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Illuminations: Explorations with Chance

Example Web Site and/or Technical Equipment Required


Website Example:

Tech Product Equipment

Computer(s), Internet access

Activity Description

In this activity, students analyze the fairness of certain games by examining the probabilities of the outcomes. The explorations provide opportunities to predict results, play the games, and calculate probabilities. Students should have had prior experiences with simple probability investigations, including flipping coins, drawing items from a set, and making tree diagrams. They should understand that the probability of an event is the ratio of the number of successful outcomes to the number of possible outcomes.


  1. Review the detailed Lesson Plan.
  2. Make copies of the three activity sheets found on the site:
    • Is it Fair
    • A Fair Hopper
    • Happy Hopper
  3. Gather other materials on the list under the Materials button.


Activity 1 – Is It Fair

  1. Divide students into groups.
  2. Pass out Is It Fair activity sheet and needed materials.
  3. Give students time to complete the activity.
  4. Walk around the room and assist as needed.
  5. Discuss any new versions of a chip game.

Activity 2 – A Fair Hopper

  1. Pass out A Fair Hopper activity sheet and needed materials.
  2. Demonstrate the game.
  3. Give students time to complete the activity.
  4. Walk around the room and assist as needed.
  5. Discuss their findings.

Activity 3 – Happy Hopper

  1. Pass out the Happy Hopper activity sheet
  2. and needed materials.
  3. Demonstrate the game.
  4. Give students time to complete the activity. Students may need additional time
  5. due to the complexity of the game.
  6. Walk around the room and assist as needed.
  7. Discuss their findings.

Teacher Tips

Follow the steps from your chosen lesson (see Prep). The lessons are prepared with learning objectives, material, instructional plan, questions for students, assessment options, and more.

More Ways

  • Explore the library of Interactives  These activities help to make math come alive. Use the Dynamic Paper tool  to create your own PDF activity sheets.
  • If you want to do any of these as a whole class activity, you may need a computer and projector for class viewing.

Select subjects and subcategories


  • Algebra
  • Calculus
  • Consumer Math
  • Geometry
  • Integrated Math
  • Math Electives
  • Trigonometry
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OTAN activities are funded by contract CN200091-A2 from the Adult Education Office, in the Career & College Transition Division, California Department of Education, with funds provided through Federal P.L., 105-220, Section 223. However, OTAN content does not necessarily reflect the position of that department or the U.S. Department of Education.