The sample material from Discrete Models of Change is the second lesson of the unit. In the first lesson, recursive formulas were used to model situations, and the effect of parameter changes on long-term behavior in these situations was examined. Lesson 2, "A Discrete View of Function Models," develops student understanding of arithmetic and geometric sequences and their connections to linear and exponential functions. Finite differences tables are used to find power function formulas for selected recursive formulas.
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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In Course 4, the Counting Models unit extends student ability to count systematically and solve enumeration problems, and develops understanding of, and ability to do, proof by mathematical induction.
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