Lesson plan

4. Finding theoretical probabilities: Marble madness (C)

teaches Common Core State Standards CCSS.Math.Content.7.SP.C.5 http://corestandards.org/Math/Content/7/SP/C/5
teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards CCSS.Math.Practice.MP4 http://corestandards.org/Math/Practice/MP4
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Lesson objective: Understand that the probability of a random event can be written as the ratio of favorable outcomes to all possible outcomes.  This can be expressed as a decimal or percent between 0 and 1.

Students bring prior knowledge of ratios from 6th Grade (6.RP.A.1). This prior knowledge is extended to probability as students write ratios to represent the probability of an event. A conceptual challenge students may encounter is thinking that the number of favorable outcomes determines the likelihood, rather than the ratio of favorable outcomes as compared to all possible outcomes. 

The concept is developed through work with ratios, which compare favorable outcomes to all possible outcomes as part-to-whole ratios. 

This work helps students deepen their understanding of number because they write probabilities as fractions, decimals, and percents.

Students engage in Mathematical Practice 4 (Model with mathematics) as they compare different combinations of marbles using fractions, decimals, and percents in order to understand which combination will give them a better chance of winning.

Key vocabulary:

  • favorable outcome
  • probability