180 degrees in a traingle

Subject: Geometry
Lesson: The three angles in a triangle add up to 180 degrees.

Five Ways to Present the Idea
1. Direct instruction: Using the whiteboard, discuss the proof suing different triangles to demonstrate. Use a large protractor and different triangle types.

2. Class activity: Cutting a triangle. Have each student cut a triangle out of a piece of paper. It should be larger that a 3x5 card. Students will then cut each vertex (corner) off of the triangle. When put together, the vertices will lien up to create a straight angle, or 180 degrees.

3. Group activity: Try to prove the theorem wrong. Is there any triangle that you can make so that the angles do not add up to 180 degrees, or do not create a straight angle when put together?

4. Youtube video: https://www.youtube.com/watch?v=umBdW7talCo

5. Group discussion/activity: If all the the angles in a triangle must add up to 180 degrees, what must the angles in a quadrilateral add up to? Angles in a pentagon? Hexagon? Is there a pattern relating the sides of a polygon to the sum of its angles?


The assessment for this lesson will include problems where student are given two angles in a triangle and must find the third. One problem will be for the student to CREATE a triable out of card stock paper, MEASURE the angles and VERIFY that they add up to 180 degrees. To challenge advanced students, they will be given a problem to try to create an equation that relates the number of sides of a polygon to the sum of its angles.

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The lesson and idea that the angles in a triangle add up to 180 degrees is fairly simple, but in math, we want the students to understand the WHY behind the theorems. The activities above will get them understand the WHY.

English Language learners will benefit from all the visual activities and the interaction with their peers. Special needs students will benefit from the grouping activities and form the tactile objects to demonstrate the theorem. Gifted and advanced students will be challenged by the final activity, generalizing the concept to a more broad category of Geometry.