Lesson Plan

Using Area to Analyze Probabilities


Grade Levels

Related Academic Standards

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Eligible Content

Big Ideas




Students solve problems in which they calculate probability by considering the area represented by each of the possible outcomes. Tree diagrams and other probability organizers are reviewed and explored. The concepts of independent and dependent events are discussed. Activities use only independent compound events. Students will:

  • use tree diagrams to list outcomes of compound events.
  • calculate probabilities using tree diagrams.
  • create and use area models to calculate probability.
  • know the difference between area models and organized charts of outcomes.
  • define the vocabulary words: area model, experimental vs. theoretical probability, independent events, organized lists and charts of outcomes, sample space, simple event, and compound events.

Essential Questions

  • What makes a tool and/or strategy appropriate for a given task?
  • In what ways are the mathematical attributes of objects or processes measured, calculated, and/or interpreted?
  • How can data be organized and represented to provide insight into the relationship between quantities?
  • How can probability and data analysis be used to make predictions?


  • Compound Event: An event made up of two or more simple events.
  • Dependent Events: Two events in which the outcome of one event affects the outcome of the other event.
  • Independent Events: Two events in which the outcome of one event does not affect the outcome of the other event.


60–90 minutes

Prerequisite Skills


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Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

  • Random generators for numbers, coins, cards, etc.


  • Sophisticated and flexible random-number generator and number-cube roller


Formative Assessment


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Instructional Procedures


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