Students learn how to calculate both theoretical and experimental probability by rotating through a series of work stations.

Understand numbers, ways of representing numbers, relationships among numbers, and number systems

• recognize and generate equivalent forms of commonly used fractions, decimals, and percents;

• collect data using observations, surveys, and experiments;
• represent data using tables and graphs such as line plots, bar graphs, and line graphs;

• 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.

• perform basic mouse manipulations such as point, click and drag.
• use a browser such as Netscape for experimenting with the activities.

• Have enough stations so that each pair of students can be working at an individual station. (You may want to have multiples of each station because some stations take longer to complete than others.)

• 2 race boards and 4 race cars
• 8 dice
• 2 pieces of paper numbered 1- 12
• 10 square pieces of paper or 10 poker chips
• an opaque bag
• 15 white marbles
• 5 red marbles
• a spinner
• 3 index cards (a mole drawn on the reverse of one card)
• 2 pennies
• a deck of playing cards

• access to a browser.
• paper.
• pencil.

1. Focus and Review
Introduce the idea of probability through a discussion about something similar to the lottery.


2. Objectives
Students will be able to calculate both experimental and theoretical probabilities as well as display probabilities in both graphical and fraction form.


3. Guided Practice
• Work through an example work station with the students.
• Fill out the appropriate section on the data collection sheet with the class.

4. Teacher Input
• Explain the procedure to be followed at each station.
• Explain that experimental probability is the actual results gathered by doing the experiment several times.
• Describe to the students how to calculate theoretical probability.
• Put the students into pairs.
• Have the students work through the stations allowing 5 minutes for each station.

5. Independent Practice
• Have students rotate between the stations and complete their data collection sheet.
• You may also want to have a computer station set up for the students to work with several probability applets that model some of the activities at the various stations.
  
  Some appropriate applets are:
  • Racing game with one die
  • Racing game with two dice
  • Adjustable Spinner Game
  • Monte Hall Game

6. Closure
• Have each group share the experimental data they collected from one experiment. Ask them if the experimental probability they calculated is the same as the theoretical probability.
• Reinforce the concepts of theoretical verses experimental probability.
• Compile the class' data for all the experiments and compare the individual group experimental results to the collective class results. The compiled class results should be closer to the theoretical probability than most individual group's results.
• Discuss why this is so.
• Discuss why computers might be helpful when working with probability experiments.