So, I've finally rearranged curriculum in a way I've always wanted to try. As a curriculum writer, I was atempted to change things in a big way...but that is tough to do when working for a mainstream publisher. The wonderful thing about being back in the classroom is that I get to respond to my students' learning rather than teach in a prescribed order.
My HS Geometry students had just finished learning trig and were getting quite good at finding missing angles and side measures of right triangles. Most did amazingly well on the test and it was time to start the next chapter. Predictably, the chapter started with area of a rectangle, triangle, trapezoid, then area of a polygon with the apothem given. Finally, students would use trig to calculate area of a regular polygon using only the side measure.
It struck me that here they are at the height of their learning and I was going to start easy with the next chapter and build up to trig again. Instead, I started with the hardest section first.
I distributed a large regular polygon (with side length given) to each person in a group (different polygon for each group), then told them they have all the knowledge in their head to find the area. I gave them a ruler but told them they couldn't use the measures. They immediately started drawing lines on the figures.
Check out their work below.
It struck me that here they are at the height of their learning and I was going to start easy with the next chapter and build up to trig again. Instead, I started with the hardest section first.
I distributed a large regular polygon (with side length given) to each person in a group (different polygon for each group), then told them they have all the knowledge in their head to find the area. I gave them a ruler but told them they couldn't use the measures. They immediately started drawing lines on the figures.
Check out their work below.
They got stuck when trying to find area of each shape...but some were making progress. I'll be honest, I need to get more comfortable with my teaching because I should have let them continue to explore in the direction they were going. But there were too many possibilities and I just didn't think I could manage them. So...I gave them all a hint. I said "Find the center."
They immediately drew diagonals and saw the triangles. We reviewed area of a triangle and someone drew an altitude. But they got stuck because they didn't know the angle measures. One student numbered the angles in the center. I showed that under the document camera and it was a quick jump for them to realize the total number of degrees is 360.
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