High School SMILE Meeting
29 November 2005

Fred Schaal (Lane Tech)               Conserving the Heat of my toes
recently broke his leg and has had a cast. How should Fred keep his toes warm with just the little "boot" that is provided to put over his stockinged foot?. He put a stocking cap over his toes, with a plastic bag over the cap, the entire "apparatus" being held in place with a bungee cord. Very enterprising, Fred!

Nneka Anigbogu  (Jones College Prep)                  Random rectangles
handed out a sheet with 100 rectangles of various dimensions displayed.  Each rectangle was composed one or more identical squares.  Our activity was to obtain an estimate of the average number of squares.  This is an activity to illustrate use of statistics. Nneka asked us to briefly look at the 100 rectangles and to shout out estimates of the average area of all 100 in "standard units" (easy because each had an area that was an integral number of the standard squares mentioned above. Estimated averages were 8, 9, 11, 17, 50. Then Nneka had us choose any 5 rectangles in a "continuous run" (e.g., rectangles 5-9) and estimate the average of those 5. We got averages of 1-12.8, for 10 samples of 5 rectangles, with an overall average of 8.82. This completed the "subjective estimate" of the mean.

Nneke also handed out a table of 450 five digit random numbers. We used the table to pick 5 numbers and use any consecutive two digits from that five digit number, match these with the numbers of the corresponding rectangles, and get another group of 5-rectangle averages. Ten averages ranged from 4.0- 8.6, with an overall average of 5.81, the "random estimate" of the mean.

It turns out that the actual average of the 100 rectangles is 7.42. Surprisingly, the subjective estimate was a bit closer to the actual than the random estimate. Nneka noted that in her class the random method gave a number almost identical to the actual average. How come ours was so far off?  Great stuff! Thanks, Nneka.

Charlotte Wood-Harrington (Gwendolyn Brooks HS)                National Boards
recently became a certified as a physics teacher by the National Board of Professional Teaching Standardshttp://www.nbpts.org. It was a long, hard process, but she felt it was worthwhile. The current out-of-pocket cost of the program is $300. Charlotte gets a stipend from the State of Illinois for $2500-3000 per year for ten years.  Charlotte used the Chicago Teachers Union as a sponsor to the process. It has a very high rate of passing, but it requires a 25 page application (there is also an entrance through the PHD (Professional Honor of Distinction) program. Charlotte said that the writing requirement for the board exam involved a new skill that had to be learned. There are 6 subject matter tests (30 minutes each) as well as submission of videos made in the classroom. It took 2 years to complete, and seemed to Charlotte to be a little harder than getting a masters degree. Regarding the material level in the process, it is probably most likely that one would have to be a high school teacher to be successful in the process.  Thanks for the encouragement and the information, Charlotte!

Arlyn Van Ek (Illiana Christian HS)                 Odds and ends
Arlyn attended a recent meeting of  the National Science Teachers Association  [NSTA] in Chicago, which was great!  He brought back these neat odds and ends to share:

Great ideas! Thanks, Arlyn!

Bud Schultz (Aurora Middle School Academy)              Easy primitive toy
showed us a "bull roarer" which is an Australian aboriginal toy. It operates to produce a roaring sound when it rotates in two planes. The bull roarer is a piece of wood carved to be about the size and shape of a spear head and suspended from a string of about 2 meters in length. Different shapes can be made; Bud's were carved out of Padauk  -- a reddish wood from Africa: http://www.exotic-wood.com/african_padauk.htm.  First Bud spun the bull roarer, --- then he held the string at the other end, and twirled the bull roarer in a vertical circle.  The sound was not produced until the rotation became quite rapid -- it requires both rapid rotation and simultaneous spinning in a second plane.  For additional information see the Virginia Tech Multimedia Music Dictionaryhttp://www.music.vt.edu/musicdictionary/textb/Bull-roarer.html. Wow-wow-wow!  Thanks, Bud.

Larry Alofs showed us the inside of a combination lock apparatus, which might once have been a locking door for a post office box. There are three round tumbler plates inside the lock, each having a notch. Each number of the combination rotates one of the plates so that the notch is aligned in a certain direction. The right sequence of numbers serves to align the three notches on the three plates, which allows the lock to be opened. Neat!  Thanks, Larry.

Porter Johnson then told us the story of how Richard Feynman, who, during his time at Los Alamos working on development of the  atomic bomb during WWII, devised a way to open combination locks. He first made these observations:

For a standard 40 number combination lock with 3 tumblers, it would take 403 = 64,000 trials to determine the correct combination. Feynman cleverly reduced the number of trials to 82 = 64, making it fairly easy to open an ordinary lock.

The following people could not present lessons today, because we ran out of time. They will be scheduled for our last SMILE meeting of the semester, Tuesday December 13. See you there!

Notes prepared by Ben Stark and Porter Johnson.