Summary:

At the Stine School in Bakersfield, California, Gerrie Kincaid and her students experience the differences between mathematical probability and experimental probability when they experiment to determine which sum will occur most frequently when two dice are rolled. This comes after a discussion and a listing of the sums that can be obtained when rolling two dice. Student teams consist of a recorder, a dice keeper, a counter, and a reporter. The reporters share group results in a class bar graph, creating an aggregate of all their data. The class concludes with students analyzing the graph and determining that their predictions (based on mathematical probability insights) for most frequent and least frequent sums are born out (based on experimental probability results).

Standard Connections:

(Practice Standards)—Being able to reason abstractly and quantitatively is the Common Core Practice Standard #2 most apparent in this clip. Prior to conducting the class experiment, two students confidently reason (without concrete data) that "seven" will be the most frequent sum, because sums of seven can be rolled in the "most ways" (i.e. 6+1, 5+2, 4+3, 3+4, 2+5, 1+6). Using similar reasoning, one girl surmised that "twelve" would be the least frequent sum rolled. After the experiments, the collected data is analyzed, and quantitative reasoning is on display. One girl's comments about combinations are related to her new quantitative insights. A boy uses the metaphor of a rocket to describe his new quantitative insights into why a bell-shaped curve best represents probabilities expectations and experimental results.

(Content Standards)—The domain suggested by this clip is Statistics and Probability 7.SP. The students "develop a probability model and use it to find probabilities of events." Also, they are able to "compare probabilities from a model to observed frequencies."

Questions to Consider:

Given that this is an early lesson in the study of probability, what would you consider as appropriate next content to cover? At the conclusion of the experiment, one student still thought sums of two would be more likely to occur than sums of 12, because previous experiences informed her thinking. What would you do to clear up these misconceptions about probability?

2. Reasoning abstractly and quantitatively

7.SP Statistics and Probability