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Probability

Tue, Jul 10, 2001; by Joe Douglas.

Dice: Title: Probability for grades 6 - 8

Teachers: This unit was created by Karen Ross and Joe Douglas

Grade Level: middle school (6-8)

Subject: Mathematics

Time Allotment: 3-5 periods

Overview:

This unit was designed to help meet the needs of all subject areas in addressing one of our QPA targets, Probability. It includes two exploration activities to provide students with hands-on experience on experimental and theoretical probability. The culminating activity can be especially beneficial for students who have been absent as well as reviewing and providing enrichment. Cross-curricular web links are included along with probability topics for the various subject areas.

Learning Objectives: Students will be able to:

  • define and find experimental and theoretical probabilities of single and/or compound events
  • write probabilities as fractions, decimals and percents
  • explain and give examples of certain and impossible events

    • Standards: Standard 4: The student uses concepts and procedures of data analysis in a variety of situations. Benchmark 1: PROBABILITY - The student uses probability to generate convincing arguments, draw conclusions, and make decisions in a variety of situations.

    Materials needed: dice, coins, spinners, counters

    Our Probability Website

    Prep for Teachers: Check web sites for broken links.

    Vocabulary:

  • experiment - an activity whose results can be observed and recorded
  • outcome - result of an experiment
  • probability - number from 0 to 1 that tells you how likely something is to happen
  • experimental probability - ratio of the number of times the outcome happened to the number of times the experiment was repeated
  • equally likely - outcomes that have the same chance of occurring
  • event - set of outcomes for a particular experiment
  • theoretical probability - ratio of the number of outcomes in the event to the total number of possible outcomes
  • impossible event - an event that cannot happen; probability of 0
  • certain event- an event that must happen; probability of 1
    • Introductory Activity: Discuss with students how probability can effect strategies for games, puzzles and real-life situations.

    Learning Activity: The teacher will need to adapt this lesson to their grade level and resources available. This lesson uses McDougal Littel Middle Grades Math Thematics, book 1, module 4, section 1.

    Step one: Students will work with a partner to complete Exploration 1 on p. 235-237. The exploration deals with experimental probabilities. It involves tossing a single coin and recording the number of head and tail for 20 tosses. Vocabulary is discussed and writing probabilities in fraction, decimal and percent form is practiced. A similar experiment can be conducted by using Ken White's Coin Flipping Page.

    Step two: Students will work with a partner to complete Exploration 2 on p. 239-241. The exploration deals with theoretical probabilities. Students will play a dice game to develop strategies for winning the game. Vocabulary is discussed and writing probabilities in fraction, decimal and percent form is practiced. Probability number lines are introduced. A similar activity can be found at The Cereal Box Problem website which compares experimental and theoretical probability.

    Culminating Activity: Take your students to the lab to review, reinforce and extend their understanding of probability. Follow this link to our Trackstar page on Probability.

    Cross-Curricular Extensions:

    Language Arts Students calculate the probability of certain letters being used more than others. Students determine theoretical probability as they participate in this activity.

    Science This site has statistics and probability links.

    Language Arts Play "Wizard of Odds" Short play using probability vocabulary.

    Chance and Data in the News These are newspaper articles relating to probability in all subject areas. There are teacher discussion as well as student questions along with the article. You will need to pick Chance and Basic Probability from the menu list. This site also offers statistics and graphing topics.

    Suggestions for probability topics:

    Science - DNA, weather forecasting, blood types, medical research, HIV

    Social Studies - Census, polling, elections, stock market

    Language Arts - Advertising, marketing

    PE/Health - Sports statistics

    Reading/Literature - newspaper

    Sample Rubric

    Student Name: ______________________ Date: ________________

    Grade: ___________

    Teacher Name: ________________

    Subject: Probability

    5 Thorough-Fully achieves the purpose of the task, while insightfully interpreting, extending beyond the task, or raising provocative questions.

    Demonstrates an in-depth understanding of concepts and content. Communicates effectively and clearly to various audiences, using dynamic and diverse means.
    4 Essential - Accomplishes the purpose of the task.
    Shows clear understandings of concepts. Communicates effectively.
    3 Limited-Purpose of the task not fully achieved; needs elaboration; some strategies may be ineffectual or not appropriate; assumptions about the purposes may be flawed.
    Gaps in conceptual understanding are evident. Limits communication to some important ideas; results may be incomplete or not clearly presented.
    2 Little-Important purposes of the task not achieved; work may need redirection; approach to task may lead away from its completion.
    Presents fragmented understanding of concepts; results may be incomplete or arguments may be weak. Attempts communication.
    1 No Understanding - Purpose of the task not accomplished.
    Shows little evidence of appropriate reasoning. Does not successfully communicate relevant ideas; presents extraneous information.
    0 No Attempt-Task not attempted


    Last update: Thursday, August 23, 2001 at 9:04:25 AM.