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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.
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Learning Progression 8: Sequences & Corresponding Functions
Focus on functions - sequences are functions on the whole numbers.
Arithmetic - linear connection. Geometric - exponential connection.
Learning Intention 2.1.A: I am learning to express arithmetic sequences found in mathematical and contextual scenarios as functions of the natural numbers.
Learning Intention 2.1.A: I am learning to express arithmetic sequences found in mathematical and contextual scenarios as functions of the natural numbers.
Success Criteria:
Learning Intention 2.1.B: I am learning to express geometric sequences found in mathematical and contextual scenarios as functions of the natural numbers.
Learning Intention 2.1.B: I am learning to express geometric sequences found in mathematical and contextual scenarios as functions of the natural numbers.
Success Criteria:
Learning Intention 2.2.A: I am learning to construct functions of the real numbers that are comparable to arithmetic and geometric sequences.
Learning Intention 2.2.A: I am learning to construct functions of the real numbers that are comparable to arithmetic and geometric sequences.
Success Criteria:
Learning Intention 2.2.B: I am learning to describe similarities and differences between linear and exponential functions.
Learning Intention 2.2.B: I am learning to describe similarities and differences between linear and exponential functions.
Success Criteria:
Learning Intention 2.1.A, 2.1.B, 2.2.A and/or 2.2.B: Optional Day - The goal is to complete 2.1-2.2 in 4-5 days.
Learning Intention 2.1.A, 2.1.B, 2.2.A and/or 2.2.B: Optional Day - The goal is to complete 2.1-2.2 in 4-5 days.
Success Criteria: See 2.1.A, 2.1.B, 2.2.A and/or 2.2.B.
Learning Progression 9: Exponential Functions
How you build them. How you manipulate them. Rules for exponents.
Success Criteria:
Learning Intention 2.3.A: Optional Day - I am learning to identify key characteristics of exponential functions.
Learning Intention 2.3.A: Optional Day - I am learning to identify key characteristics of exponential functions.
Success Criteria:
Success Criteria:
Learning Intention 2.4.A: Optional Day - I am learning to rewrite exponential expressions in equivalent forms.
Learning Intention 2.4.A: Optional Day - I am learning to rewrite exponential expressions in equivalent forms.
Success Criteria:
Learning Progression 10: More on Modeling
Exponential function modeling. 2.6 Model validation via residual plots (not r or r^2).
Learning Intention 2.5.A: I am learning to construct a model for situations involving proportional output values over equal-length input-value intervals.
Learning Intention 2.5.A: I am learning to construct a model for situations involving proportional output values over equal-length input-value intervals.
Success Criteria:
Learning Intention 2.5.B: I am learning to apply exponential models to answer questions about a data set or contextual scenario.
Learning Intention 2.5.B: I am learning to apply exponential models to answer questions about a data set or contextual scenario.
Success Criteria:
Learning Intention 2.5.A and/or 2.5.B: Optional Day - The goal is to complete 2.5.A-2.5.B in 2-3 days.
Learning Intention 2.5.A and/or 2.5.B: Optional Day - The goal is to complete 2.5.A-2.5.B in 2-3 days.
Success Criteria: See 2.5.A and/or 2.5.B.
Learning Intention 2.6.A: I am learning to construct linear, quadratic, and exponential models based on a data set.
Learning Intention 2.6.A: I am learning to construct linear, quadratic, and exponential models based on a data set.
Success Criteria:
Success Criteria:
Learning Intention 2.6.A and/or 2.6.B: Optional Day - The goal is to complete 2.6.A-2.6.B in 2-3 days.
Learning Intention 2.6.A and/or 2.6.B: Optional Day - The goal is to complete 2.6.A-2.6.B in 2-3 days.
Success Criteria: See 2.6.A and/or 2.6.B.
Learning Progression 11: Composition & Inverses
This progression can be anywhere after transformations. It is located here for direct application to logs.
Learning Intention 2.7.A: I am learning to evaluate the composition of two or more functions for given values.
Learning Intention 2.7.A: I am learning to evaluate the composition of two or more functions for given values.
Success Criteria:
Learning Intention 2.7.B: I am learning to construct a representation of the composition of two or more functions.
Learning Intention 2.7.B: I am learning to construct a representation of the composition of two or more functions.
Success Criteria:
Learning Intention 2.7.C: I am learning to rewrite a given function as a composite of two or more functions.
Learning Intention 2.7.C: I am learning to rewrite a given function as a composite of two or more functions.
Success Criteria:
Learning Intention 2.8.A: I am learning to determine the input-output pairs of the inverse of a function.
Learning Intention 2.8.A: I am learning to determine the input-output pairs of the inverse of a function.
Success Criteria:
Learning Intention 2.8.B: I am learning to determine the inverse of a function on an invertible domain.
Learning Intention 2.8.B: I am learning to determine the inverse of a function on an invertible domain.
Success Criteria:
Learning Intention 2.8.A and/or 2.8.B: Optional Day - The goal is to complete 2.8.A-2.8.B in 2-3 days.
Learning Intention 2.8.A and/or 2.8.B: Optional Day - The goal is to complete 2.8.A-2.8.B in 2-3 days.
Success Criteria: See 2.8.A and/or 2.8.B.
Learning Progression 12: All Things Logarithm
Logarithmic functions as the inverse of exponential functions.
Not just another set of rules to apply; it is another behavior we can model with a certain family of functions.
Success Criteria:
Learning Intention 2.10.A: I am learning to construct representations of the inverse of an exponential function with an initial value of 1.
Learning Intention 2.10.A: I am learning to construct representations of the inverse of an exponential function with an initial value of 1.
Success Criteria:
Learning Intention 2.10.A: Optional Day - I am learning to construct representations of the inverse of an exponential function with an initial value of 1.
Learning Intention 2.10.A: Optional Day - I am learning to construct representations of the inverse of an exponential function with an initial value of 1.
Success Criteria:
Success Criteria:
Learning Intention 2.11.A: Optional Day - I am learning to identify key characteristics of logarithmic functions.
Learning Intention 2.11.A: Optional Day - I am learning to identify key characteristics of logarithmic functions.
Success Criteria:
Success Criteria:
Learning Intention 2.12.A: Optional Day - I am learning to rewrite logarithmic expressions in equivalent forms.
Learning Intention 2.12.A: Optional Day - I am learning to rewrite logarithmic expressions in equivalent forms.
Success Criteria:
Learning Intention 2.12.A: Optional Day - I am learning to rewrite logarithmic expressions in equivalent forms.
Learning Intention 2.12.A: Optional Day - I am learning to rewrite logarithmic expressions in equivalent forms.
Success Criteria:
Learning Intention 2.13.A: I am learning to solve exponential and logarithmic equations and inequalities.
Learning Intention 2.13.A: I am learning to solve exponential and logarithmic equations and inequalities.
Success Criteria:
Learning Intention 2.13.B: I am learning to construct the inverse function for exponential and logarithmic functions.
Learning Intention 2.13.B: I am learning to construct the inverse function for exponential and logarithmic functions.
Success Criteria:
Learning Intention 2.13.A and/or 2.13.B: Optional Day - The goal is to complete 2.13.A-2.13.B in 3-4 days.
Learning Intention 2.13.A and/or 2.13.B: Optional Day - The goal is to complete 2.13.A-2.13.B in 3-4 days.
Success Criteria: See 2.13.A and/or 2.13.B.
Learning Intention 2.13.A and/or 2.13.B: Optional Day - The goal is to complete 2.13.A-2.13.B in 3-4 days.
Learning Intention 2.13.A and/or 2.13.B: Optional Day - The goal is to complete 2.13.A-2.13.B in 3-4 days.
Success Criteria: See 2.13.A and/or 2.13.B.
Success Criteria:
Learning Intention 2.14.A: Optional Day - I am learning to identify key characteristics of logarithmic functions.
Learning Intention 2.14.A: Optional Day - I am learning to identify key characteristics of logarithmic functions.
Success Criteria:
Learning Intention 2.14.A: Optional Day - I am learning to identify key characteristics of logarithmic functions.
Learning Intention 2.14.A: Optional Day - I am learning to identify key characteristics of logarithmic functions.
Success Criteria:
Learning Progression 13: Semi-log Plots
Logarithmic scale on the y-axis to linearize exponential data.
Solidifies conceptual connection: exponential and logarithmic as inverses.
Learning Intention 2.15.A: I am learning to determine if an exponential model is appropriate by examining a semi-log plot of a data set.
Learning Intention 2.15.A: I am learning to determine if an exponential model is appropriate by examining a semi-log plot of a data set.
Success Criteria:
Success Criteria:
Learning Intention 2.15.A and/or 2.15.B: Optional Day - The goal is to complete 2.15.A-2.15.B in 2-3 days.
Learning Intention 2.15.A and/or 2.15.B: Optional Day - The goal is to complete 2.15.A-2.15.B in 2-3 days.
Success Criteria: See 2.15.A and/or 2.15.B.
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