Download CM HS Math Geometry Grade 10-11 06 06

Harrison County Schools
Curriculum Guide for Math Department
Course Name: Geometry
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
Grade Level Targeted: 10 - 11
Key
Vocabulary
Activities
and
Assessments
Measuring Physical
Attributes


What is surface
area/volume?
How does it differ from
perimeter/area of two
dimensional figure?
MA-11-2.1.1
Students will
determine the surface
area and volume of
right rectangular
prisms, pyramids,
cylinders, cones, and
spheres in real-world
problems.
Surface area,
lateral area,
volume, right
rectangular prisms,
pyramids,
cylinders, cones,
spheres,
hemisphere


How does a change in
shape affect the perimeter,
area, and volume of a
figure?
What shape maximizes
perimeter, area, and
volume?
MA-11-2.1.2 DOK 3




Experiment
Volume & Cat Litter
Open Response
The Silo
DOK – 3
Perimeter, area,
Students will describe and volume
how a change in one
or more dimensions of
a geometric figure
affects the perimeter,
area, and volume of
Unit (s):
Project
Construction Project
Essential Questions
toward
Course Objectives



How do you recognize a
right triangle?
When should you use the
Pythagorean Theorem ?
trig ratios?
When can the right triangle
theorems be used to solve
real world situations?
Kentucky
Core Content
Version 4.1
the figure.
MA-11-2.1.3
Students will apply
definitions and
properties of right
triangle relationships
(right triangle
trigonometry and the
Pythagorean
theorem) to
determine length and
angle measures to
solve real-world
problems.
DOK – 3
MA-11-2.1.3a
Students will apply
special right triangles and
the converse of the
Pythagorean theorem to
solve real-world
problems.
Systems of
Measurements
Key
Vocabulary
Right triangle
trigonometry and
Pythagorean
theorem
Sine, Cosine,
Tangent, angle of
elevation, vectors,
magnitude,
direction
45-45-90 Triangle
Theorem
30-60-90 Triangle
Theorem
Activities
and
Assessments
Project
Measure the Flagpole
 Using shadows
 Using clinometers
Essential Questions
toward
Course Objectives


What units of measure
are appropriate for the
situation?
How do you make a
conversion of units
within a system of
measurement?
Kentucky
Core Content
Version 4.1
Key
Vocabulary
Activities
and
Assessments
MA-11-2.2.1a Supporting
Students will continue to
apply to both real world
and mathematical
situations U.S. customary
and metric systems of
measurement.
Shapes and
Relationships



Identify relationships
between and among points,
lines, and planes.
Define, describe properties
of, give examples of, and
apply to both real world
and mathematical
situations spatial
relationships such as
betweenness, parallelism,
and perpendicularity.
Find the intersection of
lines, planes, and solids.
MA-11-3.1.1
Students will analyze
and apply spatial
relationships (not
using Cartesian
coordinates) among
points, lines, and
planes (e.g.,
betweenness of points,
midpoint, segment
length, collinear,
coplanar, parallel,
perpendicular, skew).
DOK – 2
MA-11-3.1.1a
Students will use spatial
relationships to prove
Point, line, plane,
collinear, coplanar,
betweeness,
segment, ray,
parallel,
perpendicular,
skew, intersection,
midpoint
Segment Addition
Postulate
Hands on Activities
MIRA
Patty Paper
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
Key
Vocabulary
Activities
and
Assessments
basic theorems.



Draw, name, analyze, and
apply the different types of
angle relationships.
Describe, draw, and
construct two-dimensional
figures.
Classify according to
characteristics.
MA-11-3.1.2
Students will analyze
and apply angle
relationships (e.g.,
linear pairs, vertical,
complementary,
supplementary,
corresponding, and
alternate interior
angles) in real-world or
mathematical
situations.
DOK – 2
MA-11-3.1.2a
Students will use angle
relationships to prove
basic theorems.
MA-11-3.1.3
Students will classify
and apply properties
of two-dimensional
geometric figures
(e.g., number of sides,
vertices, length of
sides, sum of interior
and exterior angle
Angle, degrees,
ray, sides, vertex,
vertical angles,
linear pair, straight,
right, acute,
obtuse,
complementary,
supplementary,
transversal,
corresponding,
alternate interior,
alternate exterior,
same-side interior
Angle Addition
Postulate
Triangle, scalene,
isosceles,
equilateral,
equiangular, acute,
obtuse, right, legs,
hypotenuse,
quadrilateral,
pentagon, hexagon,
heptagon, octagon,
nonagon, decagon,
dodecagon, interior
Hands on Activities
Golden Rectangle Construction
Geometry Scavenger Hunt
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
measures).
DOK – 2
MA-11-3.1.3a
Students will know the
definitions and basic
properties of a circle and
will use them to prove
basic theorems and solve
problems.

What properties of
triangles can be used to
find missing sides and/or
angles? Can this info be
applied to real world
situations?
MA-11-3.1.4 DOK 3
Students will solve real
world problems by
applying properties of
triangles (e.g., Triangle
Sum Theorem and
Isosceles Triangle
Theorems)

Describe, draw, and
construct threedimensional figures.
Classify according to
characteristics.
MA-11-3.1.5

Students will classify
and apply properties
of three-dimensional
geometric figures
(e.g., number of
edges, faces, vertices).
DOK - 2
MA-11-3.1.5a
Students will describe the
intersection of a plane
Key
Vocabulary
angles, exterior
angles, regular,
parallelogram,
rhombus,
rectangle, square,
kite, trapezoid,
isosceles trapezoid,
base angles
Triangle Sum
Theorem, Exterior
Angle Theorem
Edges, faces,
vertices,
polyhedron,
regular, convex,
cross section,
Platonic solids,
tetrahedron,
octahedron,,
dodecahedron,
icosahedron, ,
prism, bases,
lateral faces, right
prism, oblique
Activities
and
Assessments
Discovery Lesson

Hands on Activities
Constructions
MIRA
Patty Paper
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
with a three-dimensional
figure


Determine height and
distance using methods of
indirect measurement
Apply concepts of
congruence to solve realworld and mathematical
problems (not including
proofs)

Apply concepts of
similarity to solve realworld and mathematical
problems (not including
proofs)

Use to solve real-world
problems
Key
Vocabulary
Activities
and
Assessments
prism,
MA-11-3.1.5b
Students will visualize
solids and surfaces in
three-dimensional space
when given twodimensional
representations (e.g.,
nets, multiple views) and
create two-dimensional
representations for the
surfaces of threedimensional objects.
MA-11-3.1.6
Students will apply
the concepts of
congruence and
similarity to solve
real-world problems.
Open Response
The Obelisk
DOK – 3
MA-11-3.1.6a
Students will prove
triangles congruent and
similar.
SSS Postulate
SAS, ASA, AAS
Theorems
HL Theorem
AA-Similarity
Theorem
Essential Questions
toward
Course Objectives


Reflect two-dimensional
figures across the x-axis,
the y-axis, or any given
lines.
Describe properties of and
give examples of geometric
transformations and apply
geometric transformations,
with and without a
coordinate plane, to both
real-world and
mathematical situations.

Perform transformations on
figures.

Interpret how figures in a
coordinate plane and their
resulting images under a
transformation are
algebraically and
geometrically related.
Kentucky
Core Content
Version 4.1
Transformations of
Shapes
Key
Vocabulary
MA-11-3.2.1
Students will describe
properties of and apply
geometric
transformations within
a plane to solve realworld problems.
DOK - 3
Transformations,
isometry, image,
preimage,
reflection, line of
reflection, line of
symmetry,
rotation,
translation, glide
reflection
Coordinate
Geometry


Represent geometric
figures and properties
using
coordinates
Connect these concepts to
MA-11-3.3.1
Students will apply
algebra or graphing
in the coordinate
plane to analyze and
Distance Formula
Midpoint Formula
Slope
Slope-Intercept
Form
Pythagorean
Activities
and
Assessments
Essential Questions
toward
Course Objectives
algebraic representations.

Describe properties of,
define, give examples of,
and
apply to both real-world
and mathematical
situations ratio measures
including slope and rate

Apply formulas for the
slope of a line,
distance between two
points, and midpoint
of a segment to solve
problems.
Kentucky
Core Content
Version 4.1
solve problems (e.g.,
finding the final
coordinates for a
specified polygon,
finding midpoints,
finding the distance
between two points,
finding the slope of a
segment).
Key
Vocabulary
Theorem
DOK - 2
Foundational
Statements

Students will be able to
apply geometric
definitions, axioms, and
theorems as they continue
throughout the course.
MA-11-3.4.1a ADP
Students will identify,
explain the necessity of,
and give examples of
definitions, axioms, and
theorems.
MA-11-3.4.1b ADP
Students will recognize that
there are geometries, other
than Euclidean geometry, in
Theorem,
Corollary,
Postulate, Proof
Activities
and
Assessments
Essential Questions
toward
Course Objectives
Kentucky
Core Content
Version 4.1
Key
Vocabulary
which the parallel postulate
is not true.
MA-11-3.4.1c ADP
Students will be able to
perform constructions
such as a line parallel to
a given line through a
point not on an a line, the
perpendicular bisector of
a line, and a bisector of
an angle.
Construction,
Compass,
Protractor,
Straightedge
Congruent
segments
Congruent angles,
Angle Bisector
Midpoint,
Perpendicular
Bisector
Perpendicular and
Parallel Lines
Median, Altitude,
Points of
Concurrency
Activities
and
Assessments