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Common Core: Math
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 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 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...

 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 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...

 Students impose a coordinate system and describe the movement of the robot in terms of line segments and points. This leads to graphing inequalities and discovering regions in the plane can be...

 Topic A leads students first to Thales' theorem (an angle drawn from a diameter of a circle to a point on the circle is sure to be a right angle), then to possible converses of Thales' theorem, and...

 Student Outcomes Students review formerly learned geometry facts and practice citing the geometric justifications in anticipation of unknown angle proofs.

 Student Outcomes Students review formerly learned geometry facts and practice citing the geometric justifications in anticipation of unknown angle proofs.

 In Topic G, students review material covered throughout the module. Additionally, students discuss the structure of geometry as an axiomatic system.

 Student Outcome Students review formerly learned geometry facts and practice citing the geometric justifications regarding angles in a triangle in anticipation of unknown angle proofs.

 Students find midpoints of segments and points that divide segments into 3 or more equal and proportional parts and extend this concept prove classical results in geometry. Students are introduced...

 Topic D brings in coordinate geometry to establish the equation of a circle. Students solve problems to find the equations of specific tangent lines or the coordinates of specific points of contact...

 The module concludes with Topic E focusing on the properties of quadrilaterals inscribed in circles and establishing Ptolemy's theorem. This result codifies the Pythagorean theorem, curious facts...

 It is convenient, as adults, to use the notation “ ” to refer to the value of the square of the sine function. However, rushing too fast to this abbreviated notation for trigonometric functions...

 Student Outcomes Students learn to construct an equilateral triangle. Students communicate mathematic ideas effectively and efficiently.

 Student Outcomes Students apply the equilateral triangle construction to more challenging problems. Students communicate mathematical concepts clearly and concisely.

 Student Outcomes Students learn how to bisect an angle as well as how to copy an angle.

 Student Outcome Students learn to construct a perpendicular bisector and about the relationship between symmetry with respect to a line and a perpendicular bisector.

 Student Outcome Students become familiar with vocabulary regarding two points of concurrencies and understand why the points are concurrent.

 Student Outcome Students write unknown angle proofs, which does not require any new geometric facts. Rather, writing proofs requires students to string together facts they already know to reveal...

 Student Outcome Students write unknown angle proofs involving auxiliary lines.

 Student Outcomes Students write unknown angle proofs involving known facts.

 Student Outcomes Students discover the gaps in specificity regarding their understanding of transformations. Students identify the parameters they need to complete any rigid motion.