Standards:
GGPE.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,√3) lies on the circle centered at
the origin and containing the point (0,2).
GGPE.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).
GGPE.B.6 Find the point on a directed line segment between
two given points that partitions the segment in a given ratio.
GGPE.B.7 Use coordinates to compute perimeters of
polygons and areas of triangles and rectangles, e.g., using the distance
formula.^{★}
Focus Standards of
Mathematical Practice:
MP.1 Make sense of problems and persevere in
solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the
reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated
reasoning.
Instructional
Outcomes:
Full Development of the Major Clusters,
Supporting Clusters, Additional Clusters and Mathematical Practices for this
unit could include the following instructional outcomes:
GGPE.B.4
·
I
can recall previous understandings of coordinate geometry (including, but not
limited to: distance, midpoint and slope formula, equations of a line,
definitions of parallel and perpendicular lines, etc.)
·
I
can use coordinate 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, 3) lies
on the circle centered at the origin and containing the point (0,2)
GGPE.B.5
·
I
can recognize that slopes of parallel lines are equal
·
I
can recognize that slopes of perpendicular lines are opposite reciprocals
(i.e., the slopes of perpendicular lines have a product of 1)
·
I
can fins the equation of a line parallel to a given line that passes through
a given point
·
I
can find the equation of a line perpendicular to a given line that passes
through a given point
·
I
can prove the slope criteria for parallel and perpendicular lines and use
them to solve geometric problems
GGPE.B.6
·
I
can recall the definition of ratio
·
I
can recall previous understandings of coordinate geometry
·
I
can, given a line segment (including those with positive and negative slopes)
and ratio, find the point on the segment that partitio9ns the segment into
the given ratio
GGPE.B.7
·
I
can use the coordinates of the vertices of a polygon to find the necessary
dimensions for finding the perimeter (i.e., the distance between vertices)
·
I
can use the coordinates of the vertices of a triangle to find the necessary
dimensions (base, height) for finding the area (i.e., the distance between
vertices by counting, distance, formula, Pythagorean Theorem, etc.)
·
I
can use coordinates of the vertices of a rectangle to find the necessary
dimensions (base, height) for finding the area (i.e., the distance between
vertices by counting, distance, formula)
·
I
can formulate a model of figures in contextual problems to compute area
and/or perimeter
