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A2-A-1-7

Page history last edited by Tashe Harris 6 years, 2 months ago

A2.A.1.7 Solve real-world and mathematical problems that can be modeled using arithmetic or finite geometric sequences or series given the nth terms and sum formulas. Graphing calculators or other appropriate technology may be used.

In a Nutshell

Students will identify geometric or arithmetic sequences/series within a real-world problem and use the appropriate formula to answer questions within the context of the problem.

Student Actions	Teacher Actions
Students will develop the ability to make conjectures and generalizations about whether a sequence or series is geometric or arithmetic from a mathematical or real-world problem. They will contextualize these mathematical ideas by connecting them to real-world situations and be able to defend their choice verbally and/or in writing. Students will develop accurate procedural fluency of the application of explicit and recursive formulas to solve a real-world problem using a geometric/arithmetic series or sequence. The will make conjectures and draw conclusions about whether a sequence or series is appropriate and if it is geometric or arithmetic based on patterns and the repeated structures present.	Implement tasks that allow students to decide which representation to use (arithmetic or geometric) to solve the problem. Build procedural fluency of both identifying whether a series or sequence is geometric or arithmetic within a problem and using the appropriate formula to answer the question.
Key Understandings	Misconceptions
Identify whether a real-world problem can be represented by a series or a sequence. Identify whether a real-world or mathematical problem can be represented by an arithmetic or geometric series/sequences. Use an explicit or recursive formula for geometric or arithmetic series/sequences to find unknowns within a real-world or mathematical problem.	Conceptual: Students do not know the difference between a series and a sequence. Students do not recognize arithmetic as repeated addition and geometric as repeated multiplication. Students do not understand the notation in a recursive formula.