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Guiding Principles of Mathematics Instruction:

  • Mathematical proficiency is defined by conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition (National Research Council, 2001).
  • Mathematical proficiency drives independent thinking, reasoning, and problem-solving.
  • Mathematical proficiency is the foundation for careers in science, technology, engineering and mathematics (STEM), and it is increasingly becoming the foundation for careers outside of STEM (NCTM, 2018)
  • Effective mathematics teaching “engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically” (NCTM, 2014).
  • Standards-based instruction accelerates student gains.
  • Students construct mathematical knowledge through exploration, discussion, and reflection.
  • Teachers are facilitators of student learning, as they engage students in rich tasks. Administrators are change agents and have the power to create and to support a culture of mathematical proficiency.
Click here to select one or multiple grades.
Select one Content Area or High School course at a time.
Search for key words within each standard's description.
Standard Grade Area/Subject Description
TR.CO.6

High School

H.S. Trigonometry

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

TR.ID.1

High School

H.S. Trigonometry

Prove the Pythagorean identity sin^2(x) + cos^2(x) = 1 and use it to find trigonometric ratios, given sin(x), cos(x), or tan(x), and the quadrant of the angle.

TR.ID.2

High School

H.S. Trigonometry

Verify trigonometric identities and simplify expressions using trigonometric identities.

TR.ID.3

High School

H.S. Trigonometry

Prove the addition and subtraction identities for sine, cosine, and tangent. Use the identities to solve problems.

TR.ID.4

High School

H.S. Trigonometry

Prove the double- and half-angle identities for sine, cosine, and tangent. Use the identities to solve problems.

TR.PC.1

High School

H.S. Trigonometry

Understand and use complex numbers, including real and imaginary numbers, on the complex plane in rectangular and polar form, and explain why the rectangular and polar forms of a given complex number represent the same number.

TR.PC.2

High School

H.S. Trigonometry

State, prove, and use DeMoivre’s Theorem.

TR.PC.3

High School

H.S. Trigonometry

Define polar coordinates and relate polar coordinates to Cartesian coordinates.

TR.PC.4

High School

H.S. Trigonometry

Translate equations from rectangular coordinates to polar coordinates and from polar coordinates to rectangular coordinates. Graph equations in the polar coordinate plane.

TR.PF.1

High School

H.S. Trigonometry

Graph trigonometric functions with and without technology. Use the graphs to model and analyze periodic phenomena, stating amplitude, period, frequency, phase shift, and midline (vertical shift).

TR.PF.2

High School

H.S. Trigonometry

Model a data set with periodicity using a sinusoidal function and explain the parameters of the model.

TR.PF.3

High School

H.S. Trigonometry

Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

TR.PF.4

High School

H.S. Trigonometry

Construct the inverse trigonometric functions of sine, cosine, and tangent by restricting the domain.

TR.PF.5

High School

H.S. Trigonometry

Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

TR.T.1

High School

H.S. Trigonometry

Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right triangles and the coordinates on the unit circle.

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