Discovery Learning: Sum of Angles

Rather than just tell students how to do something, I like them to discover it on their own.  It gives me an opportunity to later point out "Hey, remember that day we figured this out?"  On this particular day, we had been talking about angle measures and were going to be moving on to angle measures in triangles and quadrilaterals.  I decided that our Interactive Notebooks would be perfect for discovering the sums of the angles in these polygons.  Students first received two congruent triangles to cut out.  One was glued into their notebooks and the angles measured.  I casually asked the students what the sum of those angles were: 180 degrees.  "Hey!  That's the same number as the measure of a straight line!" piped up Calli.  So, I told them to go ahead and draw a straight line in their notebooks.  Then, we glued the corners of the triangle together to prove that the angles together form a straight line. 

Here is our finished product.  We tested our theory that the sum of a triangle's angles is always 180 degrees.  I found a fantastic interactive website that allows you to adjust the angles in a triangle to show they always add up to 180 degrees, no matter how you do it.  

We then followed the same process for a quadrilateral.  

The kids loved it!  The information stuck with them and they know that a triangle's angles add up to 180 degrees, while a quadrilateral adds up to 360.  One inquisitive student asked if this works for all polygons.  I challenged him to test a pentagon, hexagon, and so on to see if there is any sort of pattern relating to the number of sides in a polygon.  Of course, many students took on this challenge with protractors out and pencils writing.  It was only a matter of time when they excitedly yelled, "There IS a pattern!  You add 180 degrees every time you add a side!"  And my work here is done :)

CCSS Mathematical Practice Standards applied:

2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning