MATHEMATICS
Geometry
Unit 1
1
Course Description
Geometry stresses the ability to reason logically and to think critically, using spatial sense. A major part of the course will be devoted
to teaching the student how to present a formal proof. Geometric properties of both two and three dimensions are emphasized as they
apply to points, lines, planes, and solids. In this course students learn to recognize and work with geometric concepts in various
contexts. They build on ideas of inductive and deductive reasoning, logic, concepts, and techniques of Euclidean plane and solid
geometry and develop an understanding of mathematical structure, method, and applications of Euclidean plane and solid geometry.
Students use visualizations, spatial reasoning, and geometric modeling to solve problems. Topics of study include points, lines, and
angles; triangles; quadrilaterals and other polygons; circles; coordinate geometry; three-dimensional solids; geometric constructions;
symmetry; similarity; and the use of transformations.
Upon successful completion of this course, students will be able to: Use and prove basic theorems involving congruence and similarity
of figures; determine how changes in dimensions affect perimeter and area of common geometric figures; apply and use the properties
of proportion; perform basic constructions with straight edge and compass; prove the Pythagorean theorem; use the Pythagorean
theorem to determine distance and find missing dimensions of right triangles; know and use formulas for perimeter, circumference,
area, volume, lateral and surface area of common figures; find and use measures of sides, interior and exterior angles of polygons to
solve problems; use relationships between angles in polygons, complementary, supplementary, vertical and exterior angle properties;
use special angle and side relationships in special right triangles; understand, apply, and solve problems using basic trigonometric
functions; prove and use relationships in circles to solve problems; prove and use theorems involving properties of parallel lines cut by
a transversal, quadrilaterals and circles; write geometric proofs, including indirect proofs; construct and judge validity of logical
arguments; prove theorems using coordinate geometry including the midpoint of a segment and distance formula; understand
transformations in the coordinate plane; construct logical verifications to test conjectures and counterexamples; and write basic
mathematical arguments in paragraph and statement-reason form.
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Pacing Chart – Unit 1
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Student Learning Objective
Use the undefined notion of a point, line, and distance
along a line and distance around a circular arc to
develop definitions for angles, circles, parallel lines,
perpendicular lines and line segments.
Apply the definitions of angles, circles, parallel lines,
perpendicular lines and line segments to describe
rotations, reflections, and translations.
Develop and perform rigid transformations that
include reflections, rotations, translations and dilations
using geometric software, graph paper, tracing paper,
and geometric tools and compare them to non-rigid
transformations.
Use rigid transformations to determine, explain and
prove congruence of geometric figures.
Create proofs of theorems involving lines, angles,
triangles, and parallelograms.* (Please note G.CO.10
will be addressed again in unit2 and G.CO.11 will be
addressed again in unit 4)
Generate formal constructions with paper folding,
geometric software and geometric tools to include,
but not limited to, the construction of regular
polygons inscribed in a circle.
CCSS
Instruction: 5 weeks
G.CO.A.1
G.CO.A.1
G.CO.A.4
Assessment: 1 week
Remediation/Enrichment: 1
week
G.CO.A.2,
G.CO.A.3,
G.CO.A.4,
G.CO.A.5
G.CO.B.6,
G.CO.B.7,
G.CO.B.8
G.CO.B.9
G.CO.B.10
G.CO.B.11
G.CO.D.12
G.CO.D.13
Major Supporting Additional (Identified by PARCC Model Content Frameworks). Bold type indicates grade level fluency requirements.
(Identified by PARCC Model Content Frameworks)
3
Research about Teaching and Learning Mathematics
Structure teaching of mathematical concepts and skills around problems to be solved (Checkly, 1997; Wood & Sellars, 1996; Wood & Sellars,
1997)
Encourage students to work cooperatively with others (Johnson & Johnson, 1975; Davidson, 1990)
Use group problem-solving to stimulate students to apply their mathematical thinking skills (Artzt & Armour-Thomas, 1992)
Students interact in ways that support and challenge one another’s strategic thinking (Artzt, Armour-Thomas, & Curcio, 2008)
Activities structured in ways allowing students to explore, explain, extend, and evaluate their progress (National Research Council, 1999)
There are three critical components to effective mathematics instruction (Shellard & Moyer, 2002):
 Teaching for conceptual understanding
 Developing children’s procedural literacy
 Promoting strategic competence through meaningful problem-solving investigations
Teachers should be:
 Demonstrating acceptance and recognition of students’ divergent ideas.
 Challenging students to think deeply about the problems they are solving, extending thinking beyond the solutions and algorithms
required to solve the problem
 Influencing learning by asking challenging and interesting questions to accelerate students’ innate inquisitiveness and foster them
to examine concepts further.
 Projecting a positive attitude about mathematics and about students’ ability to “do” mathematics
Students should be:
 Actively engaging in “doing” mathematics
 Solving challenging problems
 Investigating meaningful real-world problems
 Making interdisciplinary connections
 Developing an understanding of mathematical knowledge required to “do” mathematics and connect the language of
mathematical ideas with numerical representations
 Sharing mathematical ideas, discussing mathematics with one another, refining and critiquing each other’s ideas and
understandings
 Communicating in pairs, small group, or whole group presentations
 Using multiple representations to communicate mathematical ideas
 Using connections between pictures, oral language, written symbols, manipulative models, and real-world situations
 Using technological resources and other 21st century skills to support and enhance mathematical understanding
4
Mathematics is not a stagnate field of textbook problems; rather, it is a dynamic way of constructing meaning about the
world around us, generating knowledge and understanding about the real world every day. Students should be
metaphorically rolling up their sleeves and “doing mathematics” themselves, not watching others do mathematics for
them or in front of them. (Protheroe, 2007)
Conceptual-Based Model/Course Philosophy
The purpose of the Conceptual-Based Model is to allow students the time to explore mathematical concepts to promote
academic rigor and high level of student discourse to concurrently develop conceptual understanding, procedural fluency,
and problem-solving skills. During the 90 minute block of mathematics instruction, teachers will select and set up a
mathematical task that targets the mathematical goal(s) for the lesson. The teacher sets the stage for learning by ensuring
the objective/rationale of the lesson is well-defined and connected to the task. The task should build on student’s prior
knowledge, life experiences, and culture allowing students to share their prior knowledge and life/cultural experiences as it
relates to the task to ensure that students understand the context of the problem. The instructional goal is to introduce the
activity/task to the students allowing them to have access to learning while maintaining the cognitive demands of the task.
Teachers will then support the students’ exploration of the task; this can be done independently, in pairs or in small groups
or a combination of all. It is highly recommended that students be given the opportunity to privately work on a task to
generate solutions on their own. Students are encouraged to share their findings with their peers in small group to compare
their solutions. As students are actively engaged in constructing meaning of the mathematical concept(s) being taught and
communicating their understanding of the concept(s) with their peers, the teacher monitors the development of student
understanding by observing student thinking and using questions to stimulate thinking to drive students toward the aimed
mathematical goal(s). The teacher assesses students’ understanding of key mathematical ideas, problem-solving strategies,
and the use of and connection between models and representations to determine what the student knows. The teacher
advances the students’ understanding to move the student beyond their present thinking and expand what they know to an
additional situation. Teachers have been trained to strategically select groups of students who have different solution paths
to the same task, different representations and errors/misconceptions to share, discuss, and analyze as a whole group. By
providing these instructional opportunities, the teacher will then be able to orchestrate the class discussion by providing
students with the opportunities to make their learning public as students share, discuss, analyze, clarify, extend, connect,
strengthen, and record their thinking strategies. After students discuss, justify, and challenge the various solution paths that
were shared, a summary of the learning is articulated and connected to the objective of the lesson. Students should be given
an opportunity to close the lesson with a reflection on their learning.
5
Effective Pedagogical Routines/Instructional Strategies
Collaborative Problem Solving
Analyze Student Work
Connect Previous Knowledge to New Learning
Identify Student’s Mathematical Understanding
Making Thinking Visible
Develop and Demonstrate Mathematical Practices
Identify Student’s Mathematical Misunderstandings
Interviews
Role Playing
Inquiry-Oriented and Exploratory Approach
Diagrams, Charts, Tables, and Graphs
Multiple Solution Paths and Strategies
Anticipate Likely and Possible Student Responses
Use of Multiple Representations
Collect Different Student Approaches
Explain the Rationale of your Math Work
Multiple Response Strategies
Quick Writes
Asking Assessing and Advancing Questions
Pair/Trio Sharing
Revoicing
Turn and Talk
Marking
Charting
Gallery Walks
Small Group and Whole Class Discussions
Student Modeling
Recapping
Challenging
Pressing for Accuracy and Reasoning
Maintain the Cognitive Demand
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Technology
Standards
8.1.12.A.1, 8.1.12.A.2, 8.1.12.E.1
Technology:
8.1.12.A.1 Construct a spreadsheet, enter data, and use mathematical or logical functions to manipulate data, generate charts
and graphs, and interpret the results.
8.1.12.A.2 Produce and edit a multi-page document for a commercial or professional audience using desktop publishing
and/or graphics software.
8.1.12.E.1 Develop a systematic plan of investigation with peers and experts from other countries to produce an innovative
solution to a state, national, or worldwide problem or issue.
Link: http://www.state.nj.us/education/cccs/standards/8/
7
21st-Century Life & Career Skills
Standards
9.1.12.A.1, 9.1.12.A.2, 9.1.12.B.1, 9.1.12.B.3
21st-Century Life and Careers:
9.1.12.A.1 Apply critical thinking and problem-solving strategies during structured learning experiences.
9.1.12.A.2 Participate in online strategy and planning sessions for course-based, school-based, or outside projects.
9.1.12.B.1 Present resources and data in a format that effectively communicates the meaning of the data and its implications
for solving problems, using multiple perspectives.
9.1.12.B.3 Assist in the development of innovative solutions to an onsite problem by incorporating multiple perspectives and
applying effective problem-solving strategies during structured learning experiences, service learning, or
volunteering.
Link: http://www.nj.gov/education/aps/cccs/career/
8
Differentiated Instruction
Accommodate Based on Students Individual Needs: Strategies
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Time/General
Extra time for assigned
tasks
Adjust length of assignment
Timeline with due dates for
reports and projects
Communication system
between home and school
Provide lecture
notes/outline
Assistive Technology
 Computer/whiteboard
 Tape recorder
 Video tape
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Processing
Extra Response time
Have students verbalize
steps
Repeat, clarify or reword
directions
Mini-breaks between tasks
Provide a warning for
transitions
Partnering
Tests/Quizzes/Grading
Extended time
Study guides
Shortened tests
Read directions aloud
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Comprehension
Precise processes for
conceptual model
Short manageable tasks
Brief and concrete
directions
Provide immediate
feedback
Small group instruction
Emphasize multi-sensory
learning
Behavior/Attention
 Consistent daily
structured routine
 Simple and clear
classroom rules
 Frequent feedback
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Recall
Teacher-made checklist
Use visual graphic
organizers
Reference resources to
promote independence
Visual and verbal
reminders
Graphic organizers
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Organization
Individual daily planner
Display a written agenda
Note-taking assistance
Color code materials
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Interdisciplinary Connections
Model interdisciplinary thinking to expose students to other disciplines.
ELA Connection:
Task Name:
Defining Parallel lines
Defining Perpendicular lines
Defining Rotations
Architecture and Construction Career Connection:
Task name:
Horizontal Stretch of the Plane
10
Assessments
Required District/State Assessments
Star Math
Unit # 1 Assessment
PARCC
Suggested Formative/Summative Classroom Assessments
Describe Learning Vertically
Identify Key Building Blocks
Make Connections (between and among key building blocks)
Short/Extended Constructed Response Items
Multiple-Choice Items (where multiple answer choices may be correct)
Drag and Drop Items
Use of Equation Editor
Quizzes
Journal Entries/Reflections/Quick-Writes
Accountable talk
Projects
Portfolio
Observation
Graphic Organizers/ Concept Mapping
Presentations
Role Playing
Teacher-Student and Student-Student Conferencing
Homework
11
Common Core State Standards
G.CO.A.1
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance
along a line, and distance around a circular arc.
G.CO.A.2
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in
the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation
versus horizontal stretch).
G.CO.A.3
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
G.CO.A.4
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.A.5
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry
software. Specify a sequence of transformations that will carry a given figure onto another.
Understand congruence in terms of rigid motions.
G.CO.B.6
Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two
figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
G.CO.B.7
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
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Common Core State Standards
G.CO.B.8
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
G.CO.C.9
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate
interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those
equidistant from the segment's endpoints.
G.CO.C.10
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are
congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at
a point.
G.CO.C.11
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a
parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
G.CO.D.12
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding,
dynamic geometric software, etc.).Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines,
including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
G.CO.D.13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
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Course: Geometry
Unit: 1
Topic: Congruence, Proof and Construction
CCSS:
G.CO.A.1, G.CO.A.2, G.CO.A.3, G.CO.A.4, G.CO.A.5, G.CO.B.6, G.CO.B.7, G.CO.B.8, G.CO.B.9, G.CO.B.10,
G.CO.B.11, G.CO.D.12, G.CO.D.13
Mathematical Practices:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Student Objectives
G.CO.A.1:
Use the undefined notion
of a point, line, distance
along a line and distance
around a circular arc to
develop definitions for
angles, circles, parallel
lines, perpendicular lines
and line segments.
Modified Student
Learning
Objectives/Standards
EEG.CO.1
Know the attributes of
perpendicular lines,
parallel lines, and line
segments; angles; and
circles.
Skills, Strategies &
Concepts
Have students write their
own understanding of a
given term.
Give students formal and
informal definitions of
each term and compare
Essential
Understandings/
Questions
(Accountable Talk)
Essential question: How
do you use undefined
terms as the basic
elements of geometry?
Working with diagrams is
central to geometric
thinking.
Tasks/Activities
Defining a Parallel lines
Defining a Perpendicular
lines
14
Student Objectives
Modified Student
Learning
Objectives/Standards
Skills, Strategies &
Concepts
them.
http://dynamiclearningma
ps.org/moreinfo/essential_
elements/index.html
G.CO.A.1, G.CO.A.4
Apply the definitions of
angles, circles, parallel lines,
perpendicular lines and line
segments to describe
rotations, reflections, and
translations.
EEG‐CO.4–5. Given a
geometric figure
and a rotation, reflection, or
translation of
that figure, identify the
components of the
two figures that are
congruent.
Develop precise
definitions through use of
examples and nonexamples.
Review vocabulary
associated with
transformations (e.g. point,
line, segment, angle, circle,
polygon, parallelogram,
perpendicular, rotation
reflection, translation).
Have students make a
graphic organizer that
summarizes reflections,
translations and rotations in
a coordinate plane.
Have students create their
own problem situations to
assess their understanding of
Essential
Understandings/
Questions
(Accountable Talk)
Tasks/Activities
A diagram is a
sophisticated
mathematical device for
thinking and
communicating .
Essential question: How do
you draw the image of a
figure under a reflection?
Defining Reflection
Defining Rotations
How do you draw the image
of a figure under a
translation?
How do you draw the image
of a figure under
a rotation?
Emphasize the importance
of understanding a
transformation as the
correspondence between
initial and final points,
rather than the physical
motion.
15
Student Objectives
Modified Student
Learning
Objectives/Standards
Skills, Strategies &
Concepts
critical features of rigid
transformation.
Students may use geometry
software and/or
manipulatives to model and
compare transformations.
EE.G--‐CO.4–5. Given a
geometric figure
and a rotation, reflection,
Develop and perform rigid or translation of
transformations that
that figure, identify the
include reflections,
components of the
rotations, translations and two figures that are
dilations using geometric
congruent.
using technology as a
tool, students can generate
many examples
of double reflections.
They can use these
drawings to make
conjectures about the
reflections.
.
Provide real-world
examples of rigid motions
(e.g. Ferris wheels for
rotation; mirrors for
reflection; moving
vehicles for translation).
G.CO.A.2, G.CO.A.3,
G.CO.A.4, G.CO.A.5
Essential
Understandings/
Questions
(Accountable Talk)
Tasks/Activities
Provide students with a preimage and a final,
transformed image, and ask
them to describe the steps
required to generate the
final image. Show examples
with more than one answer
(e.g., a reflection might
result in the same image as a
translation).
How can you use more
than one transformation
to map one figure onto
another?
Horizontal Stretch of the
Plane
Ferris wheel- Real life
Application
Provide both individual
and small-group
activities, allowing
adequate time for students Symmetries of rectangles
to explore and verify
conjectures about
Seven Circles II
transformations and
develop precise
definitions of rotations,
Defining Rotations
reflections and
translations.
Reflected Triangles
16
Student Objectives
Modified Student
Learning
Objectives/Standards
Skills, Strategies &
Concepts
Have students write a
journal entry in which
they
list the properties of a
double reflection across
parallel lines and the
properties of a double
reflection across
intersecting lines
Essential
Understandings/
Questions
(Accountable Talk)
Consider how a
transformation or a
composition of
transformations, maps a
tessellation onto itself.
Tasks/Activities
Showing a triangle
congruence: a particular
case
Is this a rectangle?
17
Student Learning
Objectives/Standards
Modified Student
Learning
Objectives/Standards
Skills, Strategies &
Concepts
G.CO.B.6, G.CO.B.7,
G.CO.B.8
EE.G‐CO.6–8. Identify
corresponding
congruent and similar G--‐
CO.7. Use the definition
of congruence in terms of
rigid motions to show that
parts of shapes.
Develop the relationship
between transformations
and congruency. Allow
adequate time and provide
hands-on activities for
students to visually and
physically explore rigid
motions and congruence.
Use rigid transformations
to determine, explain and
prove congruence of
geometric figures.
Use graph paper, tracing
paper or dynamic
geometry software to
obtain images of a given
figure under specified
rigid motions. Note that
size and shape are
preserved.
Build on previous learning
of transformations and
congruency to develop a
formal criterion for
proving the congruency of
triangles. Construct pairs
of triangles that satisfy the
ASA, SAS or SSS
Essential
Understandings/
Questions
(Accountable Talk)
Essential question: How
can you use properties o
rigid motions to draw
conclusions about
corresponding sides and
corresponding angles in
congruent triangles?
How can you establish
the SSS and SAS triangle
congruence criteria using
properties of rigid
motions?
Tasks/Activities
Building a tile pattern by
reflecting hexagons
Properties of Congruent
Triangles
SSS Congruence
Criterion
Why does SAS work?
How can you establish
and use the ASA and
AAS triangle congruence
criteria?
IFL: Set of Related
Tasks: Investigating
Congruence in Terms of
Rigid Motions
Have students write a
journal entry in which
they state the
Corresponding Parts of
Congruent
Triangles are Congruent
18
Student Objectives
Modified Student
Learning
Objectives/Standards
Skills, Strategies &
Concepts
Essential
Understandings/
Questions
(Accountable Talk)
congruence criteria, and
use rigid motions to verify
that they satisfy the
definition of congruent
figures. Investigate rigid
motions and congruence
both algebraically (using
coordinates) and logically
(using proofs).
Theorem in their own
words. Encourage them to
include one or more
labeled figures as part of
the journal entry.
Tasks/Activities
encourage students to
develop the habit
of mind in which they ask
themselves if the answer
to a modeling problem
seems reasonable,
G.CO.B.9, G.CO.B.10,
G.CO.B.11
Create proofs of theorems
involving lines, angles,
triangles, and
parallelograms.*
Not applicable.
Use the history of geometry
and real-world applications
to help students develop
conceptual understandings
before they begin to use
formal proof.
Essential question:
How can you establish the
SSS and SAS triangle
congruence criteria using
properties of rigid motions
and use the ASA and AAS
triangle congruence criteria?
Quadrilaterals
Congruent angles made by
parallel lines and a
transverse
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Student Objectives
Modified Student
Learning
Objectives/Standards
http://dynamiclearningmaps.
org/moreinfo/essential_elem
ents/index.html
Skills, Strategies &
Concepts
Essential
Understandings/
Questions
(Accountable Talk)
Tasks/Activities
Seven Circles I
Use dynamic geometry
software to allow students to
make conjectures that can, in
turn, be formally proven.
For example, students might
notice that the base angles of
an isosceles triangle always
appear to be congruent when
manipulating triangles on the
computer screen and could
then engage in a more
formal discussion of why
this occurs.
Students should be
encouraged to focus on the
validity of the underlying
reasoning while exploring a
variety of formats for
expressing that reasoning.
Different methods of proof
will appeal to different
learning styles in the
classroom.
Classifying Triangles
Placing a Fire Hydrant
Is this a parallelogram?
Have students write a
journal entry in which they
explain
and illustrate
thenarrative paragraphs, using flow diagrams, in two
Encourage multiple ways of writing
proofs,
such as in
ASA and
AASwords.
column format, and using diagrams
without
Congruence Criteria.
G.CO.D.12, G.CO.D.13
Generate formal
constructions with paper
folding, geometric software
and geometric tools to
include, but not limited to,
the construction of regular
polygons inscribed in a
circle.
Not applicable.
Provide meaningful
problems (e.g. constructing
the centroid or the in center
of a triangle) to offer
students practice in
executing basic
constructions.
http://dynamiclearningmaps.
org/moreinfo/essential_elem
ents/index.html
Using congruence theorems,
ask students to prove that the
constructions are correct.
Essential question: How do
you inscribe a regular
polygon in a circle?
Origami Silver Rectangle
Bisecting an angle
Ask students to write “howto” manuals, giving verbal
instructions for a particular
construction. Offer
opportunities for hands-on
practice using various
construction tools and
methods.
Paper cutting
Inscribing a hexagon in a
circle
Inscribing an equilateral
triangle in a circle
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Student Objectives
Modified Student
Learning
Objectives/Standards
Skills, Strategies &
Concepts
Have students write a
journal entry in which they
give step-by-step
instructions for inscribing a
regular hexagon and square
in a circle.
Essential
Understandings/
Questions
(Accountable Talk)
Tasks/Activities
Compare dynamic geometry
commands to sequences of
compass-and-straightedge
steps. Prove, using
congruence theorems, that
the constructions are
correct.
21
Vocabulary
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acute angle
adjacent angles
alternate exterior angles
alternate interior angles
angle
angle bisector
angle of rotation
axiom
between
center of dilation
center of rotation
center of symmetry
collinear points
complementary angles
component form
composition of transformations
congruence transformation
congruent angles
congruent figures
congruent segments
consecutive interior angles
construction
coordinate
coplanar points
corresponding angles
defined terms
dilation
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directed line segment
distance
distance from a point to a line
endpoints
Enlargement
exterior of an angle
glide reflection
horizontal component
image
initial point
interior of an angle
intersection
line
line of reflection
line of symmetry
line segment
line symmetry
linear pair
measure of an angle
midpoint
obtuse angle
opposite rays
parallel lines
parallel planes
perpendicular bisector
plane
point
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postulate
preimage
ray
reduction
reflection
right angle
rigid motion
rotation
rotational symmetry
scale factor
segment
similar figures
similarity transformation
skew lines
terminal point
transformation
translation
transversal
vector
vertical component
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References & Suggested Instructional Websites
http://www.achieve.org/ccss-cte-classroom-tasks
http://vimeo.com/44524812
http://www.insidemathematics.org/performance-assessment-tasks
http://cs.pcti.tec.nj.us/math/lessons/index.htm
http://map.mathshell.org/materials/lessons.php?gradeid=24
http://www.geometrycommoncore.com/content/unit2/gsrt1/teaching.html
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