Course Title:

clankjewishΗλεκτρονική - Συσκευές

10 Οκτ 2013 (πριν από 3 χρόνια και 8 μήνες)

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Course Title:




Geometry


Prerequisites:




C or better in Algebra 1


CSU/UC Approved:



Yes


CSU/UC Subject Area:


(c) Mathematics


Grade Level:




9, 10, 11, 12
-

depending on when student meets prerequisite


Length of Course/Type:


Year


Assigned Te
xts:



1.

Laurie Bass and Art Johnson;
Geometry
; Prentice Hall






2.

Accompanying Workbook;
Geometry Workbook
; Prentice Hall


Supplemental Materials:



Videos: topical episodes of a Caltech produced series entitled
Mathematics







(
Similarity, the Pyth
agorean Theorem, and Pi)


Brief Course Description:


This course covers the foundations of geometrical figures and their measurement.






Beginning with the component part of geometrical figures


points, lines, and






planes


and through the use of

reasoning and proof, the course encompasses the






study of triangles, quadrilaterals, other polygons, circles, and solids. Through the

study of definitions, postulates, and theorems, in addition to other related
mathematical topics, the properties of
these figures are incorporated into an
understanding and ability to construct and measure both plane figures and solids.
Major topics in the course include deductive and inductive reasoning, triangle
relationships and congruence, right triangle trigonomet
ry, similarity, areas of
plane figures, and surface areas and volumes of solids.


Course Outcomes:


A.

Fall Semester Content Outcomes

1.

Students will be able to recognize and use definitions, postulates, and

theorems concerning angles and segments, inclu
ding measurement of
segments in the coordinate plane (CSS 1, 17).

2.

Students will be able to recognize and use inductive and deductive forms


of reasoning to construct proofs and assess the validity of logical

argument (CSS 2, 3).

3.

Students will be abl
e to recognize and use the properties of parallel and
perpendicular lines to determine and prove the Polygon Angle
-
Sum
theorems and the properties of parallelograms (CSS 7, 12, 13).

4.

Students will be able to perform basic constructions with a straight
-
ed
ge
and compass, including congruent angles, angle and segment bisectors,
perpendicular bisectors, and parallel lines (CSS 16).

5.

Students will be able recognize and use postulates and theorems to
determine and prove Triangle Congruence, including correspo
nding parts
of congruent triangles (CSS 4, 5).

6.

Students will be able to recognize and use proof by contradiction to
prove and use the Triangle Inequality Theorem (CSS 2, 6).

7.

Students will be able to recognize and use definitions and theorems to
mid
segments, bisectors, and concurrent lines in triangles (CSS 16).

8.

Students will be able to recognize and use the properties of special
quadrilaterals and parallelograms to prove and solve problems
concerning all quadrilaterals (CSS 2,5,7).

B.

Spring Seme
ster Content Outcomes

1.

Students will be able to recognize and use postulates and theorems
concerning triangle similarity to determine and prove the similarity of
triangles and the relationships between their corresponding parts. (CSS 2,
4, 5)

2.

Students

will be able to recognize, use, and prove theorems concerning
Special Right Triangles and the Pythagorean Theorem to determine side
lengths of right triangles (CSS 2, 14, 15, 20).

3.

Students will be able to recognize and use basic right triangle
trigon
ometric ratios to determine the lengths and angle measures of right
triangles (CSS 18, 19).


4.

Students will be able to recognize and use formulas to compute the areas
of plane figures: triangles, quadrilaterals, regular polygons, and circles
(CSS 8, 10,
11).

5.

Students will be able to recognize and use formulas to compute the
volumes and surface areas of space figures: prisms, pyramids, cylinders,
cones, and spheres (CSS 8, 9, 11).

6.

Students will able to recognize and use ratios of side
-
lengths, perime
ters,
areas, and volumes to determine the impact of dimensional changes in
one area on the others (CSS 12).

7.

Students will be able to recognize, prove, and use relationships of
inscribed angles, chords, secants, and tangents of circles (CSS 21).

8.

Stude
nts will be able to recognize and use the principles of
transformation, rotation, and reflection on geometric figures in the
coordinate plane (CSS 22).

C.

Skill Outcomes


1.

Students will be able to prove basic theorems, and prove triangle
congruence and simi
larity.

2.

Students will be able to measure in the coordinate plane.

3.

Students will be able to find measures of areas, surface areas, and
volumes of plane and space figures.

4.

Students will be able to construct basic geometrical figures with a
straight edge and
compass.

5.

Students will be able to apply geometric knowledge in solving selected
“real
-
world” problems modeled with geometric figures, particularly in
areas related to trigonometry and the Pythagorean Theorem.

6.

Students will be able to use properties of geo
metric figures to determine
equations and solve for unknown dimensions of the figures.


Course Objectives:


1.

Students will be introduced to inductive and deductive forms of reasoning and





use of this reasoning in arriving at the fundamental proofs of

geometry.

2.

Students will be introduced to the fundamental properties of geometric figures
and the use of them in constructing and working with them.

3.

Students will be introduced to the principles of measuring components of
geometric figures such as segments

and angles.

4.

Students will be introduced to triangle relationships, including congruence,
similarity, and right triangle trigonometry.

5.

Students will introduced to the measurement of areas of plane figures and surface
area and volume of solids.