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 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 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...

 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...

 Topic A brings students back to the study of complex roots of polynomial functions. Students briefly review quadratic and cubic functions and then extend familiar polynomial identities to both...

 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...

 Student Outcomes Students write the equation for a circle in centerradius form, (x  a)2 (y  b)2 = r2 using the Pythagorean theorem or the distance formula. Students write the equation of a circle...

 Student Outcomes Students complete the square in order to write the equation of a circle in centerradius form. Students recognize when a quadratic in x and y is the equation for a circle.

 Student Outcomes Given a circle, students find the equations of two lines tangent to the circle with specified slopes. Given a circle and a point outside the circle, students find the equation of the...

 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...

 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...

 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...

 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...