Progressive Mathematics Initiative
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Mathematics Curriculum
Unit Plan # 10
Title: Quadrilaterals
Subject: Geometry
Length of Time: 2.5 weeks
Unit Summary: The unit explores the family tree of quadrilaterals. Sufficient conditions and properties of
the special triangles are explored and applied to problems. Proofs involving quadrilaterals are also created.
Learning Targets
PARCC
Major Clusters;
Supporting Clusters;
Additional Clusters
Conceptual Category: Geometry Domain: Circles
Cluster: Understand and apply theorems about circles
Standard#:
Standard:
Construct inscribed and circumscribed circles of a triangle, and prove properties of angles
G-C.3
for a quadrilateral inscribed in a circle.
Conceptual Category: Geometry Domain: Congruence
Cluster: Prove geometric theorems
Standard#:
Standard:
Prove theorems about parallelograms.
G-CO.11
Cluster: Make geometric constructions
Standard#:
Standard:
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
G-CO.13
Conceptual Category: Geometry Domain: Expressing Geometric Properties with Equations
Cluster: Use coordinates to prove simple geometric theorems algebraically
Standard#:
Standard:
Use coordinates to prove simple geometric theorems algebraically
G-GPE.4
Domain: Standards for Math Practice
Standard#:
Standard:
MP1
Making sense of problems and persevere in solving them.
MP2
Reason abstractly and quantitatively.
MP3
Construct viable arguments and critique the reasoning of others.
MP4
Model with mathematics.
MP5
Use appropriate tools strategically.
MP6
Attend to precision.
MP7
Look for and make use of structure.
MP8
Look for and express regularity in repeated reasoning.
Unit Essential Question:
Unit Enduring Understandings:
 What are the similarities and
 Interior and Exterior Angles of Polygons
differences between the different
 Properties of parallelograms, trapezoids, isosceles
quadrilaterals?
trapezoids, rectangles, kites, rhombi, and squares
 Applying quadrilateral properties to coordinate proofs
 Applying quadrilateral properties to constructions
Unit Objectives:
 Students will be able to find the measures of interior and exterior angles in polygons
 Students will be able to use the properties of quadrilaterals to find the measurements of angles and
the lengths of sides.
 Students will be able to use the properties of quadrilaterals to write and solve algebraic equations.
Geometry - Quadrilaterals
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


Students will be able to identify the members of the quadrilaterals family.
Students will be able to construct quadrilaterals by applying sufficient conditions.
Students will be able to construct arguments to write proofs involving quadrilaterals.
Evidence of Learning
Formative Assessments:
 SMART Response questions used throughout the unit.
 5 Quizzes
Summative Assessment:
 Unit Test
Lesson Plan
Topics
Topic #1: Polygons
1
Quiz 1 Angles of a Polygon
Topic #2: Properties of Parallelograms
2
Lab: Investigating Parallelograms
Lab: Quadrilaterals Party
Topic #3: Proving Quadrilaterals are Parallelograms
1
Quiz 2 Parallelograms
Topic #4: Rhombi, Rectangles, and Squares
1
Lab: Quadrilaterals in the Coordinate Plane
Topic #5: Trapezoids
1
Lab: Midsegments of a Trapezoid
Quiz 3 Rhombi, Rectangles, and Squares
Topic #6: Kites
1
Lab: Properties of Kites
Topic #7: Constructing Quadrilaterals
1
Quiz 4 Trapezoids and Kites
Topic #8: Families of Quadrilaterals
1
Lab: Inscribed Quadrilaterals
Topic#9: Proofs
1
Topic#10: Coordinate Proofs
1
Quiz 5 Proofs
Topic #11: Review and Unit Test
2
Curriculum Resources:
www.njctl.org/courses/math/geometry/
 Quadrilaterals Party WebQuest: Listed under the “Labs” section of the web page
 Video: Constructing a Parallelogram – compass & straightedge
 Video: Constructing a Parallelogram – menu options
 Video: Constructing a Rectangle – compass & straightedge
 Video: Constructing a Rectangle – menu options
 Video: Constructing a Rhombus – compass & straightedge
 Video: Constructing a Rhombus – menu options
 Video: Constructing a Square – compass & straightedge
 Video: Constructing a Square – menu options
 Video: Constructing an Isosceles Trapezoid – compass & straightedge
 Video: Constructing an Isosceles Trapezoid – menu options
 Video: Constructing a Kite – compass & straightedge
 Video: Constructing a Kite – menu options
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Lesson Components
21st Century Skills
 Financial, Economic, Business, and Entrepreneurial Literacy
21st Century Themes
 Critical Thinking and Problem Solving
 Communication and Collaboration
 Life and Career Skills
 Information Literacy
 ICT Literacy
Geometry - Quadrilaterals
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