Spin, Toss, and Roll!

Students will use hands-on experiments to find the probability that certain events will occur.

A lesson plan for grades 6–8 Mathematics

By Carol Baldwin

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Learning outcomes

Students will:

• distinguish between theoretical and experimental probability.
• understand experimental probability.
• find the complement of an event.

Teacher planning

Time required for lesson

90 Minutes

Materials/resources

• Pencils
• Set of soft die/Coin/color spinners - one for each group.
• Lab sheet (see attachment)
• Sample Application Problems (see attachment)

Technology resources

None

Pre-activities

• Students should be able to solve problems involving fractions, decimals, and ratios.
• Students should understand the concepts of “equally likely,” chance, outcomes.
• Students should already be familiar with finding theoretical probability.
• Prior to class, place your students in groups of three and determine how many groups of three you will have. This will allow you to know beforehand how many groups will be using coins, die, or spinners.

Activities

1. Ask students to tell you the answers to these questions:
   
   • “What is the theoretical probability of spinning and getting the color blue on a three color spinner?”
   • “What is the probability of getting a head when you toss a coin?”
   • “What is the probability of rolling a 6 when you roll a die?”
2. Discuss:
   
   “If the probability of rolling a 6 is 1/6, what is the probability that you will not roll a 6?”
   Explain that these are complements of one another. Give them several examples of this concept. For example, coins, spinners, rain, attendance, etc. Have them find these complements.
3. Ask students if they are confident that theoretical probability is always true. Tell them that they will be verifying the validity of theoretical probability with experiments of their own. They will draw their own conclusions and determine the difference between theoretical and experimental probability.
4. Tell students that they will be conducting experiments using coins, spinners, and dice. One person from each team will need to be the recorder, one will be the counter, and one person will do the actual spinning, rolling, and tossing. They need to collect their materials from the front table and make those decisions in no more than 5 minutes.
5. Students are self-directed at this point and the teacher assumes the role of facilitator. The lab sheet (attached) will show that they need to perform three trials.
   
   • 1st trial students will perform 50 (tosses, spins, or rolls).
   • 2nd trial students will perfom 100 (tosses, spins, or rolls).
   • 3rd trial students will perform 200 (tosses, spins, or rolls).
6. Students will see that their results should be recorded on their Lab Sheet and probabilities/percents should be determined. Students should discover that as the number of trials increases, the probability of their experiments should get closer to the theoretical probability.
7. As an extension, ask students to use their results to predict results for larger trials, such as 1000 trials, 10,000 trials.
8. Discuss findings.

Assessment

Writing assignment/Application problems from text.

• Ask students to summarize their own thoughts on the activity. They should include how they think you find theoretical probability, experimental probability, and explain how the two are related.
• There are examples of released test bank items from the NC Standard Course of Study in the Sample - Attachment.
• Written assignment should be graded on a rubric while application questions are graded for accuracy.
• Assessment for concept of complement can be judged asking the oral questions. Most students will not have difficulty with this concept.

Supplemental information

Math Blaster Mystery Software may be used to supplement the lab.

Attachments:

• Sample Application Problems
• Lab Sheet

Related websites

Activities that Practice Probability and Data Analysis Concepts http://www.shodor.org/interactivate/activities/data.html

Comments

I tend to lean toward structure. Chaos is not my thing. However, these activities are easy to bring back to order.

Don’t be detered by the number of trials. With a recorder, counter, and “doer”, it really does not take a long time to conduct the trials.