Probability and Sports

Abstract

This lesson is devoted to Internet research on a specific topic: finding topics in sports where probability is relevant. The goal of the lesson is to introduce some statistics and probability concepts by looking at practical questions that arise in professional sports.

Objectives

Upon completion of this lesson, students will:

  • have seen that knowledge of probability concepts is useful when looking at sports
  • have learned to search for a specific topic on the internet

Standards Addressed

Grade 6

  • Statistics and Probability

    • The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 7

  • Statistics and Probability

    • The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 8

  • Statistics and Probability

    • The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 9

  • Statistics and Probability

    • The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 10

  • Statistics and Probability

    • The student demonstrates a conceptual understanding of probability and counting techniques.

Third Grade

  • Measurement and Data

    • Represent and interpret data.

Seventh Grade

  • Statistics and Probability

    • Investigate chance processes and develop, use, and evaluate probability models.

Statistics and Probability

  • Using Probability to Make Decisions

    • Calculate expected values and use them to solve problems
    • Use probability to evaluate outcomes of decisions

Grades 6-8

  • Data Analysis and Probability

    • Develop and evaluate inferences and predictions that are based on data
    • Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
    • Understand and apply basic concepts of probability

Advanced Functions and Modeling

  • Data Analysis and Probability

    • Competency Goal 1: The learner will analyze data and apply probability concepts to solve problems.

Textbooks Aligned

Grade Six

  • How Likely Is It?

    • Investigation Seven: Probability and Genetics

7th

  • Module 6 - Flights of Fancy

    • Section 2: Probability
      • Reason for Alignment: Probability and Sports is a lesson that uses Internet research into any chosen sport. Students then use real data to research specific topics in the sport where probability is relevant.

8th

  • Module 2 - At the Mall

    • Section 3: Exploring Probability
      • Reason for Alignment: This lesson involves very little teacher input and mostly independent practice. The student does internet research on a sport to begin. This idea should appeal to most students and provide good real world applications for probability.

Student Prerequisites

  • Arithmetic: Students must be able to:
    • relate the sports information they collect to mathematical expression
    • use simple addition, subtraction, multiplication and division when working with the sports information they collect
  • Technological: Students must be able to:
    • perform basic mouse manipulations such as point, click and drag
    • use a browser for experimenting with the activities

Teacher Preparation

  • Access to a browser
  • Pencil and Paper

Key Terms

experimental probability

The chances of something happening, based on repeated testing and observing results. It is the ratio of the number of times an event occurred to the number of times tested. For example, to find the experimental probability of winning a game, one must play the game many times, then divide the number of games won by the total number of games played

probability

The measure of how likely it is for an event to occur. The probability of an event is always a number between zero and 100%. The meaning (interpretation) of probability is the subject of theories of probability. However, any rule for assigning probabilities to events has to satisfy the axioms of probability

theoretical probability

The chances of events happening as determined by calculating results that would occur under ideal circumstances. For example, the theoretical probability of rolling a 4 on a four-sided die is 1/4 or 25%, because there is one chance in four to roll a 4, and under ideal circumstances one out of every four rolls would be a 4. Contrast with experimental probability

Lesson Outline

  1. Focus and Review

    Remind students of what they learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:

    • How many of you like to play sports?
    • When you are getting ready to play a game, are there some teams that you know your team can beat easier than others?

  2. Objectives

    Let the students know what they will be doing and learning today. Say something like this:

    • Today, class, we are going to learn how probability applies to sports.
    • We are going to use the computers to learn about applying probability to sports, but please do not turn your computers on until I ask you to. I want to show you a little about this activity first.

  3. Teacher Input

    • Review some basic probability facts and explain to the students what they will be doing.

  4. Guided Practice

    • Have each person or group decide which sport they would like to research and monitor them as they begin their searches.
    • You can suggest people search for probability information in the web sites related to the following sports:

  5. Independent Practice

    • Have students search one of the four sports provided (or find information about a different sport, if desired) to find connections between the sport and probability. Each student or group of students can find and then share a piece of information about chances to win against a particular player or team, chances to make a "hole in one" in golf, chances of making a basket in basketball, or anything else connected with probability that they may find on these sports pages.
    • Search for answers to specific questions. Each student or group of students can come up with specific questions concerning sports, and try to find answers using Internet resources.
    • Sports challenge: "Do you believe it?" Students or groups of students find pieces of probability information on sports, and then challenge another group to confirm or refute their data. Students do not necessarily give the correct answer, making the activity more interesting. For example, having found that the record drive for a long drive in a golf contest is 448 yards, the students may challenge another group: "Is it true that the record drive is above 470 yards?" Students can give hints, for example, the address of the website where they have found the information.

  6. Closure

    • You may wish to bring the class back together for a discussion of the findings. Once the students have been allowed to share what they found, summarize the results of the lesson.

Alternate Outline

This lesson can be rearranged in several ways.

Suggested Follow-Up

After this lesson, the students will have seen practical applications of how probability is used in everyday situations such as sports. The next lesson, Ideas That Lead to Probability, introduces ideas that are the basis of probability theory. By using everyday experiences and intuitive understanding, this lesson gives students a gradual introduction to probability. Students will work with random number generators and learn what it means for a game to be fair.