# Geometry Curriculum Framework - raymondleemath

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Feb 2, 2013 (5 years and 3 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

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

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
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

and determine the validity of the
conjectures

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

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

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

Angles of Polygons

Parallelograms

Tests for Parallelograms

Rectangles

Rhombi and Squares

Trapezoids and Kites

Congruent Triangles

polygons

Use numeric and geometric
patterns to make

generalizations

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

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

Formulate and test conjectures
attributes of polygons

Derive and use formulas
involving length, slope, and
midpoint

Formulate and test conjectures
attributes of
polygons

Diagnostic assessment

Real
-
world
connection
/examples

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
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
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

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:

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
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

Practice and problem
solving

H.O.T. problems

Spiral review

Skills review

Standardized test practice

Geometry L
ab

Graphing Technology Lab

Enrichment
activities

Mid
-
chapter quiz

Practice test

Chapter/Unit test

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

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)