CURRICULUM MAP COURSE TITLE

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CURRICULUM MAP COURSE TITLE
: __Geometry A____________________



Sept Oct.

Nov. Dec. Jan


Essential
Questions







How are geometric terms and
postulates used to model,
define, compare and contrast
phenomena?


How are definitions,
postulates,

theorems, spatial sense,
geometric modeling and
measurement used to justify or
refute conjectures and
theorems and discover
solutions to problems?



How are the real world
cognitive skills of logic
-

analysis, synthesis and
justification
-
modeled

through
geometric properties, theorems
and postulates in proofs?


What and how are the real
world models of the
properties of geometric
shapes?


How are the properties of
similar figures associated in the
real world?




Content











The Coordinat
e Plane

Basic terms in geometry.

Properties of segments, angles,
and perpendicular lines.




Conditional Statements and
their converses

Properties of equality in
algebra and geometric proofs.

Simple proofs involving
segments and angle theorems

Parallel li
nes: transversals;
special relationships between
pairs of angles.

Classification of triangles

Conditions for congruency in
triangles.

Triangle congruence proofs.

Properties of isosceles and
equilateral triangles

Special segments in
Triangles.

Indirect Proo
fs

Triangle Inequalities

Properties of Quadrilaterals

Properties and Tests for
parallelograms




Ratios and Proportions

Similar Figures

Proportional parts of similar
figures.











Skills









Connect and apply the
algebraic properties of the
coordinate plane

Identify, classify, and apply
defined and undefined terms in
geometry.

Illustrate and visualize the
intersections of points, lines
and planes.

Me
asure segments involving
different units.


Calculate the distance between
two points and find the
midpoint of the segment.

Identify, measure, and classify
angles.

Explain, distinguish and apply
the difference between “pairs
of angles”(vertical, adjacent



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4.2.12 䌬 1 4.2.12.䐬a2

4.5 A⠱
-
5⤠4.5 䈨B
-


4.5 䌨C
-
S⤠4.5䐨a
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S⤠4.5䔨b
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3⤠
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4.2.12 A.⠱,3, 4⤴.2.12 䌠1,

4.5 A⠱
-
5⤠4.5 䈨B
-


4.5 䌨C
-
S⤠4.5䐨a
-
S⤠4.5䔨b
-
3⤠
4.5 c⠵)


4.2.12 A⠱,3,4⤠

4.5 A⠱
-
5⤠4.5 䈨B
-


4.5 䌨C
-
S⤠4.5䐨a
-
S⤠4.5䔨b
-
3⤠

4.5 c⠵)


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4.2.12 䔨b,2⤠4.5 A⠱
-
5⤠4.5
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-
4⤴.5 䌨C
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3⤠
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CURRICULUM MAP 2004
-
2005 COURSE TITLE:
Geometry A________



Feb. M
ar. Apr. May

June.


Essential
Questions






How are techniques of
indirect measurements used
to represent and solve real
world pro
blems?

How are the characteristics
of polygons used to simulate
and analyze real world
models?


How are the applications of
two
-
dimensional models
modified to visualize,
synthesize, and calculate
measurements of three
-

dimensional figures?


How does the in
vestigation
of transformations help us
to analyze, create, and
model iterative geometric
patterns using technology?

Culminating activities and
performance assessments.





Content










Geometric mean.

Pythagorean Theorem.

Trigonometric Ratios.

Parts

of a Circle.

Properties of chords, secants
and tangents.



Classification of polygons

Angles of convex polygons

Area of polygons

Geometric probability and
statistics.

Networks


Surface area and Volume of
three
-
dimensional solids.



Prisms /Cylinders



Cones/

Pyramids



Spheres



Vectors

Transformations

Fractals













Skills









Apply properties of
proportions to discover
properti
es of right triangles.


Use techniques of indirect
measurement to represent
and solve problems
involving Pythagorean
theorem and trigonometric
ratios.

Define the parts of a circle
and determine the
relationships that exist.

Recognize and apply
relationship
s between arcs,
chords and angles.

Apply the relationships of
chords, secants and tangents
to solve problems.

Classify and identify
polygons and their parts.

Calculate all interior and
exterior angle measures in
convex polygons.

Differentiate between area
formulas for polygons and
regular polygons.

Calculate the area of
polygons.

Find the shaded area of
polygons
(inscribed/circumscribed)
(in/about) a circle(s).

Compute area to solve
problems involving
geometric probability.

Introduce notion of
networks used

in graph
theory.


Relate the concept of three
-
dimensional figures to
tangible objects.

Create two
-
dimensional nets
for three
-
dimensional solids.

Utilize isometric dot paper
for the creation of three
-
dimensional shapes given
their net.

Utilize isometric do
t paper
to create a net for a three
-
dimensional figure.

Calculate the lateral area,
surface area and volumes of
prisms, cylinders, cones,
and pyramids.

Calculate the surface area
and volume of spheres.

Analyze real world three
-
dimensional objects to
synth
esize, connect and
calculate their different
measurements.

Find position and represent
motion in the coordinate
plane using motion.



Addition and subtraction
of vectors.

Identify the image and pre
-
image of a mapping.

Recognize an isometry or
congruence tra
nsformation.

Determine, describe, and
draw the effect of a
transformation, or a
sequence of geometric or
algebraic object.

Determine whether and
how one object can be
transformed to another by
transformation(s).

Generate and analyze
iterative geometric pa
tterns
supported by the use of
technology.





C.H.

Standard/

Benchmarks








4.2.12 A(1,3) 4.2.12.D(1
-
2)

4.2.12.E.1,2

4.5 A(1
-
5) 4.5 B(1
-
4)

4.5 C(1
-
6) 4.5D(1
-
6) 4.5E(1
-
3) 4.5
F(5)


4.2.12 A(1,3) 4.2.12.D(1
-
2)

4.2.12.E.1,2

4.5 A(1
-
5) 4.5 B(1
-
4)

4.5

C(1
-
6) 4.5D(1
-
6) 4.5E(1
-
3) 4.5
F(5)


4.2.12 A(1
-
3)

4.2.12.B 2 4.2.12.E.1,2

4.5 A(1
-
5) 4.5 B(1
-
4)

4.5 C(1
-
6) 4.5D(1
-
6) 4.5E(1
-
3) 4.5
F(5)


4.2.12 A(1
-
3) 4.2.12.B(1
-
4) 4.2.12E.1,2

4.5 A(1
-
5) 4.5 B(1
-
4)

4.5 C(1
-
6) 4.5D(1
-
6) 4.5E(1
-
3)
4.5 F(5)







Asses
sments









Activity

Exploring Geometry with
The Geometer’s Sketchpad

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