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Common Core: Math
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 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 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 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...

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

 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 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...

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

 Students begin this module with Topic A, Constructions. Major constructions include an equilateral triangle, an angle bisector, and a perpendicular bisector. Students synthesize their knowledge of...

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

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

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

 Constructions segue into Topic B, Unknown Angles, which consists of unknown angle problems and proofs. These exercises consolidate students’ prior body of geometric facts and prime students’...

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

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

 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...

 Topic C, Transformations, builds on students’ intuitive understanding developed in Grade 8. With the help of manipulatives, students observed how reflections, translations, and rotations behave...

 Student Outcomes Students manipulate rotations by each parameter—center of rotation, angle of rotation, and a point under the rotation.

 Student Outcomes Students learn why any two triangles that satisfy the SAS congruence criterion must be congruent.

 Student Outcome Students write unknown angle proofs involving auxiliary lines.

 Student Outcomes Students write unknown angle proofs involving known facts.

 Student Outcomes Students complete proofs that incorporate properties of parallelograms.

 Student Outcomes Given a physical situation (e.g., a room of a certain shape and dimensions, with objects at certain positions and a robot moving across the room), students impose a coordinate system...