Estimating Probabilities through Repeated Experiments (IM Grade 7, Unit 8, Lesson 4)
Task
Lesson Purpose In this lesson students roll a number cube many times and calculate the cumulative fraction of the trials for which an event occurs to see that in the long run this relative frequency approaches the probability of the event. Students must examine the structure of the repeated trials to recognize the connection between long-run frequency and probability (MP8). They also see that the relative frequency of a chance event will not usually exactly match the actual probability. How Tuva Enhances the lesson Tuva removes unnecessary computational and graphing barriers so students can focus on the core mathematical goal of the lesson: understanding how a cumulative fraction of wins stabilizes and represents probability. As students record the total number of wins for Mai, Tuva automatically calculates the fraction of wins and plots each data point in real time. This allows students to immediately see how the cumulative fraction changes as more trials are added, rather than spending instructional time calculating fractions or plotting points by hand. Because students insert and generate their own data, the graph updates dynamically, making the pattern of the data visible as it develops. This supports students in noticing how the fraction begins to “settle in” and provides a clear visual model of probability emerging over time. Illustrative Mathematics explicitly notes that using an applet allows students to focus on visualizing the cumulative fraction narrowing in on the probability, rather than on the mechanics of plotting on a coordinate plane. Tuva strengthens this intent by keeping all representations—data table, fractions, and graph—visible on one screen, reducing cognitive load and keeping students’ attention on the mathematics that matters most.
In the Long Run Mai plays a game in which she only wins if she rolls a 1 or a 2 with a standard number cube.
Topics and standards: Math, 7-SP-C-6, 7-SP-C-5, 7-SP-C-7-B, Grade 7, Illustrative Math & Tuva, 7.RP.A, 7.SP.C.7