This sample material consists of the two investigations of Lesson 2, "Counting Throughout Mathematics." In the first investigation, students use counting methods developed in Lesson 1 to solve probability problems. In the second investigation, the focus shifts to algebra as students learn about the connections among combinations, the Binomial Theorem, and Pascal's triangle.
Throughout the curriculum, interesting problem contexts serve as the foundation for instruction. As lessons unfold around these problem situations, classroom instruction tends to follow a common pattern as elaborated under Instructional Design.
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The counting and reasoning skills developed in this unit will be applied in future units. For example, combinations are required in Unit 5, Binomial Distributions and Statistical Inference, for the binomial probability formula, and counting arguments related to binary strings are used in Unit 9, Informatics (the final discrete mathematics unit). Pascal's triangle is revisited in Unit 10, Problem Solving, Algorithms, and Spreadsheets.
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