My geometry students work cooperatively to discover the formula for the total interior angles of any (convex) polygon. This activity sets it up so they can be successful: the students start with a quadrilateral, and break it down into two triangles, recording such information as the number of diagonals, the number of triangles, and the total of the interior degrees.
They continue to build until they notice patterns. Students will struggle with articulating the patterns they readily see, but most, with a little guidance, will correctly generate the formula 180(n - 2) after about 30 minutes.
Immediately before this worksheet, I use the resource named 'Final Exam Study Guide Geometry Fall 2013' (http://www.teacherspayteachers.com/Product/Final-Exam-Study-Guide-Geometry-Fall-2013-1082707
), and immediately after this worksheet, I use the assessment named 'Geometry Group Practice Test Proofs and Concurrency Fall 2013' (http://www.teacherspayteachers.com/Product/Geometry-Group-Practice-Test-Proofs-and-Concurrency-Fall-2013-1269995
Keywords: geometry, interior angles, interior angle formula, discovery, Jonnard