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Useful Pi day activities neeed

In my STEM (Science, Technology, Engineering, Mathematics) work, we have a "Pi Day" coming up. We are working with kids aged 10-18 specifically on that day, but I will be working with my adult learners all that week as well. In looking through the Internet, I am finding all sorts of Pi day activities that center on the fact that Pi does not repeat and most resources simply concentrate on trying to memorize as many digits as possible. Meanwhile, I ask adult and students what Pi is and why should we care and I get these blank looks as if I had just asked them what the color green smells like. This is annoying and disappointing that the best we can get out of a "mathematical" day (3/14/16 will never ever happen again) is to have people memorize numbers instead of really learning how great this constant value is. 

I am looking for activities for all ages that help people discover and play with the power that the ratio between the distance around ANY circle to the distance across the middle of the circle is the same no matter what circle one picks. When I ask people in that common language what that ratio is, almost no one starts spouting out that 3.14 nonsense. Isn't that sad? Of course if we can find activities that extend beyond this discovery to explore how we might use that constant ratio in different ways, that would be a bonus. Let me share some ideas I have found or had so far:

  1. Cylinder comparisons. This could be just circles as well...Bring in a number of different sized cylinders an have a chart for people to record the distance around each cylinder and the maximum distance across each circular shape. If this is a digital table and the ratio of the two (Circumference / Diameter) is automatically generated, learners only do about 4 or 5 measurements before they see some patterns. Then I switch the measuring tools (inches, mm, cm, lengths of string, finger widths ...) and have them record data as well to see if the pattern remains consistent. Then I challenge them to find either a measurement tool or a type of circle in which this same constant does not show up. We talk about why our charts never really are exactly 3.1415 ... and how precision of measurement factors into everything. 
  2. Properties of Circles: In this activity learners are exploring all the relationships of circles at a beginning level. Given a collection of circle objects, learners again collect data on, perimeter, diameter, radius, area, volume (if it is a container), Learners compare measures of different sized circles to see what relationships might exist between any pieces of data. Is the area related to the perimeter at all? Is there a consistent ratio between the radius and areas? How about the radius and perimeters? Learners discover and discuss many circle properties in this manner and those facts stick much longer than simply sharing a circle formula sheet for memorization.

Although both of the above activities may be effective and useful to a point, they may not be appropriate for younger kids (think dexterity issues with measurement) and it would be questionable as to how much "fun" these activities would be for most of the younger learners. In fact, for anyone that does not like to use their hands to learn may hate the above activities. Neither of these activities use Pi constructively to do anything or to help highlight why this constant ratio is so important in any area of life. 

I appreciate any ideas or suggestions out there. It seems to me that a civilization that has developed so much from sticks and mud to get where we are now should have something better than Pi=3.14 memory games, but I am feeling very disheartened by what I have found in hours of searching so far. Any fun activities you can offer that help in the discovery of what Pi is or in the practical usage of Pi in real life would be very valued by the field as there is apparently very little out there that supports this kind of learning about a very important mathematical concept. 

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