Multiple Problem-Solving Strategies and Representational Equivalence for Precalculus (CoRD)
Candace Andrews, University of Oklahoma
Carye Chapman, University of Oklahoma
Casey Violette Haskins, University of Oklahoma
Cory Wilson, Oklahoma City Community College
We present eight activities intended to function either as introductory or expository material for specific concepts in a precalculus sequence. Specifically, we focus on functions and their inverses, average rate of change, graphical transformations, solving composed equations, the ambiguous case of the law of sines, and inverse trigonometric functions and their graphs. We also present activities for modeling with contextual applications and working with multiple representations of functions.
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Graphical Transformations – An Introduction
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This activity is designed to guide students through the development of graphical transformations, and incorporates numerical, graphical, and algebraic representations. The activities are heavily scaffolded, with the intention of forcing students to slow down and give earnest thought to the similarities and differences between the types of transformations, as well as what is actually occurring when transformations are applied.
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Functions and Their Inverses
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This activity is intended to provide students with practice working with inverses of functions. We address the concept of an inverse, its use, as well as potential issues in defining an inverse function (and solutions to the issue).
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Modeling with Contextual Applications
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In this activity, we introduce two real-world situations for which students are asked to investigate different models, and determine their utility for the situation as well as other characteristics.
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Average Rate of Change
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This activity addresses average rate of change as a both a geometric and algebraic object, and attempts to bridge the two descriptions. Activities focus on algebraic, numeric, verbal, and graphical descriptions.
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Multiple Representations of Functions
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In this activity, we investigate functions under different representations, and ask students to convert between representations. Students are also asked to interpret and make sense of data and information presented in different representations.
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Solving Composed Equations
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This activity begins by easing students into solving equations which they should be familiar with, and uses them as a stepping stone to solve equations dealing with function composition. Care is taken to encourage students think critically about the similarities and differences between solving composed equations and similar, but uncomposed, equations.
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Inverse Trigonometric Functions and Graphs
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This activity aims to extend students’ understanding of inverse functions and their graphs to the class of trigonometric functions (specifically: sine, cosine, and tangent). We address the development of restricted domains for the inverse functions, and encourage exploration of that idea.
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Ambiguous Case of the Law of Sines
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This activities introduces the ambiguous case of the Law of Sines through exploration of the unit circle and the range of inverse trig functions.
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This work is licensed under CC BY-NC-SA 4.0
