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Common Core: Standard
Common Core: ELA
Common Core: Math
Resource Type: Module Topic
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 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...

 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’...

 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...

 In Topic D, Proving Properties of Geometric Figures, students use what they have learned in Topics A through C to prove properties—those that have been accepted as true and those that are new—of...

 The module closes with a return to constructions in Topic E (G.CO.13).

 Topic F is a review that highlights how geometric assumptions underpin the facts established thereafter.

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

 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...

 Students describe rectangles (with edges parallel to the axes) and triangles in the coordinate plane by means of inequalities. For example, the rectangle in the coordinate plane with lower left...

 Student Outcomes: Given two points in the coordinate plane and a rectangular or triangular region, students determine whether the line through those points meets the region, and if it does, they...

 Student Outcomes: Given a segment in the coordinate plane, students find the segments obtained by rotating the given segment by 90° counterclockwise and clockwise about one endpoint.

 The challenge of programming robot motion along segments parallel or perpendicular to a given segment leads to an analysis of slopes of parallel and perpendicular lines. Students write equations for...

 Student Outcomes: Students explain the connection between the Pythagorean Theorem and the criterion for perpendicularity.

 Student Outcomes: Students generalize the criterion for perpendicularity of two segments that meet at a point to any two segments in the Cartesian plane. Students apply the criterion to determine if...

 Student Outcomes: Students state the relationship between previously used formats for equations for lines and the new format a1x + a2y + c, recognizing the segments from (0,0) to (a1, a2) as a normal...

 Student Outcomes: Students recognize parallel and perpendicular lines from slope. Students create equations for lines satisfying criteria of the kind: “Contains a given point and is parallel/...

 Students sketch the regions, determine points of intersection (vertices), and use the distance formula to calculate perimeter and the “shoelace” formula to determine area of these regions. Students...

 Student Outcomes: Students find the perimeter of a triangle in the coordinate plane using the distance formula. Students state and apply the formula for area of a triangle with vertices (0,0),(x1, y1...

 Student Outcomes: Students find the perimeter of a quadrilateral in the coordinate plane given its vertices and edges. Students find the area of a quadrilateral in the coordinate plane given its...

 Student Outcomes: Students find the perimeter of a triangle or quadrilateral in the coordinate plane given a description by inequalities. Students find the area of a triangle or quadrilateral in the...

 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...

 Student Outcomes: Students find midpoints of segments and points that divide segments into 3, 4, or more proportional, equal parts.

 Student Outcomes: Using coordinates, students prove that the intersection of the medians of a triangle meet at a point that is twothirds of the way along each median from the intersected vertex....

 Student Outcomes: Students name several points on a line given by a parametric equation and provide the pointslope equation for a line given by a parametric equation. Students determine whether...