Lesson Title: __Triangle Sum___________________________ Course: _________Geometry_______________
Date: _____________ Teacher(s): ____________________ Start/end times:
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
G.CO.C.10
MP5: Use appropriate tools strategically.
MP7: Look for and make use of structure.
MP8: Look for and express regularity in repeated reasoning.
Lesson Launch Notes: Exactly how will you use the first five minutes of the lesson?
Have each student draw a triangle with a ruler. Have the students measure the three angles of the triangle.
(Look for evidence of MP5.)
Lesson Closure Notes: Exactly what summary activity, questions, and discussion will close the lesson and connect big ideas? List the questions. Provide a foreshadowing of tomorrow.
Ask students questions to review the learning from the lesson such as:
What is the sum of the angles of a triangle in degrees?
How do you think we can use the sum of the angles of a triangle to solve other problems?
What are parallel lines? A transversal?
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations, problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic connections to appropriate mathematical practices.
1.
Have the class discuss the findings from the Lesson Launch. What were their sums? What can we conclude about the sum of a triangle?
2.
Have students again draw a triangle or give each student a triangle. Have them tear off the three angles. Use the three angles and line them up on a line back to back. (Angle to angle) Have the students discuss what happens.
They should discover that the three angles line up to form a straight line. Therefore you can conclude that the angles of a triangle add up to 180 degrees since a line is 180 degrees. (Look for evidence of MP7 and MP8.)
3.
Assign students to small groups. Have groups work through a more formalized activity for proof using dynamic geometry software such as Geometer’s Sketchpad or GeoGebra. Have them begin with a triangle and parallel lines. Students can manipulate the vertices of the triangles and the parallel line to explore all possibilities. See example.G.CO.C12 Triangle Sum.gsp. Sketchpad document. A tutorial on how to show the triangle sum of 180 degrees on sketchpad is located at https://docs.google.com/file/d/0B_2_-NMZ5KYqRzV4MHhOOUdYeHM/edit (Look for evidence of MP7 and MP8.)
4.
Have students use the proof blocks to prove the angles of a triangle sum to 180 degrees. A sample solution using proof blocks is pictured with the proof blocks for triangle sum document. (Look for evidence of MP7 and MP8.)
5.
Listed here is an additional example for students to view of how the angles of a triangle equal 180 degrees. Have students visit or watch the video proving that a triangle’s sum is 180 degrees, available at https://www.khanacademy.org/math/geometry/angles/v/proof---sum-of-measures-of-angles-in-a-triangle-are-180
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand , S. (2009).
Accessible mathematics : 10 instructional shifts that raise student achievement. Portsmouth , NH : Heinemann .

Lesson Title: __Triangle Sum___________________________ Course: _________Geometry_______________
Date: _____________ Teacher(s): ____________________ Start/end times:
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I measure student success? That is, deliberate consideration of what performances will convince you (and any outside observer) that your students have developed a deepened and conceptual understanding.
Students will to be able to explain/ prove with words, pictures or numbers why a triangle has a sum of 180 degrees.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Reflexive congruence
Transversal
Parallel
Sum
Remember to make connections between the conceptual and formal proofs. Ask students to formulate an understanding for 180degree sum of a triangle.
Resources: for students to successfully complete the lesson tasks or activities?
Rulers
Protractors
Paper
Scissors
What materials or resources are essential
Patty paper
Geometry software
Proof Blocks
Homework: Exactly what follow-up homework tasks, problems, and/or exercises will be assigned upon the completion of the lesson?
To be determined by teacher.
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Do students have a conceptual understanding of the sum of the measures of a triangle are 180 degrees? Can they explain to you why there is 180 degrees a triangle?
Can students formally prove that the angles in a triangle sum to 180 degrees?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License .
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand , S. (2009).
Accessible mathematics : 10 instructional shifts that raise student achievement. Portsmouth , NH : Heinemann .