Summary
The purpose of this lesson is to introduce students to the normal model, mean and standard deviation, and the check for normalcy process. Students will collect data, create a histogram, and convert their data into a normal model. Working in small groups, students will check their data so see if it is indeed normal, or fits the 68%-95%-99.7% rule. We use TI-84 Calculators and manually roll dice up to fifty more times (and beyond) to collect data for this activity. Students determine that the more data they have, the more bell-shaped their data curve becomes. As a result, students analyze that there are multiple ways to produce specific numbers with the roll of the dice. For instance, 3 and 4 will produce 7: 2 and 5 will produce 7; 6 and 1 will produce 7. Also, there are further limits on producing other numbers. For instance, there is one way to produce 2 (1 and 1); there is one way to produce 12 (6 and 6). The reflection segment of this activity via the discussion forum in Schoolspace provides with an opportunity to make predictions on the outcome of the normal model distribution given other unique circumstances.
TIPC Ratings
Although research and information fluency were not emphasized in this lesson, students use search strategies to investigate the impact of normal model and the bell curve on data.
Students work in pairs to collect data based upon the 50 times that they roll the dice. After creating their histogram and bell shaped curve, students circulate the classroom to view the data display of other groups. Their purpose in viewing the data of their peers is to determine how many other sets of data are similar in shape to their own. As they observe similarities, they briefly discuss the similarities with the other group(s). Using a discussion board forum in SchoolSpace, students document their observations, including trends that were apparent. They also make predictions. For instance, they clearly see that the more the dice are rolled, the more the data conforms to a bell-shaped curve. Students also respond to the reflections of at least one other student in the classroom.
While working in pairs, students respond to each other’s questions regarding the frequency of the sums on the dice that keep coming up. For example, they conclude that there are multiple ways to make 7: 3 and 4, 2 and 5, 6 and 1. They also conclude that there was only one way to make a 2: 1 and 1, or one way to make a 12: 6 and 6. They also observe that there is no difference in the frequency of sums on the dice rolled by hand and the dice rolled on the TI-84 calculator. Students put their data in the bell curve while analyzing their data to see if it fits with the 68%-95%-99.7% rule.
