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).
INTERPRETATION OF OBJECTIVE - G.GPE.B.4
Wow.... this was one of the hardest objectives to interpret. It is just so wide.... So here is what I believe this objective to be - this is the process of using coordinates and equations to establish geometric truths. So that is using slopes and distances to establish relationships and characteristics of different geometric shapes. It is using a system of equations to learn about points of intersections and relationships between different geometric shapes.
(1) The student will be able to establish relationships and /or characteristics of geometric shapes using coordinate geometry.
(2) The student will be able to classify a quadrilateral through use of coordinate analysis.
THE BIG IDEA
Coordinate geometry empowers us to analyze and confirm many geometric truths in an algebraic way. We are able to reaffirm many geometric concepts, theorems, characteristics and properties through coordinate analysis.
TRAPS & PITFALLS
The biggest pitfall is their memory and their previous skills. This is a heavy algebra area and there isn't time to reteach everything needed to succeed here and so student need to take on more responsibility to do some reviewing on their own. We need them to know equations of lines, working with slopes, applying the distance formula, determining the solution to a system of equation... to name a few skills. These skills alone represent at least half of the algebra 1 curriculum.
The student needs a great deal of previous skills and concepts to work in this area. They need to know equations of lines, slopes, midpoints, distance formula, systems of equations to name a few. Coordinate geometry is basically the study of geometry using algebra and so all of those earlier algebra skills come in very handy.
Finally we are now taking on a topic that requires the use of mathematics from many different areas. Students need to apply previous skills and concepts to solve the current ones. This is a skill that only continues on later in mathematics. Eventually students should see math as one big whole instead of a bunch of little pieces.
MY REFLECTIONS (over line l)
Algebra skills for so many kids trip them up in this unit. Often the algebra 2 teachers complain just how little algebra the kids remember and so I am glad that I am able to revisit these skills in a meaningful way. It is frustrating how little they remember.
I do like how we review a bunch of algebra 1 skills and then apply t to the current year by answering questions about geometric shapes and relationships.