Today Geometry started with a question:
I was purposely vague, and no student went so far as to talk arc length (as opposed to arc measure in degrees). I told them to give their best guess but back it up with process and reasoning. This is what they came up with:
Students we able to trace the process of splitting into portions or multiplying into larger parts. They also tried using the context of percents without being prompted to do so. The first class didn’t automatically use units in degrees so I prompted, “If I told you the measure of this arc was 22.5 degrees, how do you think I came to that.” Students were able to articulate my process by relating it to their own. The second class had a few students actually use the process of putting the measures into degrees of a circle. Thanks to a recent tweet by NCTM illuminations:
Attn all teachers! Thx for all the hard work you do day in & day out! Let Dynamic Paper make ur life a little easier! http://t.co/Q5OlDu8hgp
— NCTM Illuminations (@NCTMIllum) May 5, 2014
I was able to quickly put together a worksheet of “spinners” as a follow up the this discussion.We practiced these in the same fashion. I made sure the students included the calculation of the arc in degrees.
I could have made this worksheet much longer, including measures in terms of percent, number, or even with angles. I wanted to keep it simple for now. Tomorrow we go further with Algebraic expressions, and start the discussion chords, area of slice of pizza and the length of string cheese. Now I want some pizza.