Interior angle sum for a triangle:

In any triangle, the sum of the interior angles of a triangle is 180°. Here are two Elementary-appropriate ways to see that this is so:

1. Cut-and-paste

· Cut out a medium sized triangle on paper or cardstock (be careful to keep all of the lines straight!)

· Tear off (don’t cut) all 3 corners.

· Put all of the corners together. What angle do they make altogether?

2. Slide through the corners:

· Draw a large triangle on paper

· Cut out a paper arrow or bumper car (make sure your bumper car has a distinct back and front)

· Start your car on the middle of one side of the triangle, and make a note of what direction it is headed in

· Drive your car along the edge of the triangle. When it gets to a corner, turn the car by keeping whatever edge is touching the corner of the triangle still, and turning the other end of the car.

· Drive (back up) to the next corner and repeat.

· Keep going until you get back to where you started.

· What direction is your car headed now? How far around did it turn?

Note: when doing this in a classroom with manipulatives, the cars should be constructed to stand upright on the paper, not to lie flat on the paper, which is why the car is shown in two possible positions in step 3

The idea for this second exploration is taken from the article:  Experimenting with Crazy Cars by Nancy C. Whitman which was published in the Journal: Teaching Children Mathematics:

October 2000, Volume 7, Issue 2, Page 70