Probability Lesson Plan

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Abstract

Students learn what probability is by predicting the outcome of planned experiments, and playing racing games.

Standards (NCTM 3-5)

Data Analysis and Probability

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

• collect data using observations, surveys, and experiments.

Understand and apply basic concepts of probability.

• Describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible.
• Predict the probability of outcomes of simple experiments and test the predictions;
• Understand that the measure of the likelihood of an event can be represented by a number from 0 to 1.

Student Prerequisites

• Technological:
  
  Students must be able to:
  • perform basic mouse manipulations such as point, click and drag
  • use a browser such as Netscape for experimenting with the activities

Teacher Preparation

Teacher will need an opaque bag containing marbles of two different colors.

Students will need:

• access to a browser
• pencil and paper
• miniature car
• race game board
• dice

Lesson Outline

1. Focus and Review
• Chose a student to come to the front of the class.
• Ask the class who they think will win if you and the student race across the classroom.
• Let the student have a 1/2 of the room head start. Now ask the class who they think will win.
• Prompt the students to use terms like: likely, unlikely, and impossible.
• Inform the students that what they are discussing has to do with the mathematical term "probability"

2. Objectives
• Students will understand mathematical terms such as more likely and less likely and apply those terms to real life situations.
• Perform simple experiments to collect data.
• Determine the probability of different experimental results.
• Understand computers can be used to help make time consuming calculations much less cumbersome.

3. Teacher Input
• Hold up your opaque bag and allow your students to see that there is nothing inside the bag.
• Place 4 white marbles in the bag. Allow the students to watch you place the marbles in the bag.
• Hold up the bag and ask the students what color marble you will pull out of the bag if you were to reach in and grab a marble.
• Prompt the students to make the connection that you will definitely pull out a white marble, because they are the only marbles in the bag.
• Place the marble back in the bag and add 4 marbles of a different color.
• Ask the students which color marble is most likely to be pulled out of the bag and why.
• If the students don't realize right away that the chances of pulling out either color marble is equally likely begin pulling out one marble at time, recording what color it is, and replacing it back in the bag. You may want to allow the students to pull the marbles out of the bag to help involve them and keep their attention.
• Empty the bag. Place 3 white marbles and 1 marble of a different color in the bag.
• Begin with this set of questions:
  • Which color marble am I more likely to pull out of the bag? Why?
  • Will I always pull out a white marble?
  • How much of a chance do I have of pulling out the other color marble?
• Explain that you have a 1 in 4 chance of pulling out a non-white marble.
• Do the experiment manually to show the students the results. The more you repeat the experiment the closer your results will be to the theoretical results.
• Explain that 1 out of 4 chances can be represented as a fraction or a percent and show them how this is done.

4. Guided Practice
• Allow the students to partner up.
• Explain to the students that they are going to perform a probability experiment. using miniature cars, a race board, and die.
• Tell them the rules you wish them to follow.
• Have the students calculate the theoretical probability of each car winning on a one step board if:
  • Player A moves when he/she rolls a 1, 2, or 3 and player B moves when he/she rolls a 4, 5, or 6.
  • Player A moves when he/she rolls a 1 or 2 and player B moves when he/she rolls a 3, 4, 5, or 6.
• Pass out the game boards and cars.
• Have the students run the races manually a few times.
• Compile the class' results and compare them to the results that the students calculated.
• Ask the class what they think caused the discrepancies in the their experimental results and their theoretical results.
• Ask the class if they believe performing the experiment more times would make their experimental results closer to the theoretical results.
• Ask them how long they think it would take them to perform that experiment 10,000 times.
• Explain that this type of experiment is one of this things that computers are really helpful for, because they can perform them extremely rapidly.
• Have the students open the Racing Game with One Die applet and show them how to operate it.
• Instruct the students to turn off their monitors.
• Have the students predict the probability of a car A winning a two step race if car A moves on rolls of 1, 2, 3, and 4 and car B moves on rolls of 5 and 6.
• Instruct the students to turn their monitors back on and run the race 10,000 times.
• Ask the students if the answers they came up differed from the computer generated answers.
• Ask the students if they have any theories as to why their answers differed from the computer generated answers.
• Show them the math behind the correct answer and point out how much quicker it was to use the computer to check their math rather than having to manually run the races using the cars and dice.

5. Independent Practice
• Have the students calculate the theoretical probabilities for each of the questions.
• Have the students use the computer to help them complete the worksheet.

6. Closure
• Review new terms: probability, theoretical probability, experimental probability, likely, unlikely, impossible, and definitely.
• Connect the vocabulary with the experiment.
• Talk about how computer applications can be useful when working with probability.

Modifications and Extensions

This lesson can easily be modified to help meet the needs of more advanced students by:

• Having them calculate the probabilities for games with more steps.
• Having them do the calculations for 2 dice and using the Racing game with Two Dice.

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