CCGPS Analytic Geometry Unit 3: Modeling Geometry
Unit Plan:
Goals/Standards of the Unit:
·Students will be able to solve a system containing a linear and quadratic equation algebraically and graphically and understand what the solution means in context. Students also understand the intersections of a line and parabola can be found by finding the zeros of another parabola. (CCGPS: MCC9-12.A.REI.7, AKS: MAGC_A2013-25)
·Students can find the equation for a circle in the Cartesian plane given a center and radius using knowledge of right triangle side length properties. (CCGPS: MCC9-12.G.GPE.1, AKS: MAGE_C2013-46)
·Students can find the equation of circle given a polynomial equation using the process of solving for vertex form or completing the square. (CCGPS: MCC9-12.G.GPE.1, AKS: MAGE_C2013-46)
·Students can define what a conic is using the terms focus and directrix. Students will be able to conceptually understand the four different curve shapes that can be generated by a conic. They will understand how each shape (parabola, hyperbola, circle, and ellipse) is defined and graphed. Students can also write general expressions to describe each shape algebraically. (CCGPS: MCC9-12.A.REI.7, AKS: MAGC_A2013-25)
·Students can use the focus and directrix to give a proper definition of the term parabola. They can use these items to define the equation of a particular parabola. (CCGPS: MCC9-12.G.GPE.2, AKS: MAGC_C2013-38)
· Students can use computation and transformation to prove various geometric theorems in the Cartesian plane using coordinates. (CCGPS: MCC9-12.G.GPE.4, AKS: MAGC_C2013-39)
·Students will be able to solve a system containing a linear and quadratic equation algebraically and graphically and understand what the solution means in context. Students also understand the intersections of a line and parabola can be found by finding the zeros of another parabola. (CCGPS: MCC9-12.A.REI.7, AKS: MAGC_A2013-25)
·Students can find the equation for a circle in the Cartesian plane given a center and radius using knowledge of right triangle side length properties. (CCGPS: MCC9-12.G.GPE.1, AKS: MAGE_C2013-46)
·Students can find the equation of circle given a polynomial equation using the process of solving for vertex form or completing the square. (CCGPS: MCC9-12.G.GPE.1, AKS: MAGE_C2013-46)
·Students can define what a conic is using the terms focus and directrix. Students will be able to conceptually understand the four different curve shapes that can be generated by a conic. They will understand how each shape (parabola, hyperbola, circle, and ellipse) is defined and graphed. Students can also write general expressions to describe each shape algebraically. (CCGPS: MCC9-12.A.REI.7, AKS: MAGC_A2013-25)
·Students can use the focus and directrix to give a proper definition of the term parabola. They can use these items to define the equation of a particular parabola. (CCGPS: MCC9-12.G.GPE.2, AKS: MAGC_C2013-38)
· Students can use computation and transformation to prove various geometric theorems in the Cartesian plane using coordinates. (CCGPS: MCC9-12.G.GPE.4, AKS: MAGC_C2013-39)
