Brendan Kelly Pub. Data Analysis,Stats and Prob

DESC.- BRENDAN KELLY PUBLISHING

Features: Data Analysis, Statistics and Probability Learning Activity

• By Dr. Brenden Kelly
• This module addresses the expectations for grades 6 through 8 in the data analysis, statistics, and probability strand of the NCTM's Principles and Standards for School Mathematics 2000. There are two units with five activities per unit. The content of the activities in each unit is described below.
• Unit 1: Activity 1 opens with a discussion of the African elephant as an endangered species and explores the causes of this endangerment. Students estimate the size of an elephant herd by counting elephants in a grid superimposed on an aerial photo of an elephant herd.
• In Activity 2, data are presented that show the depletion of the elephant populations by region between 1981 and 1989. Students create double bar graphs to compare the populations at the beginning and end of the 1980s decade.
• In Activity 3, students investigate the masses of 40 elephant tusks found in a hidden cache. They organize these data into a stem-and-leaf plot and determine the mean and median tusk masses. By examining the range of values and the extrema, students observe that some of the tusks must belong to immature elephants, suggesting that the poachers have moved from the killing of large mature male elephants to the slaughter of families. This hypothesis is further supported by articles that show how the mean mass of the tusks in the more recent reports seems to be diminishing.
• Activity 4 requires students to combine the information gleaned in the first three activities into a report in which they answer, with supporting arguments, the question, "Will the African Elephant become extinct in your lifetime."
• Unit 2: This unit challenges students with the question, s the World Series rigged?
• In Activity 1, the student is introduced to the context of the problem, and guided through a review of the fundamental language of probability. Such terms as frequency, relative frequency, outcomes, equally likely, and simulate are reviewed in this context.
• Activity 2 pairs the students in a est-four-out-of-seven coin toss simulation of a World Series. Students toss a coin until either heads or tails has occurred a total of 4 times, and they record the number of tosses required. (This is called a rial They repeat this simulation for 20 trials, tallying the number of trials that required 4, 5, 6, and 7 tosses. By calculating the relative frequency of each of these possible outcomes, students obtain an estimate of the true probability of each outcome.
• In Activity 3, students actually calculate the probability of each outcome using tree diagrams.

* Activity 4 ties the previous investigations together by having
students compare the theoretical probabilities found in Activity 3
with the experimental probabilities found in Activity 2, and then
attempt to reconcile these probabilities with the observed occurrence
of the 7-game series over the past 50 years.