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Common Core: Math
Topic: Common Core Learning Standards
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 Student Outcomes Students use tangent segments and radii of circles to conjecture and prove geometric statements, especially those that rely on the congruency of tangent segments to a circle from a...

 Geometry Module 5: Circles With and Without Coordinates This module brings together the ideas of similarity and congruence and the properties of length, area, and geometric constructions studied...

 This module revisits trigonometry that was introduced in Geometry and Algebra II, uniting and further expanding the ideas of right triangle trigonometry and the unit circle. New tools are introduced...

 Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots...

 Algebra II Module 1: Polynomial, Rational, and Radical Relationships Students connect polynomial arithmetic to computations with whole numbers and integers. Students learn that the arithmetic of...

 Geometry Module 4: Connecting Algebra and Geometry Through Coordinates In this module, students explore and experience the utility of analyzing algebra and geometry challenges through the framework...

 Geometry Module 3: Extending to Three Dimensions Module 3, Extending to Three Dimensions, builds on students’ understanding of congruence in Module 1 and similarity in Module 2 to prove volume...

 Geometry Module 2: Similarity, Proof, and Trigonometry Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2. To be able to discuss...

 Geometry Module 1: Congruence, Proof, and Constructions Module 1 embodies critical changes in Geometry as outlined by the Common Core. The heart of the module is the study of transformations and the...

 Student Outcomes Inscribe a rectangle in a circle. Understand the symmetries of inscribed rectangles across a diameter.

 Topic A helps students recall how to use special triangles positioned within the unit circle to determine geometrically the values of sine, cosine, and tangent at special angles. The unit circle is...

 Student Outcomes Students construct a tangent line from a point outside a given circle to the circle.

 In this topic, students first distinguish between discrete and continuous random variables and then focus on probability distributions for discrete random variables. In the early lessons of this...

 In this topic, students extend their understanding of probability, building on work from Grade 11. The multiplication rule for independent events introduced in Grade 11 is generalized to a rule that...

 Student Outcomes Students prove the formula Area = 1/2 bc sin(A) for a triangle. They reason geometrically and numerically to find the areas of various triangles.

 Student Outcomes Students prove the law of sines and use it to solve problems.

 Student Outcomes Students prove the law of cosines and use it to solve problems.

 Student Outcomes Students apply the law of sines or the law of cosines to determine missing measurements in realworld situations that can be modeled using nonright triangles, including situations...

 Students derive sophisticated applications of the trigonometric functions in Topic B including: the area formula for a general triangle, the law of sines, the law of cosines, and Heron’s formula. ...

 Student Outcomes Students convert between the real and complex forms of equations for ellipses. Students write equations of ellipses and represent them graphically.

 Student Outcomes Students derive the equations of ellipses given the foci, using the fact that the sum of distances from the foci is constant.

 Student Outcomes Students learn to graph equations of the form x2/a2  y2/b2 =1 . Students derive the equations of hyperbolas given the foci, using the fact that the difference of distances from the...

 Student Outcomes Students will be able to give an informal argument using Cavalieri’s principle for the formula for the volume of a sphere and other solid figures.

 Student Outcomes Students show that a quadrilateral is cyclic if and only if its opposite angles are supplementary. Students derive and apply the area of cyclic quadrilateral ABCD as 1/2 AB·CD·sin(w...