COMMON CORE OBJECTIVES G.GPE.A.1 & G.GPE.A.2

G.GPE.A.1 -- Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

 

G.GPE.A.2 -- We are preparing students to study all kinds of relationships through coordinate analysis. While we cover circles here we will look at parabolas next and then later they will look at the rest of the conic sections.


COMMON CORE OBJECTIVES G.GPE.B.4 & G.GPE.B.5

G.GPE.B.4 -- Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, sqrt(3)) lies on the circle centered at the origin and containing the point (0, 2).


G.GPE.B.5-- Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

COMMON CORE OBJECTIVES G.GPE.B.6 & G.GPE.B.7

G.GPE.6 -- Find the point on a directed line segment between two given points that partitions the segment in a given ratio.


G.GPE.7 -- Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. *(Modeling Standard)

 


   

(1) Connecting circle geometry to the coordinate grid we will first look at the equations of circles.  A major part of this objective is to learn completing the square to place the equation into vertex and radius form.  At the end of the week we will introduce the parabolic curve.

(2) This week we focus 100% on parabolas and their equations.  Early on we will do a number of activities to provide students a context for the definition and then we will build from there to the equation.

(3) To be able to solve a number of coordinate geometry problems we need to establish a number of previous concepts.  This week will be a mix of old and new as we work with coordinate geometry problems.

(4) We extend the study of lines to parallel and perpendicular lines.  This applies to problems dealing with proof of shapes through their properties.  We also look at directed line segments.

(5) This last week we finish up partitioning directed line segments and find area using coordinates.