Make Math Moments Academy › Forums › Full Workshop Reflections › Module 2: Engaging Students Using Problems That Spark Curiosity › Lesson 22: Consolidating The Sparking Curiosity Path › Lesson 22 Question › Reply To: Lesson 22 Question

We are learning about angles and particularly sum of interior angles of a polygon. To spark curiosity, I displayed a picture of The Pentagon in Washington DC and began the lesson with what do you notice and wonder? Students where in groups of 2 or 3 at the white boards. With lots of discussion around this, we finally bottomed out on what we think the total angle of The Pentagon add up to. I then asked the students to estimate what they thought it might be. We talked about what would be too low and what would be too high. They took the knowledge of obtuse angles and made educated guesses for one angle and then applied that to the 5 angles in the pentagon.
Once we got to that point we talk about shapes we already know the sum of the angles: triangles180 and quadrilaterals360. Students discussed the relationship between these two types of figures noticing that Quadrilaterals are double that of triangles. I then gave them some information about how many triangles can be drawn in a quadrilateral. I gave them time to ponder this and compare it to the pentagon to help them answer the question of the sum of the angles of a pentagon. We also discussed the size of an individual angle of this “regular shaped figure” which was a new vocabulary word for them.
From here I then gave groups a paper that had shapes from 3sided figures up to 14sided figures. On the white boards I had them use these pictures to make triangles within these figures to see if they could find a pattern and then a formula for any shaped polygon, which eventually they were able to discover. Many made tables on the whiteboards with the number of sides as one column, number of triangles in another, and sum of angles in another. They were able to see the pattern and create the formula (n2)180.
We extended this lesson on another day to find a formula of one angle of a regular shaped figure and then the sum of the exterior angles of any shaped polygon.
Students were engaged the entire time while at the white boards. Doing Notice & Wonder, withholding information, estimating, giving students the voice sparked the curiosity to persevere with the ultimate task of being able to find the sum of the angles of any shaped polygon.