Geometry Curriculum Framework - raymondleemath

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Feb 2, 2013 (4 years and 4 months ago)

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Geometry

Curriculum Framework



Sugg
este
d

Paci
ng


Themes/Concepts/Big Ideas

Standards
-
based Essential Skills

Formative/Summative
Assessments

(Writing Assignments,
Projects, Performances)

Instructional Strategies

Resources

Beginning of Year Review

20

days

Preparing for Geometry
:



Changing Units of Measure
Within Systems



Changing Units of Measure
Between Systems



Simple Probability



Algebraic Expressions



Linear Equations



Ordered Pairs



Systems of Linear Equations



Square Roots and
Simplifying Radicals



Convert units of measure
between the customary and
metric systems



Find the probability of simple
events



Use the order of operations to
evaluate algebraic expressions



Use algebra to solve linear
equations



Use algebra to solve linear
inequalities



Name and gr
aph points in the
coordinate plane



Use graphing, substitution, and
elimination to solve systems of
linear equations



Evaluate square roots and
simplify radical expressions



Diagnostic assessment



Real world
connection
/examples



Ticket out the door



Practice/review activities



Problem solving activities



Post
-
test




Activate prior
knowledge



Scaffolding questions



K
-
W
-
L



Cooperative learning



Response cards



Reciprocal teaching



Writing to Learn
strategies



Vocabulary notecards



Lesson summaries



Journal prompts



E
ntrance/e
xit tickets



Graphic organizers



Visualization



Four
-
step problem
solving



Differentiated
activities



Glencoe McGraw
-
Hill Geometry

(2010) student and teacher
editions



Research
-
Based Strategies:
Narrowing the Achievement Gap
for Under
-
Resourced Studen
ts
by
Ruby Payne, Ph.D.



Online teacher resources:
http://glencoe.mcgraw
-
hill.com/sites/0078884845/student
_view0/




Online student edition:
http://glencoe.mcgraw
-
hill.com/sites/0078884845/student
_view0/




Math websites (see attachment)



Personal Tutor



Homework Help



Virtual manipulatives/calculator



Math journals


Sugg
este
d

Paci
ng


Themes/Concepts/Big Ideas

Standards
-
based Essential Skills

Formative/Summative
Assessments

(Writing Assignments,
Projects, Performances)

Instructional Strategies

Resources

Unit 1

39

days

Geometric Structure


Tools
of Geometry



Points, Lines, and Planes



Linear Measure



Distance and Midpoints



Angle Measure



Angle Relationships



Two
-
Dimensional Figures



Three
-
Dimensional Figures


Reasoning and Proof



Inductive Reasoning and
Conjecture



Logic



Conditional Statements



Deductive R
easoning



Postulates and Paragraph
Proofs



Algebraic Proof



Proving Segment
Relationships



Proving Angle Relationships


Parallel and Perpendicular Lines



Parallel Lines and
Transversals



Angles and Parallel Lines



Slopes of Lines



Equations and Lines



Proving Lines

Parallel



Perpendiculars and Distance

Tools of Geometry



Develop an awareness of the
structure of a mathematical
system, connecting definitions,
postulates, logical reasoning, and
theorems



Use construction to explore
attributes of geometric figures
and to m
ake conjectures about
geometric relationships



Use one
-

and two
-
dimensional
coordinate systems to represent
points, lines, rays, line segments,
and figures


Reasoning and Proof



Use inductive reasoning to
formulate a conjecture



Use logical reasoning to prove

statements are true and find
counterexamples to disprove
statements that are false



Determine the validity of a
conditional statement, its
converse, inverse, and
contrapostive



Use deductive reasoning to
prove a statement


Parallel and Perpendicular Lines



Make conjectures about lines
and determine the validity of the
conjectures



Make conjectures about angles
and determine the validity of the
conjectures



Use slopes of equations of lines
to investigate geometric
relationships, including parallel
lines and per
pendicular lines



Diagnostic assessment



Real
-
world
connection
/examples



Check your understanding



Practice and problem
solving



H.O.T. problems



Spiral review



Skills review



Standardized test pra
ctice



Geometry

L
ab



Graphing Technology Lab



Enrichment activities



Mid
-
chapter q
uiz



Practice test



Chapter/Unit test



Chapter 1 Project: Map
Your Town



Chapter 2 Project:
Scientific Method



Chapter 3 Project:
Function of Lines in
Construction



Activate prior
knowledge



Scaffolding questions



K
-
W
-
L



Cooperative learning



Reciprocal teaching



Peer tutoring



Writing to Learn
strategies



E
ntrance/e
xit tickets



Graphic organizers



Visualization



Four
-
step problem
solving



Differentiated
activities



Glencoe McGraw
-
Hill Geometry

(2010) student and teacher
editions



Research
-
Based Strategies:
Narrowing the Achievement Gap
for Under
-
Resourced Students
by
Ruby Payne, Ph.D.



Online teacher resources:
http:
//glencoe.mcgraw
-
hill.com/sites/0078884845/student
_view0/




Online student edition:
http://glencoe.mcgraw
-
hill.com/sites/0078884845/student
_view0/




Math websites (see attachment
)



Personal Tutor



Homework Help



Virtual manipulatives/calculator



Math journals


Sugg
este
d

Paci
ng


Themes/Concepts/Big Ideas

Standards
-
based Essential Skills

Formative/Summative
Assessments

(Writing Assignments,
Projects, Performances)

Instructional Strategies

Resources

Unit 2

35

days

Congruence


Congruent Triangles



Classifying Triangles



Angles of Triangles



Congruent Triangles



Proving Triangles:
Congruent, SSS, SAS



Proving Triangles Congruent:

ASA, AAS



Isosceles and Equilateral
Triangles



Congruence Transformations



Triangles and Coordinate
Proof


Relationships in Triangles



Bisectors of Triangles



Medians and Altitudes of
Triangles



Inequalities in One Triangle



Indirect Proof



The Triangle Inequali
ty



Inequalities in Two Triangles


Quadrilaterals



Angles of Polygons



Parallelograms



Tests for Parallelograms



Rectangles



Rhombi and Squares



Trapezoids and Kites




Congruent Triangles



Make conjectures about
polygons



Use numeric and geometric
patterns to make

generalizations
about geometric properties



Use logical reasoning to prove
statements


Relationships in Triangles



Use slope and equations of lines
to investigate geometric
relationships, including special
segments of triangles



Recognize and know historical

development of geometric
systems and know that
mathematics was developed for a
variety of purposes



Analyze geometric relationships
in order to verify conjectures


Quadrilaterals



Use numeric and geometric
patterns to make generalizations
about geometric
properties,
including properties of polygons



Formulate and test conjectures
about the properties and
attributes of polygons



Derive and use formulas
involving length, slope, and
midpoint



Formulate and test conjectures
about the properties and
attributes of
polygons




Diagnostic assessment



Real
-
world
connection
/examples



Check your understanding



Practice and problem
solving



H.O.T. problems



Spiral review



Skills review



Standardized test practice



Geometry

L
ab



Graphing Technology Lab



Enrichment activities



Mid
-
chapt
er quiz



Practice test



Chapter/Unit test



Chapte
r 4 Project:
Classifying Triangles



Chapter 5 P
roject:
Architecture: Triangular
Design



Chapt
er 6 Project: Real
World: Game Time




Activate prior
knowledge



Scaffolding questions



K
-
W
-
L



Cooperative learning



Response cards



Reciprocal teaching



Writing to Learn
strategies



E
ntrance/e
xit tickets



Graphic organizers



Visualization



Four
-
step problem
solving



Differentiated
activities



Glencoe McGraw
-
Hill Geometry
(2010) student and teacher
editions



Research
-
Based Strate
gies:
Narrowing the Achievement Gap
for Under
-
Resourced Students
by
Ruby Payne, Ph.D.



Online teacher resources:
http://glencoe.mcgraw
-
hill.com/sites/0078884845/student
_view0/




Online student edition:
http://glencoe.mcgraw
-
hill.com/sites/0078884845/student
_view0/




Math websites (see attachment)



Personal Tutor



Homework Help



Virtual manipulatives/calcu
lator



Math journals


Sugg
este
d

Paci
ng


Themes/Concepts/Big Ideas

Standards
-
based Essential Skills

Formative/Summative
Assessments

(Writing Assignments,
Projects, Performances)

Instructional Strategies

Resources

Unit 3

36

days

Similarity


Proportions and Similarity



Ratios and Proportions



Similar Polygons



Similar Triangles



Parallel Lines and
Proportional Parts



Parts of Similar Triangles



Similarity Transformations



Scale Drawings and Models


Right Triangles and Trigonometry



Geometric Mean



The Pythagorean Theorem
and its Converse



Special Right Triangles



Trigonometry



Angles of Elevation and
Depression



The Law of Sines and Law of
Cosines



Vectors


Transformations and Symmetry



Reflections



Translations



Rotations



Compositions of
Transformations



Symmetry



Dilations

Proportions and Similarity



Use ratios to solve problems
involving similar figures



Formulate and test conjectures
about the properties and
attributes of polygons and their
component p
arts based on
explorations and concrete
models


Right Triangles and Trigonometry



Use and extend similarity
properties to explore and justify
conjectures about geometric
figures



Derive, extend, and use the
Pythagorean Theorem



Identify and apply patterns fro
m
right triangles to solve
meaningful problems, including
special right triangles

(45°,
-
45°,
-
90° and 30°,
-
60°,
-
90°)
and triangles with sides that are
Pythagorean triplets



Develop, apply, and justify
triangle similarity relationships,
such as tri
gonometric ratios
using a variety of methods


Transformations and Symmetry



Use congruence transformations
to make conjectures and justify
properties of geometric figures










Diagnostic assessment



Real
-
world
connection/examples



Check your understanding



Practice and problem
solving



H.O.T. problems



Spiral review



Skills review



Standardized test practice



Geometry

lab



Graphing Technology Lab



Geometry Software Lab



Enrichment activities



Mid
-
chapter quiz



Practice test



Chapter/Unit test



Ch
apter 7 Project: Time
for a Rebound



Chapter 8 Project:
Graduation Planning



Chapter 9 Project:
Picture
This: Photography and
Tessellations



Activate prior
knowledge



Scaffolding questions



K
-
W
-
L



Cooperative learning



Response cards



Reciprocal teaching



Writing to Learn
strategies



Entrance/exit tickets



Graphic organizers



Visualization



Four
-
step problem
solving



Differentiated
activities



Glencoe McGraw
-
Hill Geometry

(2010) student and teacher
editions



Research
-
Based Strategies:
Narrowing the Achievement Gap
for Under
-
Resourced Stude
nts
by
Ruby Payne, Ph.D.



Online teacher resources:
http://glencoe.mcgraw
-
hill.com/sites/0078884845/student
_view0/




Online student edition:
http://glencoe.mcgraw
-
hill.com/sites/0078884845/student
_view0/




http://www.tessellations.org/




Totally Tessellated
http://library.thinkquest.org/16661
/




M.C. Escher Official Website
http://www.mcescher.com/




Math websites (see attachment)



Personal Tutor



Homework Help



Virtual manipulatives/calculator



Math journals


Sugg
este
d

Paci
ng


Themes/Concepts/Big Ideas

Standards
-
based Essential Skills

Formative/Summative
Assessments

(Writing Assignments,
Projects, Performances)

Instructional Strategies

Resources

Unit 4

33

days

Measurement


Circles



Circles and Circumference



Measuring Angles and Arcs



Arcs and Chords



Inscribed Angles



Tangents



Secants, Tangents, and Angle
Measures



Special Segments in a Circle



Equations of Circles


Areas of Polygons and Circles



Areas of
Parallelograms and
Triangles



Areas of Trapezoids,
Rhombi, and Kites



Areas of Circles and Sectors



Areas of Regular Polygons
and Composite Figures



Areas of Similar Figures


Extending Surface Area and Volume



Representations of Three
-
Dimensional Figures



Surfac
e Areas of Prisms and
Cylinders



Surface Areas of Pyramids
and Cones



Volumes of Prisms and
Cylinders



Volumes of Pyramids and
Cones



Spherical Geometry



Congruent and Similar Solids


Probability and Measurement



Representing Sample Spaces

Circles



Find areas of sectors and arc
lengths of circles using
proportional reasoning



Use numeric a
nd geometric
patterns to make generalizations
about geometric properties
including properties of angle
relationships in circles


Areas of Polygons and Circles



Find areas of rectangular
polygons, circles, and composite
figures



Find areas of sectors and arc
lengths of circles using
proportional reasoning


Extending Surface Area and Volume



Find surface areas and volumes
of prisms, pyramids, spheres,
cones, cylinders, and composites
of these figures



Describe the effect on area and
volume when one or more
dimens
ions of a figure are
changed


Probability and Measurement



Understand sample spaces and
design simulations



Compute probabilities for
independent, dependent,
mutually exclusive, not mutually
exclusive, and conditional events



Calculate geometric probabilities







Diagnostic assessment



Real
-
world
connection/examples



Check your understanding



Practice and problem
solving



H.O.T. problems



Spiral review



Skills review



Standardized test practice



Geometry L
ab



Graphing Technology Lab



Spreadsheet Lab



Enrichment
activities



Mid
-
chapter quiz



Practice test



Chapter/Unit test



Chapt
er 10 Project:
History of Crop Circles:
Circumference, Diameter,
Radius, and Tangents



Chapter
11 Project: Fun
With Arts and Crafts:
Cubes



Chapter 12 Project:
Geometry in Architecture:
S
olid Idea



Chapter 13 Project:
Carnival Time: Fun and
Games?




Activate prior
knowledge



Scaffolding questions



K
-
W
-
L



Cooperative learning



Response cards



Reciprocal teaching



Writing to Learn
strategies



Entrance/exit tickets



Graphic organizers



Visualization



Four
-
step problem
solving



Differentiated
activities



Glencoe McGraw
-
Hill Geometry

(2010) student and teacher
editions



Research
-
Based Strategies:
Narrowing the Achievement Gap
for Under
-
Resourced Students
by
Ruby Payne, Ph.D.



Online teacher resources:
http://glencoe.mcgraw
-
hill.com/sites/0078884845/student
_view0/




Online student edition:
http://glenco
e.mcgraw
-
hill.com/sites/0078884845/student
_view0/




Math websites (see attachment)



Personal Tutor



Homework Help



Virtual manipulatives/calculator



Math journals



Movie
Signs
(2002)