Download SUBJECT: Geometry

SUBJECT: Geometry
STRAND: Language of Geometry
CONTENT STANDARDS:
Standard 1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems,
properties, and postulates.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
4
OBJECTIVES
Logic and Reasoning
LG.1.G.1 Define,
compare and contrast
inductive reasoning and
deductive reasoning for
making predictions based
on real world situations
 venn diagrams
 matrix logic
 conditional
statements
(statement,
inverse, converse,
and
contrapositive)
 *figural patterns
LG.1.G.3 Describe
relationships derived
from geometric figures
or figural patterns
LG.1.G.6 Give
justification for
conclusions reached by
deductive reasoning
*State and prove key
basic theorems in
geometry (i.e., the
Pythagorean theorem, the
sum of the measures of
the angles of a triangle is
180° , and the line
joining the midpoints of
two sides of a triangle is
parallel to the third side
and half it’s length
1.
2.
3.
4.
5.
Compare and
contrast inductive
and deductive
reasoning.
Use Venn Diagrams
to solve problems.
Use Matrix Logic to
solve problems.
Identify the inverse,
converse and
contrapositive of a
statement.
Recognize and
describe
relationships derived
from figural
patterns.
X
SUBJECT: Geometry
STRAND: Language of Geometry
CONTENT STANDARDS:
Standard 1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems,
properties, and postulates.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
4
OBJECTIVES
Points, Lines, & Planes
LG.1.G.2
Represent points, lines,
and planes pictorially
with proper
identification, as well as
basic concepts derived
from these undefined
terms, such as segments,
rays, and angles
1.
2.
3.
4.
5.
6.
Represent points
pictorially with
proper identification.
Represent lines
pictorially with
proper identification.
Represent rays
pictorially with
proper identification.
Represent line
segments pictorially
with proper
identification
Represent angles
pictorially with
proper identification.
Represent planes
pictorially with
proper identification.
X
SUBJECT: Geometry
STRAND: Language of Geometry
CONTENT STANDARDS:
Standard 1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems,
properties, and postulates.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
4
OBJECTIVES
Angle Relationships
LG.1.G.4 Apply, with
and without appropriate
technology, definitions,
theorems, properties, and
1.
Solve problems
involving
complementary
angles.
X
postulates related to such
topics as complementary,
supplementary, vertical
angles, linear pairs, and
angles formed by
perpendicular lines
LG.1.G.5 Explore, with
and without appropriate
technology, the
relationship between
angles formed by two
lines cut by a transversal
to justify when lines are
parallel
M.3.G.5 *Identify and
apply properties of and
theorems about parallel
and perpendicular lines
to prove other theorems
and perform basic
Euclidean constructions
2.
3.
4.
5.
6.
7.
Solve problems
involving
supplementary
angles
Solve problems
involving vertical
angles.
Solve problems
involving linear
pairs of angles.
Solve problems
involving angles
formed by
perpendicular lines.
Solve problems
involving parallel
lines cut by a
transversal.
Perform basic
Euclidean
constructions.
SUBJECT: Geometry
STRAND: Coordinate Geometry and Transformations
CONTENT STANDARDS:
Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
OBJECTIVES
Slope and Equations of
Lines
CGT.5.G.1 Use
coordinate geometry to
find the distance between
two points, the midpoint
of a segment, and the
slopes of parallel,
perpendicular,
horizontal, and vertical
lines
1.
CGT.5.G.2 *Write the
3.
2.
Identity horizontal
and vertical lines by
calculating the slope.
Determine if sets of
lines are parallel or
perpendicular by
calculating their
slope.
Write the equation
X
3
4
equation of a line parallel
to a line through a given
point not on the line
CGT.5.G.3 *Write the
equation of a line
perpendicular to a line
through a given point
CGT.5.G.4 *Write the
equation of the
perpendicular bisector of
a line segment
4.
5.
of a line parallel to a
line through a point
not on the line.
Write the equation
of a line
perpendicular to a
line through a given
point.
Write the equation
of the perpendicular
bisector of a line
segment.
SUBJECT: Geometry
STRAND: Relationships between two- and three- dimensions
CONTENT STANDARDS:
Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop
mathematical arguments about geometric relationships.
STRAND: Coordinate Geometry and Transformations
CONTENT STANDARDS:
Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
OBJECTIVES
Properties of Polygons
R.4.G.1
Explore and verify the
properties of
quadrilaterals
1.
2.
R.4.G.2 Solve problems
using properties of
polygons:
 sum of the
measures of the
interior angles
of a polygon
 interior and
exterior angle
measure of a
regular polygon
or irregular
3.
Use properties of
quadrilaterals to
solve problems.
Solve problems
involving the sum of
the measures of the
interior angles of a
polygon.
Solve problems
involving the
interior and exterior
angle measures of
regular and irregular
polygons.
X
4
polygon
number of sides
or angles of a
polygon
4.
CGT.5.G.5 Determine,
given a set of points, the
type of figure based on
its properties
(parallelogram, isosceles
triangle, trapezoid)
5.

6.
Solve problems
involving the
number of sides and
angles of polygons.
Classify figures
given the set of
points that form the
vertices of the
figure.
Prove theorems
about polygons
SUBJECT: Geometry
STRAND: Relationships between two- and three- dimensions
CONTENT STANDARDS:
Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop
mathematical arguments about geometric relationships.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
OBJECTIVES
Non-Euclidean
Geometrics
R.4.G.9 *Explore nonEuclidean geometries,
such as spherical
geometry and identify its
unique properties which
result from a change in
the parallel postulate
1.
Identify unique
properties which
result when the
parallel postulate is
not included as one
of the postulates for
a geometry.
4
X
SUBJECT: Geometry
STRAND: Triangles
CONTENT STANDARDS:
Standard 2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the
properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to
solve problems in real world situations.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
4
OBJECTIVES
Special Segments of
Triangles
T.2.G.3 Identify and use
the special segments of
triangles (altitude,
1.
Identify altitudes of
triangles and use
them to solve
X
median, angle bisector,
perpendicular bisector,
and midsegment) to
solve problems
2.
3.
4.
5.
problems.
Identity medians of
triangles and use
them to solve
problems.
Identify angle
bisectors of triangles
and use them to
solve problems.
Identity
perpendicular
bisectors of triangles
and use them to
solve problems.
Identity
midsegments of
triangles and use
them to solve
problems.
SUBJECT: Geometry
STRAND: Triangles
CONTENT STANDARDS:
Standard 2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the
properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to
solve problems in real world situations.
STRAND: Coordinate Geometry and Transformations
CONTENT STANDARDS:
Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
4
OBJECTIVES
Pythagorean Theorem
& Related Topics
T.2.G.2
Investigate the measures
of segments to determine
the existence of triangles
(triangle inequality
theorem)
T.2.G.4 Apply the
1.
2.
Prove the
Pythagorean
Theorem
Use the Pythagorean
Theorem and its
converse to solve
X
Pythagorean Theorem
and its converse in
solving practical
problems
CGT.5.G.1 Use
coordinate geometry to
find the distance between
two points, the midpoint
of a segment, and the
slopes of parallel,
perpendicular,
horizontal, and vertical
lines
3.
4.
5.
problems
Find the distance
between two points
in a rectangular
coordinate system.
Find the coordinates
of the midpoint of a
line segment in the
coordinate plane.
Apply the triangle
inequality to solve
problems.
SUBJECT: Geometry
STRAND: Triangles
CONTENT STANDARDS:
Standard 2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the
properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to
solve problems in real world situations.
STRAND: Measurement
CONTENT STANDARDS:
Standard 3: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing
with length, perimeter, area and volume.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
4
OBJECTIVES
Proportional
Reasoning
T.2.G.1 Apply
congruence (SSS …) and
similarity (AA ...)
correspondences and
properties of figures to
find missing parts of
geometric figures and
provide logical
justification
1.
M.3.G.4 Use (given
similar geometric
objects) proportional
reasoning to solve
practical problems
3.
2.
Find missing
measures of figures
based on congruence
relationships.
Find missing
measures of figures
based on similarity
relationships.
Use properties of
parallel lines and
proportional
reasoning to find
lengths of segments.
X
(including scale
drawings)
M.3.G.5 *Identify and
apply properties of and
theorems about parallel
and perpendicular lines
to prove other theorems
and perform basic
Euclidean constructions
SUBJECT: Geometry
STRAND: Triangles
CONTENT STANDARDS:
Standard 2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the
properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to
solve problems in real world situations.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
4
OBJECTIVES
Trigonometry
T.2.G.5 Use the special
right triangle
relationships (30˚-60˚90˚ and 45˚-45˚-90˚) to
solve problems
1.
2.
T.2.G.6 Use
trigonometric ratios
(sine, cosine, tangent) to
determine lengths of
sides and measures of
angles in right triangles
including angles of
elevation and angles of
depression
T.2.G.7 *Use similarity
of right triangles to
express the sine, cosine,
and tangent of an angle
in a right triangle as a
ratio of given lengths of
sides
3.
4.
5.
Use trigonometric
ratios to find the
measures of sides of
right triangles to
solve problems.
Use trigonometric
ratios to find the
measures of angles
in right triangles to
solve problems.
Use trigonometric
ratios to solve
problems involving
angles of elevation.
Use trigonometric
ratios to solve
problems involving
angles of depression.
Use the special right
triangle relationships
to solve problems.
X
SUBJECT: Geometry
STRAND: Measurement
CONTENT STANDARDS:
Standard 3: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing
with length, perimeter, area and volume.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
4
OBJECTIVES
Perimeter & Area
M.3.G.1 Calculate
probabilities arising in
geometric contexts (Ex.
Find the probability of
hitting a particular ring
on a dartboard.)
M.3.G.2 Apply, using
appropriate units,
appropriate formulas
(area, perimeter, surface
area, volume) to solve
application problems
involving polygons,
prisms, pyramids, cones,
cylinders, spheres as well
as composite figures,
expressing solutions in
both exact and
approximate forms
1.
2.
3.
4.
5.
6.
Solve problems
involving perimeter
of polygons.
Solve problems
involving the
circumference of
circles.
Solve problems
involving perimeter
of composite figures.
Solve problems
involving area of
polygons.
Solve problems
involving area of
circles.
Solve problems
involving area of
composite figures.
X
SUBJECT: Geometry
STRAND: Relationships between two- and three- dimensions
CONTENT STANDARDS:
Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop
mathematical arguments about geometric relationships.
STRAND: Coordinate Geometry and Transformations
CONTENT STANDARDS:
Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
OBJECTIVES
4
Circles
R.4.G.5 Investigate and
use the properties of
angles (central and
inscribed) arcs, chords,
tangents, and secants to
solve problems involving
circles
1.
2.
R.4.G.6 Solve problems
using inscribed and
circumscribed figures
CGT.5.G.6 Write, in
standard form, the
equation of a circle given
a graph on a coordinate
plane or the center and
radius of a circle
3.
4.
5.
6.
7.
8.
9.
Write the equation
of a circle in
standard form given
a coordinate graph
of the circle.
Write the equation
of a circle in
standard form given
the coordinates of
the center of the
circle and the radius
of the circle
Use properties of
central angles o a
circle to solve
problems.
Use properties of
central angles of
circles to solve
problems.
Use properties of
angles inscribed in
circles to solve
problems.
Use properties of arc
of circles to solve
problems.
Use properties of
chords of circles to
solve problems.
Use properties of
line tangent to
circles to solve
problems.
Use properties of
lines secant to
circles to solve
problems.
X
10. Solve problems
using inscribed
figures
11. Solve problems
using circumscribed
figures.
SUBJECT: Geometry
STRAND: Measurement
CONTENT STANDARDS:
Standard 3: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing
with length, perimeter, area and volume.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
4
OBJECTIVES
Surface Area &
M.3.G.2 Apply, using
X
7. Solve problems
Volume
appropriate units,
appropriate formulas
(area, perimeter, surface
area, volume) to solve
application problems
involving polygons,
prisms, pyramids, cones,
cylinders, spheres as well
as composite figures,
expressing solutions in
both exact and
approximate forms
M.3.G.3 Relate changes
in the measurement of
one attribute of an object
to changes in other
attributes (Ex. How does
changing the radius or
height of a cylinder
affect its surface area or
volume?)
8.
9.
10.
11.
12.
13.
14.
involving surface
area of prisms.
Solve problems
involving surface
area of pyramids.
Solve problems
involving surface
area of cones.
Solve problems
involving surface
area of cylinders.
Solve problems
involving surface
area of spheres.
Solve problems
involving the surface
area of composite
objects.
Solve problems
involving volume of
prisms.
Solve problems
15.
16.
17.
18.
19.
20.
involving volume at
pyramids.
Solve problems
involving volume of
cones.
Solve problems
involving volume of
cylinders
Solve problems
involving volume of
spheres.
Solve problems
involving volume of
composite objects.
Relate changes in
the measurement of
one attribute of an
object to changes in
the measurement of
other attributes.
Use area models to
calculate
probabilities.
SUBJECT: Geometry
STRAND: Relationships between two- and three- dimensions
CONTENT STANDARDS:
Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop
mathematical arguments about geometric relationships.
STRAND: Coordinate Geometry and Transformations
CONTENT STANDARDS:
Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
OBJECTIVES
Transformations
R.4.G.3 Identify and
explain why figures
tessellate
R.4.G.4 Identify the
1.
Draw and interpret
the results of
transformations and
successive
4
X
attributes of the five
Platonic Solids
CGT.5.G.7 Draw and
interpret the results of
transformations and
successive
transformations on
figures in the coordinate
plane
 translations
 reflections
 rotations (90˚,
180˚, clockwise
and
counterclockwis
e about the
origin)
 dilations (scale
factor)
2.
3.
transformations on
figures in the
coordinate plane.
Identify and explain
why figures
tessellate.
Identify the
attributes of the five
Platonic Solids.
SUBJECT: Geometry
STRAND: Relationships between two- and three- dimensions
CONTENT STANDARDS:
Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop
mathematical arguments about geometric relationships.
BIG IDEA
PRIMARY SLE
PRIMARY SLE
RELATED SLEs
ASSESSMENT
1
2
3
OBJECTIVES
2-D Representation of
3-D Objects
R.4.G.4 Identify the
attributes of the five
Platonic Solids
R.4.G.7 Use
orthographic drawings
(top, front, side) and
isometric drawings
(corner) to represent
three-dimensional
objects
R.4.G.8 Draw, examine,
and classify crosssections of three-
1.
2.
3.
Use orthographic
drawings to
represent three
dimensional objects.
Use isometric
drawings to
represent threedimensional objects.
Draw, examine and
classify crosssections of threedimensional objects.
4
X
dimensional objects