Mathematical Practices
Can also be used as Embedded Common Formative Assessments
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AP Precalculus centers on functions modeling dynamic phenomena. Research indicates that deep understanding of functions and their graphs as embodying dynamic covariation of quantities best supports student preparation for calculus.
AP Precalculus Mathematical Practices
Click the skill for Questions to Ask Students & Sample Activities.
Solve equations & inequalities represented analytically, with and without technology.
Express functions, equations, or expressions in analytically equivalent forms that are useful in a given mathematical or applied context.
Construct new functions using transformations, compositions, inverses, or regressions, that may be useful in modeling contexts, criteria, or data, with and without technology.
Identify information from graphical, numerical, analytical, and verbal representations to answer a question or construct a model, with and without technology.
Construct equivalent graphical, numerical, analytical, and verbal representations of functions that are useful in a given mathematical or applied context, with and without technology.
Describe the characteristics of a function with varying levels of precision, depending on the function representation and available mathematical tools.
Apply numerical results in a given mathematical or applied context.
Support conclusions or choices with a logical rationale or appropriate data.
Building Mathematical Practices in Unit 4
Conic Sections, Vectors & Matrices
When encountering new function types, students should engage with multiple representations of each function type and practice communicating precise characteristics of these function types. For parametric and vector-valued functions, students will need to use care in communicating about the position or velocity of an object, depending on the function that is given. Students should practice the precise language used with particle motion in the plane and refer specifically to position, direction, and motion. It will be valuable for students to provide clear rationales when setting up and working with matrices as linear transformation functions on vectors. Students should explain why they took the steps they did.
See AP Classroom for more information.
To further build in math practices, check out the Assessment tab!
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