Geometric Probability Lesson Plan

Instructor: Maria Airth

Maria has a Doctorate of Education and over 20 years of experience teaching psychology and math related courses at the university level.

In this lesson plan, teachers will find a guide to presenting the formula and method of finding geometric probabilities. Students will practice the method through active manipulation and composition of quizzes.

Learning Objectives

After this lesson, students will be able to:

  • Define geometric probabilities
  • Demonstrate an understanding of geometric probabilities
  • Explain the likelihood of an event based on geometric probabilities


45 - 60 Minutes

Curriculum Standards


Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or,' 'and,' 'not').


(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.


Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*


  • Transcripts of the video lesson Geometric Probability: Definition, Formula & Examples and hard copies of the lesson quiz
  • Audio/visual equipment
  • Sidewalk chalk (or masking/painter's tape)
  • Small bean bags (tossing bags)
  • Measuring tape
  • Activity Worksheet including the following:
    • Draw a scale diagram of your group's geometric design.
    • What geometric shapes were used?
    • What are the dimensions of the shapes used?
    • What is the geometric probability of tossing a bag into the smaller area?
    • What is the geometric probability of tossing a bag into the larger area?
    • What is the geometric probability of tossing a bag into the smaller area or the larger area?
    • What were your group's results after each member tossed the bag five times?
    • Was this expected? Why or why not?
    • What explanations might there be for unexpected results?

Warm Up

  • Begin the lesson by asking if anyone remembers the formulas for finding the area of common geometric shapes.
  • Write the shape names and area formulas on the board as students suggest them. Make sure to include shapes such as a square, rectangle, circle and/or triangle.
  • Ask for a volunteer to give the definition of probability. Confirm or correct the student's definition for the class.
  • Draw a geometric pattern on the board with one shape completely inside another. Ask students to imagine that they were going to throw a bag at the board:
    • What would be the probability of hitting the diagram?
    • Particular parts of the diagram?
    • Somewhere on the board itself?
  • Tell your class that today's lesson is about geometric probabilities and that by the end of the lesson they should be able to answer these questions.


  • Hand out hard transcripts of the video lesson Geometric Probability: Definition, Formula & Examples.
  • Begin the video lesson.
  • Pause the video at time marker 1:17 and check to see if there are any questions thus far. Ask:
    • Can anyone give me another scenario that would have a probability of 1? 0?
    • Why should we ignore probabilities like the coin landing on the edge?
  • Continue the video pausing periodically after calculations to have students write down the calculations themselves and give students an opportunity to ask questions they may have.
  • Write formulas and calculations on the board as they are discussed in the video.
  • After the video finishes, return to your previously drawn geometric shape (the one you drew during the warm-up) and ask students to help guide you through calculating the probabilities of the questions you asked related to the diagram. You will need to use a measuring tape to model measuring the shapes and labeling their sides.
  • Give students a final chance to ask questions before the quiz.
  • Hand out the lesson quiz. Go over each question and answer with the class after they have finished it.


Activity 1 - Active Game


  • Sidewalk chalk
  • Tossing bean bags
  • Measuring tape

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