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Common Core: Math
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 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...

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

 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 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...

 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 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...

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

 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 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 explain the connection between the Pythagorean Theorem and the criterion for perpendicularity.

 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: 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.

 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...

 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 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...

 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...

 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...

 Student Outcomes Students apply the geometric transformation of dilation to show that all parabolas are similar.

 Student Outcomes Students learn the vertex form of the equation of a parabola and how is arises from the definition of a parabola. Students perform geometric operations, such as rotations,...

 Student Outcomes Students model the locus of points at equal distance between a point (focus) and a line (directrix). They construct a parabola and understand this geometric definition of the curve....

 Students solve polynomial, rational, and radical equations, and apply these types of equations to realworld situations. They examine the conditions under which an extraneous solution is introduced...

 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...