SMILE Mathematics-Physics High School Meeting
November 09, 1999
Notes prepared by Earl Zwicker

Bill Colson (Morgan Park HS - Math)

drew 2 lines that intersect to form an angle. In his geometry class Bill uses a book titled Line Design. Some students have difficulty understanding what an angle is, and by getting them involved in such constructions using straight lines, they develop a feeling for the idea of angle. Example: start with two straight lines intersecting at 90o, and mark off equal divisions beginning at the intersection. Draw two additional lines connecting the divisions (1 & 2) and (2 & 1). The two lines intersect at one point. Now repeat this on a new drawing, making 4 lines connecting (4&1), (3&2), (2&3) and (1&4). These 4 lines intersect at 3 points. By repeating this process next for divisions 6,5,4,3,2,1 - it becomes quite clear that the intersecting straight lines come to more and more closely define a curved line. And the idea of approaching something as the limit of a process repeated an "infinite" number of times becomes an experience that is useful in more advanced math. Bill passed around examples of beautiful art work his students made using these ideas. Very nice!

Ann Brandon (Joliet West HS)

held up a liquid crystal thermometer in the form of a thin aluminum plate shaped like a very broad, inverted U, (about 12 cm long x 8 cm wide, with 2 cm "legs") with strips of liquid crystal film mounted on its top surface. Ann pointed out the patch of color on the strips of film, indicating room temperature. Two shallow dishes were placed on the table, and cold water was placed in one, hot water in the other. Ann put the thermometer down so that one aluminum "leg" rested in the hot water and the other in cold water. As we gathered around, we could see the temperature-indicating color patches on the strips moving until they formed a straight, diagonal line connecting the hot end to the cold end. What a beautiful, graphic, convincing way to show linear temperature drop from heat source to heat sink for uniform thermal conductivity through the aluminum! (A Giveaway from an ISPP meeting at DePaul!) Thanks, Ann!

Carol Zimmerman (Lane Tech HS)

showed us several experiments - which she gets her students involved with before studying Newton's laws. The table cloth yank (slippery table cloth, glasses or other objects on top, yank the table cloth out from under, leaving the objects at rest on the table!). Next - bottle on table, balance circular flexible hoop on top at bottle's opening, place chalk vertically on top of hoop, lined up with opening of bottle below - then sweep your hand horizontally, grabbing the hoop away, so the chalk falls down into the bottle! Then Carol placed a stack of wooden blocks on the table, and swept a meter stick horizontally over the table top, knocking the bottom block out from under those above, leaving them still stacked! This was repeated, depleting entire stack. (We call these Betty's blocks, after Betty Roombos who first showed us this at a 1970s meeting. Good ideas don't die!) Carol then held up a spring scales, attached a weight to its end, and we could see what the scales read. But then she accelerated the scales upward - and we saw the pointer indicate greater weight! Finally, Carol covered the table with a pretty green felt cloth, improvising a pool table. Using chalk, she drew a circle on the cloth (about 37 cm diameter), placed a pool ball at the center of the circle and put a penney on top of the ball. Offering a cue stick, she challenged us to strike the ball with the cue (held parallel to the table) so that the penney would land outside the circle. Several of us tried, one after the other, without success. Carol finally told us that under Newton's laws, it was not possible for anyone to do this! These demonstrations of inertia prompted others of us to do the "grab the coin" from a person's hand (Betty R); "Where will the string break?" (Arlyn Van Ek - who may do this for us next meeting.)

Bill Blunk (Joliet Central HS)

showed us how he involved his students in projectile motion using an air-powered rocket (Arbor Scientific, 2000 Catalog). He uses two boards, hinged at one end, with the launcher mounted on the top board. The top board can then be tilted to a desired angle by turning a screw down against the bottom board, thus controlling the angle of projection for the rocket (handout). To get rocket altitude, Bill lays out a 50 m base line (using trundle wheel), and then they sight on the rocket at its peak altitude using a height finder (Estes or Flynn catalog), which easily captures the angle. Bill "fired" the rocket using a bicycle pump to pressurize the launcher, but we couldn't do it outdoors because of wind and darkness, so he covered it with a box (to prevent impact with the room ceiling). Pow! It worked!

Fred Farnell (Lane Tech HS)

showed us a new twist on inertia. He placed an inverted glass on the table, then a flat card on top the glass, and then a circular roll of tape on top the card. When he snapped the card horizontally, the card flew out from under the roll, which then dropped down around the glass to rest on the table. Nice! Then he tried it with the glass placed open end up. Harder to do, because of the now greater diameter which the tape roll had to clear. But it finally worked!

Great ideas! Don't miss the next meeting!