be used in the lesson:

Activity Time: Broken down over several days.

Concepts Taught: The students will be able to discuss the origin of probability; investigate to compare and contrast

The teacher will need fifteen computers for the students to be able to access the Internet for a probability web quest that was designed the teacher. This web quest will teach the origin of probability; theoretical and simulated probability; computing the probability of two independent events; and mutually exclusive events. The plain paper, rubric and colored pencils are to be used to create a probability book incorporating all the components of probability.The instructional strategy for this product appeals to the students sense of adventure. The probability activities involve sports, shopping, and the stock market. There are some activities that have a game show theme as well. Before the students begin their web quest, they will brainstorm real-life situations that deal with probability. After the brainstorming session, the students will participate in a web quest that will enable them to research the origin of probability. (See below for web resources) They will then participate in a question and answer session. This web quest will also enable them to participate in activities that will develop an understanding of theoretical and simulated probability. The students will individually create a Venn Diagram comparing and contrasting the two, then they will write a report based on their Venn Diagram. When the students have completed the activity from the web quest computing independent events in pairs, they will turn in their work for a formal assessment. After the students complete the web quest, they will individually create a probability book by writing their own probability situations involving theoretical and simulated probability as well as situations involving the probability of two independent events. They will also discuss their understanding of mutually exclusive events in this book.

(See "Variations/Options", for evaluating students performance.)

Before the students begin their web quest, they will brainstorm real-life situations that deal with probability.Evaluate student performance:

During the informal question and answer session, The teacher will ask the students to write down on their paper the answers to the following questions:

1. Why was probability originated?

2. Who developed probability?

3. In what time frame was

probability originated?The teacher will have Popsicle sticks with the names of the students in the class written on each stick. He/She then pull a Popsicle stick to randomly call on students to share their answers.

The Venn diagram will be graded on the accuracy of comparing and contrasting theoretical and simulated probability. If the students can correctly compare and contrast 4 out of the 5 components (80%), then they will have met the objective.

Students will have to compute the probability of two independent events with 80% accuracy. These questions will be found throughout the web quest.

As students are working on their web quests, The teacher will go to each pair of students and ask them to show me an example of a mutually exclusive event. They will then tell how they know that it is a mutually exclusive event.

The probability books will be scored with the following rubric. The students must score a 3 or above to show mastery.CATEGORY:

Explanation

(4) Explanation is detailed and clear.

(3) Explanation is clear.

(2) Explanation is a little difficult to understand, but includes critical components.

(1) Explanation is difficult to understand and is missing several components OR was not included.Mathematical Concepts

(4) Explanation shows complete understanding of the mathematical concepts used to solve the problem(s).

(3) Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s). (2) Explanation shows some understanding of the mathematical concepts needed to solve the problem(s) (1) Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written.Mathematical Reasoning

(4) Uses complex and refined mathematical reasoning.

(3) Uses effective mathematical reasoning.

(2) Some evidence of mathematical reasoning.

(1) Little evidence of mathematical reasoning.Mathematical Errors

(4) 90-100% of the steps and solutions have no mathematical errors.

(3) Almost all (85-89%) of the steps and solutions have no mathematical errors.

(2) Most (75-84%) of the steps and solutions have no mathematical errors. (1) More than 75% of the steps and solutions have mathematical errors.

Neatness and Organization

(4) The work is presented in a neat, clear, organized fashion that is easy to read.

(3) The work is presented in a neat and organized fashion that is usually easy to read.

(2) The work is presented in an organized fashion but may be hard to read at times.

(1) The work appears sloppy and unorganized. It is hard to know what information goes together.Completion

(4) All problems are completed.

(3) All but 1 of the problems are completed.

(2) All but 2 of the problems are completed.

(1) Several of the problems are not completed.Strategy/Procedures

(4) Typically, uses an efficient and effective strategy to solve the problem(s).

(3) Typically, uses an effective strategy to solve the problem(s).

(2) Sometimes uses an effective strategy to solve problems, but does not do it consistently.

(1) Rarely uses an effective strategy to solve problems.Mathematical Terminology and Notation (4) Correct terminology and notation are always used, making it easy to understand what was done.

(3) Correct terminology and notation are usually used, making it fairly easy to understand what was done.

(2) Correct terminology and notation are used, but it is sometimes not easy to understand what was done.

(1) There is little use, or a lot of inappropriate use, of terminology and notation.Make a note for revision in the future.

Evaluate media components:Ask several colleagues to try the web quest either individually or with their students. Their feedback will help evaluate the web quest. Also rely on the feedback from students.

Make a note for revision in the future.

Evaluate instructor performance:

Evaluate performance in two ways: analyzing the academic achievement of students, and student feedback.

Make a note for revision in the future.

Assure model examples:

6th Edition: Pages 90, 125, 152, 172, 195, 247, 270, 296, & 329

Adapted from:

Heinich, R., Molenda, M, Russell, J. & Smaldino, S. (1999). Instructional Media and Technologies for Learning, 6th Ed.So, you like to take risks, huh? Did you know that the probability concept was originated to settle gambling disputes? To find out more about the origin of probability, visit http://www.cc.gatech.edu/classes/cs6751_97_winter/Topics/stat-meas/probHist.html

. Answer the following questions on a piece of paper:

1. Why was probability

originated?

2. Who developed probability?

3. In what time frame was

probability originated?

Now that you have learned some interesting historical things about probability, it is time to learn about the difference between experimental probability and theoretical probability at http://www.mathgoodies.com/lessons/vol6/intro_probability.html .

Here you will enjoy an interactive lesson of tossing dice and spinning spinners to discover the exciting world of probability. While you are participating in this activity, be sure to decide whether or not the events are mutually exclusive.

Now that you know something about probability are you ready to play a game? Visit http://www.shodor.org/interactivate/activities/chances/ to play the "Crazy Choices Game," where you have control over the entire experiment. After you have conducted your experiments, you will then compare the experimental and theoretical probability results. After you have completed this activity, create an individual Venn Diagram comparing and contrasting theoretical and experimental probability. Write a report based on your Venn Diagram.

If you are a racing fan, you will enjoy the next activity. Go to http://www.shodor.org/interactivate/activities/racing/ for an exciting probability game that involves a race between you and your partner.

After this race, you are probably feeling pretty competitive right now. GREAT!! Visit the following web site for a basketball probability lesson that you are going to love: http://score.kings.k12.ca.us/lessons/robin/winedge/startpg.html . When you open the web page, be sure to click on the "worksheet one" and "worksheet two" links, and print those worksheets to use during the lesson. Please turn in your worksheets for a grade.

Do you like taking risks? Well, if you do, then you are going to enjoy the "Let"s Make a Deal" probability game at http://www.shodor.org/interactivate/activities/monty3/ . Check behind each door to find out the probability of winning prizes!!

Do you want to make a lot of money when you grow up? Well, one way to make tons of money is through the stock market!! Go to http://www.shodor.org/interactivate/activities/stock/ and use probability in the stock market.

Are getting "fired up" on probability, yet? Well, I have the perfect site for you to visit. http://polymer.bu.edu/java/java/blaze/blaze.html. This site provides a probability lesson on "Forest Fires and Percolation." Have fun!!

Now that you have been racing, making deals, playing the stock market, and fighting forest fires, you are probably feeling a little hungry. Wouldn't cereal would be a good snack right now? Speaking of cereal, if you go to http://www.mste.uiuc.edu/reese/cereal/cereal.html, you will find a lesson on the probability of getting six different prizes out of six different cereal boxes on thirty different shopping trips. Just click on the "Model of the problem for your classroom" link, and follow the directions. After you have calculated the experimental value, click on the "theoretical value" link to compare the two values.

Are you losing your marbles, yet? Well, I just so happen to have a probability lesson that deals with marbles for you. Go to http://www.shodor.org/interactivate/activities/marbles/ and enjoy this marble lesson.

Now that the tour of probability is over, I hope you enjoyed learning about

probability! Please create a probability book by writing your own probability

situations involving theoretical and simulated probability as well as situations involving

the probability of two independent events. You will also discuss your understanding

of mutually exclusive events in this book. You will find the rubric on the table in the

front of the room.