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Learning Progressions, Learning Intentions & Success Criteria

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 14: Periodic Phenomena

Exploring periodic phenomena prior to formal modeling.

Learning Intention 3.1.A: I am learning to construct graphs of periodic relationships based on verbal representations.

Success Criteria:

Learning Intention 3.1.B: I am learning to describe key characteristics of a periodic function based on a verbal representation.

Success Criteria:

Learning Progression 15: Sine & Cosine

Tangent also defined. Unit circle.

No degree conversion included as we are trying to develop native radian thinkers.

Learning Intention 3.2.A: I am learning to determine the sine, cosine, and tangent of an angle using the unit circle.

Success Criteria:

Learning Intention 3.2.A: Optional Day - I am learning to determine the sine, cosine, and tangent of an angle using the unit circle.

Success Criteria:

Learning Intention 3.2.A: Optional Day - I am learning to determine the sine, cosine, and tangent of an angle using the unit circle.

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Learning Intention 3.3.A: I am learning to determine coordinates of points on a circle centered at the origin.

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Learning Intention 3.3.A: Optional Day - I am learning to determine coordinates of points on a circle centered at the origin.

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Learning Intention 3.3.A: Optional Day - I am learning to determine coordinates of points on a circle centered at the origin.

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Learning Intention 3.4.A: I am learning to construct representations of the sine and cosine functions using the unit circle.

Success Criteria:

Learning Intention 3.4.A: Optional Day - I am learning to construct representations of the sine and cosine functions using the unit circle.

Success Criteria:

Learning Intention 3.4.A: Optional Day - I am learning to construct representations of the sine and cosine functions using the unit circle.

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Learning Progression 16: Sinusidial Modeling

Sinusoidal function and transformations. Modeling scenarios and data sets.

Learning Intention 3.5.A: I am learning to identify key characteristics of the sine and cosine functions.

Success Criteria:

Learning Intention 3.5.A: Optional Day - I am learning to identify key characteristics of the sine and cosine functions.

Success Criteria:

Learning Intention 3.5.A: Optional Day - I am learning to identify key characteristics of the sine and cosine functions.

Success Criteria:

Learning Intention 3.6.A: I am learning to identify the amplitude, vertical shift, period, and phase shift of a sinusoidal function.

Success Criteria:

Learning Intention 3.6.A: Optional Day - I am learning to identify the amplitude, vertical shift, period, and phase shift of a sinusoidal function.

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Learning Intention 3.6.A: Optional Day - I am learning to identify the amplitude, vertical shift, period, and phase shift of a sinusoidal function.

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Learning Intention 3.7.A: I am learning to construct sinusoidal function models of periodic phenomena by estimating key values.

Success Criteria:

Learning Intention 3.7.A: Optional Day - I am learning to construct sinusoidal function models of periodic phenomena by estimating key values.

Success Criteria:

Learning Intention 3.7.A: Optional Day - I am learning to construct sinusoidal function models of periodic phenomena by estimating key values.

Success Criteria:

Learning Progression 17: Trigonometry

Inverse trig. Reciprocal functions.

Identities (equivalent representations) limited to: Pythagorean and its related identities, angle sum for sine and cosine, difference for sine and cosine, and double angle for sine and cosine.

Law Of Sines and Law Of Cosines are reserved for vectors, but can be done here.

Learning Intention 3.8.A: I am learning to construct representations of the tangent function using the unit circle.

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Learning Intention 3.8.B: I am learning to describe key characteristics of the tangent function.

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Learning Intention 3.8.C: I am learning to describe additive and multiplicative transformations involving the tangent function.

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Learning Intention 3.9.A: I am learning to construct analytical and graphical representations of the inverse of the sine, cosine, and tangent functions over a restricted domain.

Success Criteria:

Learning Intention 3.9.A: Optional Day - I am learning to construct analytical and graphical representations of the inverse of the sine, cosine, and tangent functions over a restricted domain.

Success Criteria:

Learning Intention 3.9.A: Optional Day - I am learning to construct analytical and graphical representations of the inverse of the sine, cosine, and tangent functions over a restricted domain.

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Learning Intention 3.10.A: I am learning to solve equations and inequalities involving trigonometric functions.

Success Criteria:

Learning Intention 3.10.A: Optional Day - I am learning to solve equations and inequalities involving trigonometric functions.

Success Criteria:

Learning Intention 3.10.A: Optional Day - I am learning to solve equations and inequalities involving trigonometric functions.

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Learning Intention 3.10.A: Optional Day - I am learning to solve equations and inequalities involving trigonometric functions.

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Learning Intention 3.11.A: I am learning to identify key characteristics of functions that involve quotients of the sine and cosine functions.

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Learning Intention 3.11.A: Optional Day - I am learning to identify key characteristics of functions that involve quotients of the sine and cosine functions.

Success Criteria:

Learning Intention 3.12.A: I am learning to construct sinusoidal function models of periodic phenomena by estimating key values.

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Learning Intention 3.12.B: I am learning to rewrite trigonometric expressions in equivalent forms with sine and cosine sum identities.

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Learning Intention 3.12.C: I am learning to solve equations using equivalent analytic representations of trigonometric functions.

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Learning Intention 3.12.A, 3.12.B and/or 3.12.C: Optional Day - The goal is to complete 3.12.A-3.12.C in 3-4 days.

Success Criteria: See 3.12.A, 3.12.B and/or 3.12.C.

Learning Progression 18: Polar

Trig connection and conversions from polar to rectangular.

Including complex numbers in trigonometric form. Covariation focus.

Learning Intention 3.13.A: I am learning to determine the location of a point in the plane using both rectangular and polar coordinates.

Success Criteria:

Learning Intention 3.13.A: Optional Day - I am learning to determine the location of a point in the plane using both rectangular and polar coordinates.

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Learning Intention 3.13.A: Optional Day - I am learning to determine the location of a point in the plane using both rectangular and polar coordinates.

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Learning Intention 3.14.A: I am learning to construct graphs of polar functions.

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Learning Intention 3.14.A: Optional Day - I am learning to construct graphs of polar functions.

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Learning Intention 3.14.A: Optional Day - I am learning to construct graphs of polar functions.

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Learning Intention 3.15.A: I am learning to describe characteristics of the graph of a polar function.

Success Criteria:

Learning Intention 3.15.A: Optional Day - I am learning to describe characteristics of the graph of a polar function.

Success Criteria:

Learning Intention 3.15.A: Optional Day - I am learning to describe characteristics of the graph of a polar function.

Success Criteria:

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