MATHEMATICS
Concept Name
Concept Description
4TH SIX WEEKS
GEOMETRY
Attributes of Polygons
The attributes of polygons relate to the concept of geometric figures and their properties. Geometry consists of
the study of geometric figures of zero, one, two, and three dimensions and the relationships among them.
Students study properties and relationships having to do with size, shape, location, direction, and orientation
of these figures. There are critical attributes that are used to classify polygons.
Pacing (optional)
Sequence
Unit Name
Pacing*
Overarching Idea
Polygon Properties
Sequence
Relationships between the critical attributes of polygons determine classification and connect to algebraic
generalizations of patterns in geometric figures.


Guiding Questions
What role do triangles play in determining properties of regular and irregular polygons?
What is a real-life application that uses polygon angle measurement to solve problems?
Culminating
Activity for Unit
Unit Notes
Vocabulary
Type
Resources
Title
Assessments
Type
Description
Type
Description
Author
Description
Pub Date
URL
ISBN
Actions
Actions
*Pacing (45-50, 90, 135, 180, multi-lesson, short-term, long-term, N/A)
Arc Title
Habits of
Thinking
Quadrilaterals
Guiding
Questions
 What is the relationship between the sides and the angles of different quadrilaterals?
 How can models and constructions be used by students to formulate and test conjectures about the properties
of quadrilaterals?
 How do the concepts of the slope of parallel and perpendicular lines relate to the properties of quadrilaterals?
 How can students prove that a given quadrilateral is a parallelogram?
 How can properties of quadrilaterals be used to solve problems?
Title
Type
Description Author
Pub Date
URL
ISBN
Actions
Resources
Curriculum Specialist
AISD Secondary Mathematics Dept.
Today’s date: 3/9/16
1/5
last updated: 6/1/09
MATHEMATICS
4TH SIX WEEKS
GEOMETRY
Lesson Overview Lesson Summary
Lesson Name – Discovering Properties of Various Quadrilaterals
Pacing – 3-4 45 minute class periods
Level – Geometry
Sequence
Submission Date – November 30, 2009
Authors – Geometry Curriculum Writing Team
Language
Homework
Lesson Objective (Intended Learnings)
Students, after having already defined various types of quadrilaterals, will now work to discover properties of these same
quadrilaterals (parallelogram, rectangle, rhombus, square, trapezoid, isosceles trapezoid, and kite).
Students will then accurately apply the properties when solving problems.
Universal Themes: Change, Patterns, Structure, Systems, Orders vs. Chaos, Conflict, Relationships
Lesson Objective (TEKS)
TEKS #
Knowledge Skills:
Assessments
Actions
G.3.B
G.2.A
G.2.B
G.3.E
G.7.A
G.7.B
G.7.C
G.10.B
SE:
SE:
Related TEKS
TEKS #
Content Area
Knowledge Skills:
SE:
Actions
Lesson Assessments
Type
Further Information
Essential Questions
Description
Technology Integration
Health Integration
Special Education
Health Connections
English Language Learners
Gifted & Talented
General Notes
Vocabulary: Type
Consecutive, congruent, base angles, legs, bisect, equiangular,
equilateral, quadrilateral, parallelogram, rectangle, rhombus,
square, trapezoid, isosceles trapezoid, kite
ELPS #
Knowledge Skills:
Description
SE:
Actions
Curriculum Writer
AISD Secondary Mathematics Dept.
Today’s date: 3/9/16
2/5
last updated: 6/1/09
MATHEMATICS
Lesson Stages/ Current Stages
Name
Materials/Supplies, Suggested Pacing
Warmup/Numerical Fluency/Foundation
Engage/Set-up/Launch
Explore
Explain/ Share, Discuss and Analyze
Summary
AISD Secondary Mathematics Dept.
Today’s date: 3/9/16
GEOMETRY
4TH SIX WEEKS
Description
4- 45minute class periods
Computer access and Geometer’s Sketchpad software
Inspiration software
Activity worksheet
Review with students the definitions of the various types of
quadrilaterals. It would be good, too, to revisit the graphic
organizer from the prior lesson.
Begin as a class with the teacher using the already started
Inspiration file titled “Quadrilaterals FILL IN” to type in
the definitions of the various types of quadrilaterals along
with the basic properties discovered in the prior lesson AS
THE STUDENTS recall them. If computer technology or
software is an issue, the teacher could record the class
contributions on the board. (Quadrilateral FILL IN
example also provided)
Students, in groups of 3 or 4, will use Geometer’s Sketchpad
sketches with the word “properties” in their titles. A
worksheet titled “DISCOVERY properties” has been
included for students to record their findings and fill-in-theblanks as they work on the computer with the various
Geometer’s Sketchpad sketches.

Properties of Quadrilaterals

Properties of Parallelograms

Properties of Rectangles

Properties of Rhombus

Properties of Square

Properties of Trapezoid

Properties of Isosceles Trapezoid

Properties of Kite
The teacher could also choose to modify the sketches using
Geometer’s Sketchpad 4.07 to save the sketches as html files
using Java, and then students could access through the
internet. This has been left for the individual teacher to do if
desired. If time is a concern, it could even be possible to
assign groups only a few of the quadrilaterals to discover
properties for instead of the entire set.
Actions
The use of technology will make the discovery of the
properties happen more efficiently and faster, but the teacher
could certainly use patty paper or constructions to accomplish
the same end results. The students could record their findings
in the provided worksheet titled “Properties Study Sheet”.
It would, however, likely take longer to complete the activity.
Once all groups are done, the teacher could pair up groups to
form larger groups of 6-8 where students compare and
contrast their results, revisiting the sketches as needed to see
if additional properties are true.
Once every group has had the opportunity to share with
another group and revise their findings if needed, the teacher
could go back to the Inspiration file and begin to list the
additional properties of each quadrilateral as the students
share what they found. The teacher would serve as the
recorder, and can ask guiding questions as students leave out
key properties. The teacher can then print off the graphic
organizer and corresponding note outline to run off copies for
students to put in their notes.
3/5
last updated: 6/1/09
4TH SIX WEEKS
MATHEMATICS
GEOMETRY
Elaborate
The teacher could again lead students through making
connections between types of quadrilaterals using “always.
sometimes, never” statements. For example, the teacher
could state “the diagonals of a rectangle are ______(always,
sometimes, or never) congruent.”
Students could complete the worksheet “Organizing
Properties” to see if they have mastered the properties of the
various types of quadrilaterals.
Evaluate/Assessment
Quizzes have also been included for the teacher to
incorporate if so desired.

Quiz Special Parallelograms

Quiz Kites and Trapezoids

Quiz Trapezoids and parallelograms

Quiz Mixed Quadrilaterals
Student Work Products
Extended Learning (Homework)
There are three worksheets to practice applying the
discovered properties:

Parallelograms Hodge-Podge worksheet,

Kites and Trapezoids worksheet,

Quadrilateral Hodge-Podge worksheet
This lesson is designed to follow the lesson where students
have defined the types of quadrilaterals, which would
hopefully take 2 days, but 3 at the most. With this lesson, the
discovery of the additional properties would hopefully take 2
days, leaving 2 days for practice if the previous definition
lesson took 3 days, and leaving 3 days for practice if the
previous definition lesson took only 2 days. This lesson
could also be designed for students to discover properties of a
couple of quadrilaterals each day, completing the worksheet
practice each evening before starting the new discovery the
next day. Overall, the teacher has flexibility in the structure
of the lesson.
Principles of Learning
Resources
Worksheet
Activity
Geometer’s
Sketchpad
Sketch
Geometer’s
Sketchpad
Sketch
Geometer’s
Sketchpad
Sketch
Geometer’s
Sketchpad
Sketch
Geometer’s
Sketchpad
Sketch
Geometer’s
Sketchpad
Sketch
Geometer’s
Sketchpad
Sketch
Title
DISCOVERY
Properties
Properties of
Quadrilateral
Type
Description
AISD generated
Pub Date
URL
ISBN
AISD generated
Properties of
Parallelogram
AISD generated
Properties of
Rectangle
AISD generated
Properties of
Rhombus
AISD generated
Properties of
Square
AISD generated
Properties of
Trapezoid
AISD generated
Properties of
Isosceles
Trapezoid
AISD generated
AISD Secondary Mathematics Dept.
Today’s date: 3/9/16
Author
4/5
last updated: 6/1/09
Actions
MATHEMATICS
Geometer’s
Sketchpad
Sketch
Inspiration
File
Inspiration
File
Properties of
Kite
GEOMETRY
4TH SIX WEEKS
AISD generated
Quadrilaterals
AISD generated
FILL IN
Quadrilaterals
AISD generated
FILL IN –
example from
8th Period
Worksheet
Properties Study
AISD generated
Sheet
Worksheet
Parallelograms
AISD generated
Worksheet
Kites and
AISD generated
Trapezoids
Worksheet
Quadrilateral
AISD generated
Hodge-Podge
Worksheet
Organizing
AISD generated
Properties
Quiz
Special
AISD generated
Parallelograms
Quiz
Kites and
AISD generated
Trapezoids
Quiz
Trapezoids and
AISD generated
Parallelograms
Quiz
Mixed
AISD generated
Quadrilaterals
*Pacing (45-50, 90, 135, 180, multi-lesson, short-term, long-term, N/A)
AISD Secondary Mathematics Dept.
Today’s date: 3/9/16
5/5
last updated: 6/1/09