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Unit Narrative
This unit both introduces the concept of sequences, and also provides an opportunity to revisit various representations of functions (including graphs, tables, and expressions) at the beginning of the Algebra 2 course. Through many concrete examples, students learn that geometric sequences are characterized by a common ratio, and arithmetic sequences are characterized by a common di erence.
After several lessons describing such sequences informally, students learn to describe them more formally using recursive and closed-form de nitions. In previous courses, students wrote expressions de ning linear and exponential functions. In this unit, students encounter tables and graphs that relate the number giving the position of the term and value of the term for arithmetic and geometric sequences. These representations are familiar from students' earlier study of linear and exponential functions, so they can build on prior knowledge to write closed-form de nitions of arithmetic and geometric sequences. The closed-form de nitions are also built up through expressing regularity in repeated reasoning (MP8). For example, the geometric sequence 6, 18, 54, 162, . . . could be written which makes it easy to see that the th term can be de ned (assuming we start at the 0th term, or )
In order to emphasize that sequences are functions, function notation is used to de ne sequences. For example the arithmetic sequence 2, 6, 10, 14, . . . might be de ned
for or
In the last part of the unit, students model several situations with sequences represented in di erents ways (MP4). This isn't meant to be full-blown modeling, but to touch on some practices that must be attended to while modeling, such as choosing a good model and expressing numbers with an appropriate level of precision. Students also recognize that a sequence is a function whose domain is a subset of the integers. Finally, students encounter some situations where it makes sense to compute the sum of a nite sequence. Developing a formula for such a sum occurs in a future unit.
Unit 1 Table of Contents 5