So many choices, so little time

This lesson will introduce students to Theoretical and Experimental Probability using Crazy Choices and Spinner, a resource of Shodor Education Foundation, Inc. Permission has been granted for the use of the materials as part of the workshop Interactivate Your Bored Math Students.

A lesson plan for grades 6–7 Mathematics

By Beth Jorgensen

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Related pages

• Spin away: Children will work in groups using spinners with 4 colors to make predictions about probability, gather and record data, and make conclusions about outcome.
• Exploring probability : Part 1 of 2: This lesson will introduce students to probability using resources of Shodor Education Foundation, Inc. Permission has been granted for the use of the materials as part of the workshop Interactivate Your Bored Math Students. Students will discover the rule for calculating simple probability as well as explore the ideas of experimental and theoretical probability.
• French fries up and down: The students will get hands-on practice working with patterns and translating them to numerical sequences. This lesson reaches visual, auditory, and kinesthetic learners all at the same time.

Related topics

• Learn more about estimation, mathematics, and probability.

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Learning outcomes

Students will:

• clarify the definition of probability
• investigate the probability outcomes.
• calculate experimental probability

Teacher planning

Time required for lesson

90 minutes

Materials/resources

• Pen & Paper for each student
• Crazy Choices Worksheet
• Crazy Choices Game Tally Table
• Spinner
• Spinning Tally Sheet (see attachment)
• Class Tally Sheet (see attachment)
• Rubric (see attachment)

Technology resources

• Color monitor with access to the Internet for each student
• Either a computer lab with Internet access or a one-computer classroom with an Internet connection.
• Check to make sure the browser supports the Shodor applets.

Pre-activities

Students should review basic math calculations and should be familiar with calculating experimental probability when given the formula.

Activities

There are two activities involved in this lesson. The first one involves individual students working alone at a computer and gathering some information that will be used to form groups of 3 and work with those groups. For the sake of time students should be at the computers when you begin this lesson.

As an introduction to experimental and theoretical probability the discussion on Probability and Outcomes is a great lead in. This will be followed up by:

Activity 1

1. Students will have a Spinning Tally Sheet to keep track of what they find. This will determine what number they are in the Crazy Choices Game. The discussion you have prior to this will make them aware that theoretically every number on the die has an equal chance of winning, of course experimentally that may not be the case. Spinner
2. Model the activity for the students.
3. Each student will spin the spinner 25 times and keep a tally on their individual tally sheet for spinning.
4. The teacher will group 3 students together however is most efficient for the class and those 3 students (who all have a different winning number) will now go to Crazy Choices Game.

Activity 2

1. Students are in their groups and are at Crazy Choices. Every student should also have a copy of the Crazy Choices Tally sheet
2. Students will play the Crazy Choices Game play the game in groups using the computer to show how probabilities can be compared experimentally. The following data will be recorded by the program:
• number of games played
• number of times each player won
• experimental probability of winning
3. Shodor.org explanation of the game:
   “The goal of the game is to determine which player has better chances of winning if players use different devices to determine whether they win. For example, to compare the chances of the player who flips a coin (winning in 1 out of 2 possible outcomes) and the chances of the player who rolls a six-sided die (winning if it rolls a 1 or 2, or in 2 out of 6 possible outcomes). The advantage of the software is that it can simulate many games in a single run. This saves time, and helps students see how experimental probabilities get closer and closer to theoretical probabilities (the Law of Large Numbers).”
4. The students should “run” for 100 trials and do that 25 times. At the end of that time they should see whose number is winning.
5. Regroup the class and discuss whether our experiment confirmed our theory based on the results of the whole class. Using the class tally sheet (attachment) as an overhead transparency tally the student’s results. Did we expect the results we got. Why or why not? Review the concepts of probability, experimental and theoretical once more.

Assessment

The goal of this lesson was to use an experiment to test theoretical probability and to test the results. Their assignment would be to go to the spinner and choose 2 sectors. Choose one color to be heads and one tails. Run the spinner 25 times and based on those results you will play the Crazy Choices Game for 100 runs, and doing that 20 times.

After the student has collected all this data they will present the data in a tally sheet for both the spinner and Crazy Choices and then write up an explanation for the results that they came up.

See rubric for grading.

Supplemental information

• Spinning
• Class Tally

Comments

The assessment may take as long as the Activities take. I think that it is a very important part of the lesson and that the lesson prepares them to do that.