Download Digital Unit Plan Template Unit Title: Geometric Proofs Name

Digital Unit Plan Template
Unit Title: Geometric Proofs
Name: Elizabeth George
Content Area: Mathematics/Geometry
Grade Level: 9th-10th
CA Content Standard(s)/Common Core Standard(s):
Prove geometric theorems. [Focus on validity of underlying reasoning while using variety of ways of writing proofs.
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.
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.
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
Big Ideas:
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Visually understand Geometric Theorems of triangles, lines and angles.
Learn the framework to formalize information and reasons to produce logical conclusions.
Learn how to write a two column proof and understand how they will aide us in the display of a geometric argument.
Unit Goals and Objectives:
1.) We will learn about the most important use and study of valid reasoning, logic!
-Inductive reasoning
-Deductive reasoning
-How it is used in Geometric proof writing
2.) Explore theorems, definitions, and postulates pertaining to lines, angles, and triangles.
-congruent angles
-triangle congruence (SAS, SSS, ASA, AAS)
-median and midpoints of a triangle
3.) Finally, we will learn the appropriate steps and methods for writing a formal geometric proof.
-two column proofs
Unit Summary:
In this unit, we will be exploring many geometric theorems and postulates by engaging in many technology rich class activities, lectures, and projects. Our focus for this
section will be proving theorems about lines, angles, and triangles. We will get to investigate these theorems using Geogebra, and we will have an opportunity to create the
theorems visually through this digital software. We will also journey down...down...down..the rabbit hole where we will explore logic and understand how and why it is used
both in geometry and in the world around us. This will lead us to a fun class project where we will get to pick sides of a statement and argue its validity in a classroom
debate. Then, using the knowledge we learn about logic and the understanding we acquire from our theorems and definitions we will finally be able to write a geometric
proof.
Assessment Plan:
Entry-Level:
-Review quiz: Algebra Entry Assessment
Formative:
-Quick write: How logic is used with Proofs
-Concept Map: The order of a Proof
-Webercise: Triangle Congruency
-Mid Lesson quiz: Logic and two-column Algebraic
Proofs
Summative:
-Unit Exam: Logic, Understanding Angles and Triangles,
Geometric Proofs
-Presentation: Geometric Debate
Lesson 1
Student Learning Objective:
Acceptable Evidence:
Learn and understand logic
with proofs. Understand
Algebraic proofs relating to
logic.
Each student will be able to
use logic and understand the
process and rules for an
Algebraic Proof.
Instructional Strategies:
☒ Communication
☐ Collection
☐ Collaboration
☒ Presentation
☐ Organization
☐ Interaction
Lesson Activities:
Instructional Strategies:
☐ Communication
☒ Collection
☐ Collaboration
☐ Presentation
☐ Organization
☒ Interaction
Lesson Activities:
Instructional Strategies:
☐ Communication
☐ Collection
☒ Collaboration
☒ Presentation
☒ Organization
☐ Interaction
Lesson Activities:
-Review Quiz: Test prior knowledge
-Prezi video lesson about logic and proof writing.
-Quick write: How logic is used with proof writing
Lesson 2
Student Learning Objective:
Acceptable Evidence:
Learn and understand
theorems and postulates
pertaining to lines, angles,
and triangles.
Each student will be able to
state different axioms and
postulates relating to triangle,
lines and angles and
understand how they are
used with one another
-Webercise: Proving two triangles are congruent.
-Mid Lesson Quiz
-Concept map: The order of a Proof
Lesson 3
Student Learning Objective:
Acceptable Evidence:
Learn steps and methods for
writing a geometric proof.
Each student will be able to
write a formal two column
proof and be able to visually
understand each postulate
through the use of GeoGebra.
Unit Resources:
Class Math Book: Mc Dougal Littel Geometry Book
GeoGebra
-Graphic Organizer: Creating a triangle congruency postulate through Geogebra.
-Class Presentation: Geometric Debate. Argue Pros and Cons of a Theorem.
-Unit Exam: Logic, Understanding Angles and Triangles, proofs
Word Docs
Use of Internet
Useful Websites:
Math Goodies- Presents important vocabulary terms and lessons about logic.
Math Playground- Logic games to help better understand the terms and definitions.
3E Lewis Carroll Puzzles- A fun site explaining Lewis Carroll and his role in logic. Presents 3 puzzles that Lewis Carroll has created using logic. Can you figure them out??
Definition and Theorem Review- Link to a page listing definitions, theorems and postulates in Geometry.
Education.com- Fun activities relating to many Geometric theorems addressed throughout the lesson.
Regents Prep Center- Lessons and practice tests on Geometry concepts from definitions and theorems to proof writing.
Math Warehouse- Detailed lessons about Geometric Theorems and practice quiz's to go along with the lessons.
Spark Notes: Geometry- General information on geometric proofs, terms, structure of a proof and types of proofs.
Sophia Proof Tutorials- Tutorial videos about writing two column proofs and formal proofs.
Wiki How- Presents an 11 step method for writing a geometric proof