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.

A lesson plan for grade 6 Mathematics

By Wendy Korbusieski

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Learning outcomes

Upon completion of this lesson, students will:

• have clarified the definition of probability
• have learned about events and outcomes in probability
• know how to calculate experimental and theoretical probability

Goals taken from: http://www.Shodor.org

Teacher planning

Time required for lesson

90 minutes

Materials/resources

• Pencil and paper
• Computer lab with access to the Internet for all students
• Coins, Spinners, Dice, Cards with which to run experiments
• Chalk board or overhead projector

Technology resources

• Color monitor with access to the Internet for each student
• Access to Excel spreadsheet program
• Calculators (optional)
• Projection capability for teacher’s computer

Pre-activities

Students must be able to:

• convert between fractions, decimals and percents
• be familiar with spreadsheets

The teacher should be able to:

• be familiar with spreadsheets
• be able to work within multiple windows
• be familiar with the Spinner and Converter activities on the Shodor website

Activities

Begin a discussion on games of chance (or even more interesting to NC students, maybe the idea of a state lottery). Ask questions such as “Who takes the biggest risk, the player or the gamer? Are all games set up with an equal chance for each to win? The design of games such as these is based on probability”.

Define probability:

Define event:
Define outcome:

Prompt students that they will begin an investigation on how to calculate probability:

Projecting from the teacher screen go to the Spinner activity on the Shodor website http://www.shodor.org/interactivate/activities/spinner3/index.html Describe the design and how it works.

Ask each student to go to the website and spend a minute or two collecting data for 20 trials with the spinner. The teacher should walk around and check for progress. Once the teacher is satisfied that everyone is at the site she should then open an Excel spreadsheet and prepare to collect trial results. An example of this chart can be found as the attachment samplechart. It is recommended that this spreadsheet be created and saved in advance but it is not necessary. It will be helpful for the teacher to show both the Spinner and spreadsheet windows at the same time.

Collect data from each student and record it in the spreadsheet. Determine the sum for each color and the total number of trials. Quickly review procedures on how to change each of these values to a fraction, then decimal, then percent. Calculate the winning percentage for each color on the spinner using Excel, a calculator or the Converter on the Shodor website http://www.shodor.org/interactivate/activities/conversions/index.html Discuss the results. Do any colors seem to have a better chance of winning? What would happen if we increased the number of trials?

Go back to the Spinner using the “How many spins?” box, ask each student to complete 1000 spins. Re-calculate your results in the chart using the new values.

Discuss the results noting that each probability is getting closer and closer to 25%. These values are called experimental probabilities.
Using mental math, calculators or the Converter http://www.shodor.org/interactivate/activities/conversions/index.html , change 25% to a decimal 0.25 and then fraction 1/4. Ask students to look at the spinner noting its construction. Ask “What do you believe can be used as a “short-cut” for finding the probability of each section? If two of the sections were green, how would the probability change?”

Use the “number of sections” button to increase the number to 5. Ask “Without running trials, what is be the probability of landing on the green section? How do you know?”

Brainstorm the formula for probability posting it on the overhead projector or chalkboard. P(event)= number of ways an event can happen / number of possible outcomes. Tell students to go back and add this to their definitions. This is called the theoretical probability.

Discuss that probability can be expressed as a valued between 0 and 1. 0 - never will happen, 1 - will always happen. Give examples of each.

For guided practice, use the overhead/board to ask some simple probability questions. Example: Tiles numbered 1-10 are put in a box. Determine the probability of each event occurring. P(2), P(even), P(prime), P(0), P(>10), P(<11)

Assessment

Students will be asked to create an experiment that will test a theoretical probability using a spinner, die, coin, deck of cards or other item of student choice deemed appropriate by the teacher. Experiment plans need to be teacher approved prior to proceeeding. See attached grading rubric for requirements.

Supplemental information

Attachments:

• Grading Rubric
• Sample Chart

Related websites

Conversions Activity
http://www.shodor.org/interactivate/activities/conversions/index.html

Spinner Activity
http://www.shodor.org/interactivate/activities/spinner3/index.html

Comments

Teacher needs to be comfortable using Excel.

The instruction can possibly be completed in 45 min if the assessment is given as an “at home” project. 90 min if you would like to allow class time to complete experiments.