The Smithville Families
Probability
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Objective
Students will create the number sequences of Pascal's triangle and discover a
relationship that this triangle has to theoretical probability.
Overview of the Lesson
First, students review Pascal’s Triangle by completing and discussing the entries of
the first eight rows. They then engage in an activity designed to determine the total
number of possible girl/boy combinations in a five-child family. This is
accomplished by having students investigate the number and make-up of different
five-child families that could be born in a town called Smithville. A coin is used to
simulate the births of different children. If the coin shows a head, the child is a girl
and if it shows a tail, the child is a boy. The different combinations are presented in
an organized manner so that students can discover patterns that will enable them to
identify all possibilities. Students are encouraged to look for patterns that will assist
them in generating the numbers in subsequent rows of Pascal’s Triangle. Finally,
students work collaboratively to address and analyze questions regarding the
theoretical probabilities of other multiple-child families using Pascal's Triangle.
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