# Day 48: Coffee Filter Radians

This activity has been done in so many ways that I’m not sure I can add anything to the body of knowledge.  Here is a fuller explanation from last year’s “What in the World is a Radian?” activity.

However, based on a workshop I attended at the Northwest Mathematics Conference in Whistler, BC. last month called  Folded Paper and String Graphs of Sinusoidal Functions given by Susan Robinson (Gulf Islands Secondary School, Salt Spring Island, BC), I did a little more with the activity.  Once we had located the whole number radians on the coffee filter and developed the idea of what a radian really was, students readily named the location of π and 2π on their Unit circle.  I used this to leverage the quadrantal angles via folding the filter into quarters.  We labeled the angles using a chosen color.

Then the thinking caps came on!!  They were familiar with the special angles in degree form, so I asked them how we would get 45º angles…and they played right into my hands, saying “fold the quarters in half.” So we did and then discussed what the radian equivalent would be, and they said π/4.  We then counted around the circle and name the other non-quadrantal angles.  They chose a different color and labeled all of these angles on their filter.  We looked at patterns in the values and they came up with “π/4 multiplied with odd numbers.”  We also talked about why we didn’t include the “π/4 multiplied with even numbers.”  You see where this is going, huh?  Sense-making is soooooo FUN!!  We continued for the π/3 and π/6 families of angles.  By the time we got to π/6 angles, they were answering the questions before I asked them.

In reflection, I will continue with this new addition to the activity because I think it was a missing link in year’s past.  I particularly like the idea of color-coding the angle names.

NOTE 11/18:

Today, we took out the coffee filter and then began to talk about the “family of angles” and related trig ratios.  The color-coded angles really brought home the relationship between the angles in the family, the related right triangle and the trig values.  Definitely I will continue to build the Unit circle in this way!!