As we dive into the unit on Circles – a long and difficult unit for the students – I wanted to create an intuitive idea of how arcs, chords, and central angles are related. We have used patty paper only once before this term, and the students seemed nervous – what did this crazy Geometry teacher want them to do NOW?
But as I posed questions – how do you prove congruence with patty paper? Or confirm parallel lines with corresponding angles? How can you find a perpendicular bisector? How can you bisect an angle? – the room grew quiet, except for the sound of rustling. Patty paper being traced upon, folded, played with. And private smiles and light bulbs going off as they figured out how to manipulate the paper to prove – everything. When I asked them to make a conjecture regarding congruent arcs and their chords, and then try to prove it, they began to get creative. One student said “I don’t really need an entire circle, do I?” and just drew a segment of a circle to work his proof. Some students played with 2 arcs in one circle, while others drew 2 circles to create their congruent arcs.
That was all we had time for today; I can’t wait to watch them discover some of the other chord theorems with them tomorrow.