Understanding By Design Unit/Lesson Template
Title of Unit Congruent Triangles Grade Level High School
Curriculum Area Mathematics – Geometry Time Frame 2 days
Developed By Isaac Pischke
Rationale for retooling current lesson
Last year, this lesson seemed very abstract – students had a hard time comprehending when triangles are
congruent and what that means
21st Century Skills or Classroom Instruction That Works strategies
In this lesson, students will learn and apply critical thinking and problem solving skills as well as linguistic
communication skills.
Identify Desired Results (Stage 1)
Established Goals (Standards)
State Standard(C.12.3) Demonstrate an understanding of congruence and the SSS, SAS, ASA and AAS shortcuts of
showing congruence
Understandings Essential Questions
-What does it mean for polygons, including triangles to be
-Students will know that there are shortcuts to identify congruent
congruent?
triangles
-How can we use shortcuts to determine if triangles are
-Students will know that the positions of the sides or angles matter
congruent?
in determining if triangles are congruent
-Why does the order of the congruent parts matter?
-Where in life do we see congruent triangles?
Knowledge Skills
Students will know… Students will be able to…
-The Students will know that congruent triangles are triangles in -The students will be able to identify congruent polygons.
which all corresponding sides and angles are congruent -The students will be able to identify congruent triangles using
-Students will know that not all triangles are congruent the triangle congruence SSS, SAS, ASA and AAS shortcuts.
-Students will know that for triangles to be congruent there must be -The students will be able to identify corresponding parts of
at least three corresponding parts congruent congruent triangles.
Assessment Evidence (Stage 2)
Performance Tasks: Other Evidence: Examples of homework problems.
QUIZ
1. What are examples of sets of corresponding
congruent parts of triangles that do not guarantee
congruent triangles? Why?
2. What common misconceptions arise when two
triangles have three corresponding congruent angles?
How do we correctly describe these triangles?
3. Two triangles have a corresponding angle congruent
and two corresponding sides congruent. Are these
triangles necessarily congruent? Why or why not?
PROJECT: Finding buried treasures. A hands on project using
triangle shortcuts to locate hidden treasures!!
Learning Plan (Stage 3)
Where are your students headed? Where have Students will next be using triangle congruence shortcuts to find more similarities in isosceles
they been? How will you make sure the triangles and then use their triangle shortcuts to prove parts of triangles congruent. Prior to
students know where they are going? this lesson, students were working with triangles to find angle measure in triangles
How will you hook students at the beginning of In life, “heated discussions” will arise and one must use logic and critical thought to convey and
the unit? prove your points. In this lesson we’ll use triangles to practice logical thought.
What events will help students experience and Students will have already used geometry sketch pad and construction tools. To explore if
explore the big idea and questions in the unit? triangle shortcuts work, students will be given set lengths and angles and share the other
How will you equip them with needed skills and angles and side lengths once their triangle is created. If a shortcut works, students will find
knowledge? their other sides and angles are the same as all their classmates.
How will you cause students to reflect and After students have gained some experience using the shortcuts to determine congruent
rethink? How will you guide them in rehearsing, triangles, students have to explain their steps and justification for their conclusion. Students
revising, and refining their work? will have opportunities to do peer reviews to fine tune their skills.
How will you help students to exhibit and self- Students will be able to show their growing skills with a quiz and reflect upon what they have
evaluate their growing skills, knowledge, and learned with a journal entry following the quiz.
understanding throughout the unit?
How will you tailor and otherwise personalize Students will all start with the same basic problems. We will do several together as practice.
the learning plan to optimize the engagement Over the next couple of days, students will always have some of the same basic problems so
and effectiveness of ALL students, without students having a tough time comprehending will build confidence. High performance learners
compromising the goals of the unit? will be given optional high level problems in place of parts of the traditional assignment. As a
final project for the lesson, students will complete a project using their triangle congruence
shortcuts. This will appeal to those students who like hands on activities.
How will you organize and sequence the To start the lesson, students will investigate possible shortcuts and build connections and
learning activities to optimize the engagement understandings from the experience. Once finding the shortcuts, I will start with more basic
and achievement of ALL students? examples and exercises on the homework applying the shortcuts. Problems will become
progressively harder.
Please include a narrative of your lesson if it
warrants further explanation as well as all
handouts, assessments, and activities you have
prepared thus far.
From: Wiggins, Grant and J. Mc Tighe. (1998). Understanding by Design, Association for Supervision and Curriculum Development
ISBN # 0-87120-313-8 (ppk)