High School Mathematics-Physics SMILE Meeting
1997-2006 Academic Years
Teaching Pedagogy

27 October 1998: Ann Brandon [Joliet West HS]
She reviewed the difference between Scalars and Vectors.
She asked which of the following are vectors (V) or scalars (S):
Distance: (S)
Displacement:(V)
Speed:(S)
Velocity:(V)
Acceleration:(V)

She also showed a game in which velocity vectors are illustrated. There was a sort of maze through which two players should travel in a race without hitting the walls. They could change the x- and y-components of velocity by only one unit from the previous move. The winner goes through in the least number of moves without hitting the wall.

10 November 1998: Alex Junievicz [CPS Substitute]
He made 2 comments, First he brought a maze that helps get the difference between Distance/Displacement across. Find the route through the maze, measure it in meters (expand the relationship of cm to m) and the figure out the displacement (direct vector route) in meters and direction. remember North is zero...or use the meteorological ESE East-South-North-West, etc.

Second, he mentioned a way of keeping electrical meters from being destroyed. By placing at least 2 silicon diodes in opposite directions across the movement, thus the voltage should not exceed 0.6 V saving the meter. if 0.6 V affects the full scale readings, 2 can be put in series--1.2 V. Another device used for protection is the neon bulb which fires at about 90 V depending upon ambient light.

06 April 1999: Karlene Joseph [Lane Tech HS]
She asked the question: How do you get a balloon completely inside a 500 cc Florence Flask? The students in her class had various opinions, which were interesting to consider from the viewpoint of basic physics and "common sense". She then got a balloon to go inside by putting a little water [" 50 cc] inside the flask, and boiling away most of it. Then, she took the flask off the heating element and put the balloon around the lip of the flask. After a few seconds the balloon was pulled inside the flask, and as more of the water vapor condensed the balloon filled up with air. Verrrrrrry interesting!

Next she demonstrated an OCARINA, which she had obtained from the craft store at Berea College in Berea, Kentucky [Latitude: 37o 34.2', Longitude: 84o 17.6']. She played on octave on the instrument, and then asked how to explain the sounds from the size and shape of the holes. Of course, nobody knew!

Addition information has been obtained by Lilla Green [Hartigan School]

I was in TN for some years and know a little about the Ocarina. It is sometimes referred to as a "globular flute." I think it is actually a very ancient instrument, although many cultures have embraced it and put their own touches to it. I think it originated with Native Americans, who made them out of clay. Now, they are made from wood or Terra Cotta or even plastic. They are made in all kinds of shapes, like animals or faces. The "sweet potato" Ocarina is also common (It's just shaped like a blob basically). I have seen them in antique stores and little gift shops, but I have never heard one played. If I were to guess, though I would say the physics is very similar to the flute or recorder, where you blow in and change the frequency that comes out by obstructing various outlets.

--Aubrey T. Hanbicki; The James Franck Institute; University of Chicago

Also, see following websites: http://www.ocarina.co.uk/.

02 February 1999: Bill Colson [Morgan Park HS]
How is it possible to suck spaghetti into your mouth?

The audience experienced the phenomenon with samples of foul-tasting pseudo-spaghetti, and drew these conclusions:

There is a pressure difference and the spaghetti will enter the mouth because the friction of the spaghetti will allow the spaghetti to be pushed by the pressure difference toward the lower pressure inside region.

See Readers Digest for January 1999.

01 February 2000: John Scavo (Richards Career Academy)
(handout - see http://www.ed.gov/pubs/parents/Science/soap.html) placed a pan on the table and filled it half full of water. Then he cut a small boat shape (about 5 cm long) from an index card. After using a paper punch to make a hole at the center of the boat, he used scissors to cut a narrow slot from the back of the boat to the hole - making a "keyhole" in it. We gathered around to see him place the boat on the water, and then he squeezed one drop of dishwashing soap into the hole, and the boat was rapidly propelled from one end of the pan to the other! A soap-powered boat! Actually, the soap reduces the surface tension of the water at the back of the boat, and the surface tension forces on the boat become unbalanced, propelling it. Neat!

14 March 2000: Bill Blunk (Joliet Central HS)
set up the Millikan Oil Drop Experiment on the table. It is a dandy piece of equipment sold by Sargent Welch, and expensive, so his school could afford only one, Bill explained. So when he sets it up for his students, only one at a time can look through the telescope to see the oil drop(s).

He then showed us a new addition to his technology - a small video camera that he had bought for $90 at the ISPP meeting at New Trier HS. (It's the sort of thing being used on computers these days when people are "talking" to each other.) It was now connected to a large TV set in front of us, and when Bill aimed the camera at us, we could see ourselves on the TV.

He reviewed for us how the Millikan Oil Drop Experiment [http://www.daedalon.com/oildrop.html] works; a pair of horizontal, parallel conducting plates are placed about 1 cm apart, and an electric harge is placed on them. Then some "oil drops" are squirted into the space between them (using an atomizer with a hollow needle such as for inflating a basketball).

Some of the drops become charged and may have 1, 2, 3, etc electrons on them. (Millikan used oil drops because he found small water drops evaporate rapidly, oil drops don't.) With the aid of a dandy diagram on the board which showed a charged sphere and a rod nearby, Bill showed us how opposite charges attract and repel. He used colorful magnets that had the + and - charge signs on them. They stuck to the board on the diagram and Bill could move them around to show how charges respond to each other -- a la Bill Shanks.

Bill Blunk also explained that nowadays fairly uniform latex spheres averaging 913 nm in diameter and carried by water drops from the atomizer are what he squirts into the space between the plates. A sphere (drop) with one electron negative charge would be attracted toward the upper positively charged plate. If a drop had 2 electrons and twice the negative charge (assuming they are all alike), then it would move twice as fast. By observing the motion of the drops through the telescope against a reticule (grid), one could calculate their speeds.

At this point, Bill placed the video camera to "look" right into the telescope, and we could then see the drops on the TV screen! With the voltage off (no charge) the drops would gradually move upward (which was really down, since the telescope inverts the image) under gravity. But with the voltage on, some would move down (actually, up, as seen on the TV!). But they moved with different speeds, and the differences between their speeds was always the same amount, which means that the electron charges on the drops always differed by the same amount. Bill could now show this to the entire class at once with the aid of his new video camera. Great! And it is affordable!

11 April 2000: Carl Martikean (Wallace HS, Gary, IN)
placed a capped jar with a greenish liquid in it on the table, then wrote on the board: Pediculus humanus capitus. "Does anyone know that this is?" he asked, referring to the writing. One person raised her hand. "What's the answer?" asked Carl. To which she replied, "Head lice!" And Carl said, "Right! Head lice!" Carl said that the liquid in the jar was sewer water, and twisted off the cap. Then he opened a plastic bag that he said contained new insects that live in sewers, and dumped some into the jar of sewer water. "Just look!" Carl said, pointing to the jar. "They come to life almost immediately!" -- as the particles moved up and down in the jar. "Would anybody like to drink some of this?" asked Carl. With no volunteers, Carl said, "OK - I'll drink some myself!" - and much to our disgust and astonishment - he did! "More?" asked Carl. And then he drank down half the jar. Of course, by now most of us guessed it was a fake. Carl explained that the "sewer water" was really a mix of ginger ale (for carbonation) and Frosh (a soft drink for green color). The "insects" from the plastic bag were really dried currants. "Kids will believe almost anything you tell them," Carl said. He explained that he wants his students to question him (and what they see on TV and elsewhere) about everything, and this is one way he tries to make skeptics of them.

05 September 2000 Don Kanner (Lane Tech HS)
showed us Galileo's inclined plane experiment. Galileo used a source of water drops as a clock (equal time intervals between drips) in order to time how long it took for an object to move down a plane inclined at a measured angle above the vertical. To have calibrate elapsed time, one would measure the amount of water collected in 10 seconds. One would do this for increasing angles of inclination, and make a graph of acceleration down the plane vs angle of inclination. As the angle approaches 90 deg (ie, vertical), the acceleration would approach that of an object in free fall, the acceleration due to gravity, which can be inferred from extrapolation on the graph. The inclined plane, in a sense, "dilutes" the acceleration due to gravity so that motion may be measured over the long time intervals available on a water clock of that era. Great ideas! Thanks, Don!

10 October 2000 Don Kanner (Lane Tech HS)
showed us a "Test Tube Black Box." He held up a cardboard tube about 45 cm long and 7 cm in diameter. About 2 cm from the left end, a string passed through the tube through a pair of diametrically opposed holes.  (On each end of the string were small metal rings to prevent the string from coming free of the tube.) Another string passed through the tube at its right end, in an identical manner, except it was longer. Looking at us with a grin, Don pulled down on the left string, and the string on the right end shortened. When he pulled down on the right end string, the left end string shortened. But then he pulled UP on the right end string - and it moved straight up until it was stopped by its bottom ring. And the left end string did not become shorter or move at all! How was this possible!? After showing us again with some variations, Don challenged us to come up with an explanation or make our own version. He explained that a chemistry colleague at Lane Tech  uses this to catch the attention of his students and to make them put their minds to work. So ... how about us!? Any ideas? Maybe Don will show us more next time.

30 January 2001 Ann Brandon (Joliet West HS)
presented an exercise entitled Millikan's Eggs. The idea is to determine how many plastic chickens [of identical mass] are inside each plastic egg [plastic shells of identical mass, not counting the chickens inside].  The students are to weigh each egg carefully, and then organize the data in such a form (a bar graph is helpful) as to determine the number of chickens and the mass of a chicken.  If an egg has n chickens, each of mass m, and if the plastic shell has mass M, then the mass of that egg will be

Mass(n) = M + n ´ m .

This exercise is analogous to  the analysis in Millikan's Oil Drop Experiment, to determine how many extra electrons are on an oil drop, and thereby the charge of one electron.  The students found it surprisingly difficult to get started on the analysis.

27 March 2001 Don Kanner (Lane Tech HS, Physics)
mentioned a self-checking graph, associated with the Toilet Flushing Experiment designed circa 20 years ago by Roy Coleman.  Working in pairs, students were asked to flush a toilet, and to record the depth of water in the reservoir behind the toilet seat, as a function of time, in intervals of roughly two seconds. Most students got a graph like that appearing on the left below, which resembles a check mark.  Upon occasion, student teams would obtain a graph like the one on the right below.  Those students, who had not followed instructions properly, were measuring water depth in the wrong chamber!

 

01 May 2001 Estellvenia Sanders (Chicago Vocational HS) Teeing for Angles
made a rectangle on the floor about 2 ft wide and 10 ft long using masking tape. She marked the tape at 1 ft intervals. She then gave each of three volunteers a toy plastic golf club and plastic ball. Each volunteer was asked to putt the ball to see the distance it would go before it either stopped or went out-of-bounds. A chart was drawn on the board, with each person's name displayed on the vertical-axis, and the distance on the horizontal-axis. Each distance was located as a dot on the chart. Straight lines were drawn to connect each pair of dots on the chart as data was obtained. The lines made various angles with each other, which the we were asked to identify as obtuse, acute, right angle, etc. A geometry vocabulary was thus motivated by this game: angle, point, plane, line, etc. Estellvenia uses hand signing to communicate with her deaf students, and this kind of activity proves quite helpful. Thanks, Estellvenia!

25 September 2001 Ann Brandon (Joliet West HS, Physics)
Ann gave the following handout sheet of 4 graphs of distance versus time D-T, velocity versus time V-T, and acceleration versus time A-T.


Click here to see the full-sized sheet.
The problem was to match them up.***see below.

Ann continued her presentation of  the 11 September 2001 SMILE meeting, in which she dropped a transparent plastic tennis ball tube, with washers attached to  its inside bottom end with rubber bands.  Using the Video camera, Jami English carefully recorded the tube as it fell through the air, so we could see more clearly when and how the washers fell inside the tube.  The following tentative conclusions were made:

These conclusions are tentative, pending examination of the video.

11 September 2001: Bill Shanks (Joliet Central HS, retired)
began a presentation, but promptly discovered that the apparatus was broken.  He will do it next time.

*** The Answers:  D, B, C  ... C, A, A or D ...  B, C, A or D ... A, D, B

06 November 2001: Karlene Joseph (Lane Tech HS, Biology) A Measuring Activity
This activity is based on a fairly recent exercise in SMILE Physics. The idea is, like Galileo in his inclined plane experiments, to invent our own system of units.  She passed out a thin dowel about 6 inches or 15 cm in length.  The length of the stick is defined  as one unit, and for reasons of personal gratification Karlene named hers one Joseph --- abbreviated as Jo. Karlene made this stick into a ruler, and used it to estimate units to the nearest 0.1 Jo, or tenth of Joseph.  Other distances could be expressed in terms of Josephs; for example, 1 my-unit » 1.4 Jo.

We then measured the lengths, widths, and diameters for other shapes, expressing the answers in Jo.

As an aid to measurement, Karlene had us hold our sticks at an angle across ruled notebook paper, so that one end was on a line, and the other end was lying exactly ten lines below it. We then marked the stick at each place where it crossed a line.  This divided the stick into 10 equally spaced intervals, and we thus obtained a deci-Joseph (de-Jo) ruler. We then repeated the measurements described above, thereby estimating lengths with a precision of hundredths of a Joseph, or centi-Jo.

Next we calculated the areas of a rectangle, triangle, trapezoid, and circle, and expressed the answers in square-Josephs, or Jo2.  What a beautiful set of mind-opening ideas for our students!

05 February 2002: Roy Coleman (Morgan Park HS, Physics) Various:

Let's hope the second law of thermodynamics isn't repealed also.  Very fine, Roy!

05 November 2002: John Bozovsky [Bowen High School, Physics]    Pushing a paper straw through a potato
John
described an experiment in which he pushed one end of an ordinary paper straw through a potato, after first putting his finger over the other end.  Unless you close the other end, the trick will not work.  He showed the experiment to his daughter, who said "I really hate science in school, but I love Physics!" Good point, John!

25 February 2003: Monica Seelman [St James School]      Surface Tension with Cheerios
Monica
has always enjoyed eating Cheerios™ cereal for breakfast, and was particularly fascinated by the fact that these pressed toroidal cereal pieces tend to clump while floating on milk. How come?  At Monica's invitation, in groups of 2, we put some milk into a bowl and began to add a few Cheerios, which floated on the surface.  Monica had expressed some concern that she had only been able to get 2% milk, versus her usual skim milk at breakfast, and wondered how it would work.  We found that it worked very well, and that it worked at least as well, and possibly better, with water.  The cereal pieces floated on the surface until they came close, and then seemed to stick together along their edges.  Presumably, the surface energy, which is proportion the surface perimeter between cereal and fluid, is reduced by having the cereal pieces to adhere. The same principles apply to adhesion of algae in a pond, clotting of blood, etc.

Very interesting --- even though you haven't been eating your Wheaties™, Monica!

25 March 2003: Ben Butler [Laura Ward Elementary School, Science Teacher]        What's a Million?
Ben
showed several exercises that he has presented to his students.

  1. First he showed us two capped containers [about 2 gallons or 10 liters] that contained colored, tiny plastic beads.  He remarked that each container contained 1 million individual pieces. The container with yellow beads contained one black bead.  Surprisingly, it was fairly easy to find that bead, since it migrated to the top as we shook the container.  Ben shook it to the tune of the chorus [Bounce-Bounce-Bounce- ... ] of the R Kelly rap song, Ignition. without the lyrics. [Ben occasionally does this chant in class, to let the students know that he is not totally ignorant of their world.]  Ben passed around another container with a million blue plastic pieces, and one black one, which is much harder to find.
  2. Ben next showed us the mechanism for a bar stool turntable.  First he used it  to demonstrate the relation between the radius R and circumference c of a circle: c = 2 p R.  He measured the radius (6" or 15 cm) with a ruler, and then calculated the circumference.  He demonstrated the expression by putting 3 sheets of notebook paper [11" or 33 cm each] around the edge, and then showing that he needs just a little more to make the circumference [37.7" or 96 cm]
  3. Ben next had a volunteer to stand on the mechanism, and Ben rotated him around several times. He asked us how far the edge of the mechanism had moved in, say, 5 complete revolutions --- more than 15 feet or nearly 5 meters.  The participant got very dizzy while being spun around, for some strange reason!
  4. The volume of a cylinder of radius R and height H is V = p R2 H, and the area of its lateral surface is A = 2 p R H. Starting with two  8.5" ´ 11" transparency sheets, Ben folded one into a long, 11" tall cylinder, and the other into an 8.5" short cylinder. With their bottom ends blocked off, which way  cylinder would hold the greater volume?  Most students expect that the taller cylinder will have a greater volume than the shorter one.  Ben stood both cylinders inside a large transparent container, with the shorter one encircling the taller one.  Then Ben showed us the answer by using Uncle Ben's Rice™ to fill the long cylinder completely. He then lifted the long cylinder, so that the rice inside it spilled into the shorter cylinder  --- which was then only partially filed with rice. Ben was able to add quite a bit more rice in filling the shorter cylinder! In the interest of full disclosure, Ben pointed out that he has no relation to either Uncle Ben™ or his rice!

A good set of ideas, Ben!

25 March 2003: Don Kanner [Lane Tech HS, Physics]      Proclamation Concerning Areas and Volumes
Don remarked that, because the lateral surface area of a cylinder of radius R and height H is A = 2 p R H, whereas its volume is V = p R2 H, it should follow that the cylinder of greatest volume for a given lateral area should be one of large radius R and very small height H. Do you believe this?

Don promised to prove it next time! We await edification, Don!

08 April 2003: Don Kanner [Lane Tech HS, Physics]      Paradox and a Pair o' Docks
Don had remarked at the last meeting that, because the lateral surface area of a cylinder of radius R and height H is A = 2 p R H, whereas its volume is V = p R2 H, it should follow that the cylinder of greatest volume for a given lateral area should be one of large radius R and very small height H. To illustrate the point, Don placed three transparent cylinders so they stood upright on the table. One was tall and skinny; it was made from a single transparency sheet with its short side (width w) folded around into a circle (circumference w) and its long side (height H) standing up. Its lateral area was therefore H w. The second (medium) cylinder was only half as tall, with height H/2 and circumference 2w, and therefore lateral area of (H/2) (2w) = Hw, the same as the tall one. The third cylinder was short and squat, half as high as the second one, with a height of H/4, and circumference of 4w, and therefore a lateral area of (H/4) (4w) = Hw, the same as the first two. Don arranged them on the table to lie concentrically and coaxial with each other, ie., the tall one was surrounded by the shorter medium one, which in turn was surrounded by the short squat one, all standing with a common vertical axis. Their bottom ends were closed off by the table, but their top ends were open. What next?

Don poured rice into the tall skinny cylinder in the center, filling it completely full to its very top. He pointed out that the volume of the rice must equal the volume of the tall skinny cylinder. Then -- beautiful to see! -- Don slowly and carefully raised the tall cylinder up off the table. As he did so, the rice spilled from its now open bottom end to occupy some of the volume within the medium cylinder. Don smoothed the rice flat, and we could see that it filled the medium cylinder to just half its volume. Wow! So the medium cylinder must be capable of holding twice the volume of rice as the tall skinny one! Finally, Don slowly raised the medium cylinder to spill the rice from its bottom end to occupy some of the volume enclosed within the short squat cylinder. When he smoothed the rice flat, we could see that it occupied just 1/4 of the volume of the short squat cylinder! Don then appealed to the fact that, if this process is continued indefinitely, the enclosed volume can be made arbitrarily large, as is illustrated in the following table, beginning with a sheet of height H and width w:

Number Height Width /
Circumference
Lateral
Surface
Area
Cylinder
Radius
R
Cylinder
Area
pR2
Cylinder
Volume
pR2 H
1 H w H w w / (2p) w2/(4p) w2/(4p) H
2 H  /2 2w H w w / p w2/p w2/(2p) H
3 H / 4 4w H w 2w / p 4 w2/p w2 H / p
4 H  /8 8w  H w 4w/ p 16 w2/p 2 w2 H/ p
5 H / 16 16w H w 8w/ p 64 w2/p 4 w2 H/ p
.   .   .
¥ 0 ¥ H a ¥
 ¥ ¥

Don mentioned that zero and ¥ often occur together in physical problems; i.e,  infinite resistance goes with zero current; infinite kinetic energy requires zero time elapsed; etc.

Don, you have done as promised!  Very nice!

06 May 2003: Roy Coleman [Morgan Park HS, Physics]        Using Marbles to Determine the Size of the Monster Behind Door
Roy
handed out a sheet containing the following information:

The Size of a Monster
There is a very hungry monster in an almost completely closed room.   There is a door to enter and a thin horizontal slit at the bottom along the entire length of a side.  Before you enter the room you must determine the width of the monster. You also have a large supply of small rocks.

Using a monster that looks remarkably like a soft drink can and rocks that look like marbles, you are to determine its experimental width and compare that value to its actual width.  Each time the monster is hit it grumbles (klinks?) and moves, never touching any of the walls.

A couple of hints:

  1. Each group will need to throw at least 200 rocks randomly through the slit into the room.
  2. What is the probability of hitting the monster if it is half the size of the room?
  3. Look up information on the Rutherford Scattering experiment.
  4. Does the size of the rock itself make a difference?

Good luck in gauging the size of the monster, Roy. Thanks!

09 September 2003: Fred Farnell [Lane Tech HS, physics]        Balancing an Egg on End
Fred
began by describing this activity as an illustration of the application of the Scientific Method.  He showed a dozen fresh eggs, which he had asked his class to vote on the following hypothesis concerning balancing an egg on end:

Choices: 
Number of Votes
Not possible 45
Only on vernal equinox 34
Only on autumnal equinox  7
Broad end only 35
Pointy end only 1
On either end 10
Only at equator 1
Four eggs were successfully  balanced on their broad ends, by  Marilyn Stone and Betty Roombos [twins!].  Others tried to balance the eggs, without success.  The moral is that it requires patience, steady nerves, and effort to balance an egg. It is also possible to balance an egg on its pointy end. This question is discussed in the book Bad Astronomy: Misconceptions and Misuses Revealed, from Astrology to the moon-landing hoax by Phillip Plait [Wiley 2002, ISBN 0-4714-09766].  Note that some of the choices are not reasonable, such as the fact that balancing can be done on the vernal equinox, but not on the autumnal equinox.  Still, there are many people who believe in such pseudo-scientific folklore.  For details see the Egg Balancing Website: http://www.badastronomy.com/bad/misc/egg_spin.html.

Thanks for sharing this with us, Fred!

23 September 2003: Roy Coleman [Morgan Park HS, physics]        Pulling on a Spool with a String
Roy
brought in a very large wire spool [rough dimensions: outer diameter 40 cm, inner diameter of 15 cm, height 40 cm]. He wrapped a heavy cord around the inner portion, and went through the classic demonstration of pulling the cord, as described on the website Julien C Sprott: Physics Demonstrations: Motion [http://sprott.physics.wisc.edu/demobook/chapter1.htm, item 1.12].  He made the spool come toward him, go away from him, stand still and slip, and slide toward him, just by pulling with various orientations of the cord. Roy then rolled the gigantic spool on the chalk tray of the board, attaching a marker to the edge.  The marker traced a cycloid on the board -- Beautiful! 

Bigger spools are better, definitely!  Neat, Roy!

Roy also called our attention to the American Association Physics Teachers [AAPT] High School Photo Contest, as described in the Fall 2003 issue of the AAPT Announcer [Vol 33, No 3].  [also, see the website http://www.aapt.org/Contests/pc03.cfm]  The First Place winner by Jared Hill of Durham NC, is shown on its front cover.  It  shows a hard-boiled egg spinning in a thin layer of water.  The water is creeping up the side of the egg until it is thrown outward, creating a fountain effect. See the journal article "Fluid flow up the Wall of a Spinning Egg" by Gutiérrez, Fehr, Calzadilla, and Figueroa, American Journal of Physics 66, 442-445 (May 1998).  Our own Ann Brandon is a guiding spirit of this contest!

07 October 2003: Robert Albert [Roosevelt HS, science]       Observation and Inference
Robert
took out a shopping bag filled with cubes made from empty milk cartons -- the cubes had one missing side where the carton tops had been cut off.  Our cubes were similar, with the numbers 4 and 3 on the front and back sides, 1 and 6 on the left and right sides, and 5 on the bottom. All cubes were identical.  Each person saw only the numbers on one cube. We then were asked to seek a pattern, to predict what number should have been placed upon the missing face.  We first saw only the numbers on the sides; since the cubes were identical, each person had the same information in order to extrapolate.  These numbers represent observations, and it might be difficult to suggest a pattern. The possible pattern became more evident when we looked at the base, with 5 on it.  It was suggested that the sum of front-back, left-right, and up-down numbers might be 7, since  4 + 3 = 7, 1+ 6 = 7 and 2 + 5 = 7.  The missing number [2] could then be predicted from this inference.  Of course, that prediction cannot be confirmed until and unless we see the number on the missing side.  So it goes with scientific analysis.

Next we replaced the numbers by names:

front-back: hat + fat         sides: bat + cat          bottom-top: mat + ___
What should be written on the top of the cube? Presumably, a three-letter word, ending in "at".  There were several suggestions:
Guess Rationale
Nat A name, opposite Mat
Pat Another name
Pat Letter spacing: b-c ... f-g-h ... m-n-o-p
Rat An animal: bat cat rat
Sat A fat (cat or bat) sat on a (hat or mat).
There is more than one pattern, and more than one "good guess" here.

Next set of cubes:

front-back: Alma + Alfred          sides: Rob + Roberta          bottom-top: Frank + ___
Presumably, it is a person's first name. These observations may suggest that the missing word is a feminine name corresponding to Frank, such as Franka, Frances, Francoise, Francene, Francesca, etc.  This puzzle is much more ill-posed, and the predictions more tentative.

Robert uses this exercise in class to highlight the difference in observations and inferences. You really made us think!

07 October 2003: Imara Abdullah [Douglas Academy,  science]        Posters
Imara
provided us with poster paper, colored markers, and tape, and asked each of us to prepare a poster to illustrate some concept or process in mathematics or science.  We came up with the following displays:

Name Display description  Concept or process illustrated
Porter Johnson blank sheet of paper Vacuum, empty space, cosmic void
Bill Colson Flow chart 3 ® 1 3 conditions for triangle congruence
Roy Coleman I'm a p r2 (big wheel)  Area and circumference of circle
Elizabeth Roombos Rock hurled off cliff Projectile motion
Marilynn Stone Click-clack apparatus Momentum conservation
Monica Seelman 45°-45°-90° triangle Pythagorean Theorem
Earl Zwicker Sequential images of ball
on inclined plane
Galileo experiments in mechanics
Imara Abdullah Walking dog around block Perimeter
John Bozovsky Kneeling carpenter drilling into wall Niels Bohr (kneeling and boring)
Larry Alofs Rectangle at new IIT student center   Golden rectangle  -- or not?
Jane Shields Colored strips on paper Northern lights
Babatunde Taiwo
Rocks thrown simultaneously
up and down
Do they hit the ground
at the same time?
Walter McDonald Headlight beam image Illumination: Inverse square law
Rich Goberville Projectile shot from cannon Action-reaction Forces
Bill Shanks Plumb bob demons Universal gravitation
Fred Farnell Light charged balls on strings Coulomb's Law: Electrostatics
Leticia Rodriguez See-through skeleton Systems in human body
John Bozovsky Truck accident How the Mercedes bends
Imara showed us how to display individual posters, using two sheets of transparent Plexiglas™ sheets, held by two binder clips.  Nifty, eh!

We were all on our feet and involved!  Beautiful Activity, Imara.

04 November 2003: Monica Seelman [ST James Elementary School, science]        How much paper is there in a roll?
Monica
brought a wrapped cylindrical roll of paper about 1.36 meters in height.  The roll had an inner circumference of  11.6 cm, an outer circumference of 23.6 cm, corresponding to an average circumference of 17.6 cm.  The thickness of a stack of 25 sheets was measured to be 0.6 cm, corresponding 0.024 cm per sheet. Since the paper was 2.0 cm thick on the roll, Monica felt that there were about 83 sheets in the roll.  Thus, she estimated the roll to be 14.7 meters long --- and with a height of 1.36 meters, this corresponds to an area of 20 square metersLarry Alofs suggested an alternative method of estimating the amount of paper, by weighing a small piece of paper of known area, and then weighing the entire roll.  This might have been more accurate, in practice.  We could have done both, and then rolled the paper out to see how long it actually was.

Thanks for showing us the way, Monica!

18 November 2003: Carol Giles [Collins HS]         INTERNET EXPERIENCE
Carol
provided us with  simulated internet research projects by dividing us up in triads, giving each group several "information sheets" on a specific topic she had obtained from surfing the net.  She asked us to prepare an overhead transparency that one of the group members would present to all of us. The following topics were considered:

We all enjoyed the discussions which followed the presentations and got a better understanding of what our students go through when using the internet to prepare reports. Thanks, Carol for such an insightful experience!

09 December 2003: Brenda Daniel  [Fuller Elementary School]         Science Fair Materials + Scavenger Hunt
Brenda
passed around an educators MAP and other information obtained from the Museum of Science and Industry in Chicago [http://www.msichicago.org/]. Using this information, she led us through two distinct exercises:

Very thought-provoking! Thanks, Brenda.

09 March 2004: Wanda Pitts [Douglas Elem] Two Sticklers by Terry Stickels [http://www.terrystickels.com/]
Wanda
gave us these two puzzles that she has used in her fifth grade classes to stimulate interest in learning:

  1. Q: "The numbers 6009 and 6119 are both numbers that can be rotated 180° and still be read the same. Can you figure out the first number preceding 6009 that holds this same characteristic?"
    A1961
  2. Q: "How many triangles are there in the figure?"
    A: 8 triangles: ABC, ABD, ABE, ABF, ACD, AEF, BCF, BDE
Really good puzzles, Wanda! Thanks.

06 April 2004: John Scavo  [Evergreen Park HS, Physics]         Cub Scout Science
John
passed around copies of an article, Amazing Science Tricks by Michio Goto, which appeared in the April 2004 issue of Boy's Life® http://www.boyslife.org/, official magazine of the Boy Scouts of America®.  See also the book Amazing Science Tricks by Michio Goto: http://www.thejapanpage.com/html/book_directory/Detailed/329.shtmlJohn called particular attention to the lessons entitled Keeping Water Separate, A Candle that Sucks Water, Bending Light through Water, and Toothpick Torpedo.  He demonstrated the bending of light through water by poking a hole in a 2 liter soft drink bottle with an awl, and then filling it with water.  When the bottle was placed on the table (in an aluminum oven pan!) in an upright position with the cap off, water flowed out of the hole in a steady stream.  He held a flashlight at the level of the hole and on the opposite side of the bottle, and turned it on.  Light shined through the bottle, and came out into the stream of water, and was totally reflected internally along the stream.  Beautiful!  He showed us the Toothpick Torpedo.  First John dabbed a little shampoo on the blunt end of a wooden toothpick, and dropped the toothpick horizontally into a pan of water. The toothpick began moving in the direction of the sharp end.  Why?  Shampoo reduces the surface tension in the fluid near the blunt end of the toothpick, and thus the floating toothpick experiences an unbalanced force, and goes forward.

 Isn't Science Amazing?  Thanks, John

04 May 2004: Joyce Bordelon [Moos Elementary School]         Simple Machines
Joyce
passed around some information on simple machines, which contained patterns for each of the six simple machines --the inclined plane, the wedge, the lever, the wheel and axle, the pulley, and the screw.  These template patterns could be cut out and glued or taped together to make each of the machines.  The information packet, Simple Machines, was prepared by Carmen O Pagán and Lily T Reyes, bilingual teachers at Talcott School. For more information see the Simple Machines Learning Site:  http://www.coe.uh.edu/archive/science/science_lessons/scienceles1/finalhome.htm.We discussed the simple machines that are found in various mechanical systems in the human body.  Levers are present in the arms and the jaw, the teeth constitute a wedge, and ball-and-socket joints probably correspond to a wheel and axle system.

Interesting points, Joyce! Thanks!

04 May 2004: Lilla Green  [Hartigan Elementary School, retired]         A Discovery Activity
Lilla
fitted three volunteers with blindfolds, and then gave them a series of items, which they tried to identify only by touching and feeling  The first item, for example, was a clothespin.  Other items were balloons, a small piece of play dough, a rubber band, and various paper clips.  Lilla stated that the Shakers invented the clothespin. For more details see the Public Broadcasting Service website The Shakers for Educators: http://www.pbs.org/kenburns/shakers/educators/Lilla passed out a lesson plan for using clothespins in a discovery activity, relating to their properties, their history, the application of simple machines in the design and construction of clothespins, and other uses for them.  In particular, she described an exercise for using one or more clothespins, along with other materials, to design a useful tool, such as a bag closer or a recipe holder.  As an extension, she suggested that the anatomy of a fish's mouth determines their food source.  The fish has to catch, hold, chew, and swallow their food.

Very interesting ideas, Lilla!

07 December 2004: Sally Hill [Clemente HS]           Physics Catapult Project  (handout)
The following has been extracted from the handout passed out by Sally:

  1. Goal: Create a device that will launch a ball at a target with proper distance and accuracy.
  2. Competition Rules
  3. Testing Procedure
Sally brought in a winning catapult, and used it to fire a tennis ball across the room.  Stretched fabric was used to provide the potential energy needed for launch.  We found that the catapult was more powerful when a large, strong rubber band was wrapped around the pivot point of the catapult -- the tennis ball went about 8 meters across the room.

08 March 2005: Fred Schaal [Lane Tech HS, mathematics]              RANDINT(1,14,4)+50
Fred
used the Pseudo-random Number Generator RANDINT, which is programmed into the TI-83 calculator. He generated a random, equally-distributed set of 200 integers from 1 through 14, and obtained the following number-of-occurrences of the generated numbers:

Generated Number   1 2 3 4 5 6 7 8 9 10 11 12 13 14
Number-of-occurrences   13  12  13  18  17   14  20  15  13  13  17  10  13  12
Does this appear to be a "random" set of numbers? The answer is "Yes", despite the fact that the number-of-occurrences ranges between 10 and 20. On statistical grounds, we would expect the average number of occurrences to be about 200/14 = 14.3, with a spread (standard deviation) of Ö14.3 = 3.8.  Thus, about 2/3 of the number-of-occurrences should lie between 11 and 17. That is consistent with the spread in the data. Curiously, only the number "6" occurs exactly 14 times.

Porter Johnson mentioned that "everybody knows" that it is unlikely for a randomly flipped coin to come up H (Heads) ten times in a row. However, not everybody realizes that the alternating sequence H T H T H T H T H T is equally unlikely. Furthermore, it is quite unlikely that in 1000 coin flips, Heads will occur exactly 500 times.

For a general discussion of Pseudorandom Number Generators see the Wikipedia webpage: http://en.wikipedia.org/wiki/Pseudorandom_number_generator.

Fred also brought in his metal candy box, for which we had taken exterior measurements last time mp022205.html to determine a volume of about 910 cm3.  We took a graduated cylinder filled with water, from which we were able to pour about 800 cm3 of water before the box became full. Our estimated volume was too large by over 10%. Why?

Fred also pointed out that the planet Mercury would be visible next to the New Moon just after sunset in the next few days. Thanks for the ideas, Fred! 

10 May 2005: Roy Coleman appeared on the Channel 5 (NBC) news on Monday 09 May.  His classroom work with college-bound students was shown on that program, in keeping with his wide-spread, well-deserved reputation as an excellent physics teacher. You looked great, Roy!

18 October 2005: Betty Roombos (Gordon Tech HS, physics)               Explore, Plan, and ACT
Betty recently proctored a pre-ACT Plan Test [http://www.act.org/plan/] -- a practice test for the ACT that is often taken by 10th graders. Biology, weathering, conservation of mass and water, wave-particle model with photoelectric effect, and centripetal force were among the topics covered. Betty felt that this sophomore level test included topics beyond what the sophomores should be expected to know.  She asked whether the Plan Test was thus appropriate for practice.  Another concern was that the students were not given enough time to reason out the information in the test -- which was given via complicated charts and graphs.  Good questions!  Thanks, Betty.

15 November 2005: Don Kanner (Lane Tech HS, physics)                Any Questions?
Don
showed a strategy for getting class participation.  He handed out a card to each student.  When students asked a question or gave an answer (after being called on), he stamped their cards.  At the end of class, the students put their names on their card, and Don collected them.  Each stamp on the card was worth extra credit on a future examination. Students quickly took an interest in class discussion.  Don illustrated the strategy using two balloons containing Helium gas.  We asked the following questions:

  1. Why are the 2 balloons repelling? (like charges repel)
  2. Why are the balloons floating in air? (anti-gravity shields? -- ha)
  3. How do we know that Helium is in the balloons? (Don inhaled Helium from the balloon and then spoke in a high-pitched voice.)
The students appreciated getting credit for their participation.  Good ideas!  Thanks, Don.

24 January 2006: Don Kanner (Lane Tech, physics)            Siphoning the net
Don
gives students in his classes a chance to redeem themselves over the Christmas holidays.  He asks them to write paragraphs on 26 items, such as A: Atwood's Machine, and S: Siphon.  Students should also find a picture describing the item, as a way of learning to use the internet. As examples of how such searching can lead to confusion and misunderstanding, Don showed a picture of a siphon found on the net, and the explanation (text) at this site was riddled with spelling errors—not a good example for kids. Two other sites had incorrect explanations of how the siphon works. Cecil Adams (http://www.straightdope.com/columns/010105.html) had a rather complete explanation of how siphons work.

21 February 2006: Roy Coleman (Morgan Park HS, retired!)                Torques
Roy
described a useful way to teach the right hand rule.

t = R ´ F
That is, the torque t is equal to the cross product of radius R and the force F. Let the radius R represent  “your right aRm”, the force F  “your Fingers”, and the torque t "your thumb". Point your right aRm in the direction of the first vector R and its bent Fingers in the direction of the second vector F; then the thumb will point in the direction of the torque (cross product).

Tres simple, non! Thanks, Roy.

07 March 2006: Bill Colson (Morgan Park HS, math)               Assorted Literature
Bill
shared several items with us:

Thanks, Bill!

18 April 2006: Benson Uwumarogie (Dunbar HS, Mathematics)                    Attempts to Improve Math Scores
Benson
has been attempting to help his students to obtain higher scores on standardized tests by assigning questions that are similar in spirit to those questions that were "frequently missed" on last years examinations. The following is a paraphrase (diagrams not included) of a frequently missed question: 

A gardener installs 4 sprinklers (with each centered in the four quadrants) in a square plot with sides that are 12 feet long.  Each sprinkler waters a circular region with a radius of 3 feet. No portion of the plot is watered by more than 1 sprinkler.  What is the approximate area, in square feet, of the portion of the plot that is NOT watered by the sprinkler?
This question is rather similar in character to the previous one:
In the doughnut shop, Fred is assigned to put sprinkles on the chocolate-covered doughnuts .  There are 8 doughnuts on a tray, which don't touch one another.  Each doughnut has a 4-inch diameter and a 1-inch hole.  The tray is 20 inches long and 12 inches wide.  Fred distributes sprinkles randomly and uniformly over the entire tray.
  1. What is the probability that a sprinkle with land on a doughnut? Explain.
  2. What is the probability that a sprinkle will land on the cookie sheet? How is this related to the probability in 1? Explain.
  3. If Fred distributes 4000 sprinkles over the cookie sheet, predict how many of them will land on the doughnut. Explain.   
This is a reasonable approach to a challenging problem. We hope it works well! Thanks Benson.

02 May 2006: Nneka Anigbogu (Jones College Prep, math)              Math Ideas for Non-College Prep Students
Nneka showed us a way to teach exponential decay using M&Ms® or Skittles®! We divided into three groups, each with a small bag of M&M’s and a medium sized plastic cup. We counted the number of candies in our bag and put them into the cup (53-55 were the numbers to start). Then we shook the cup and tossed the M&Ms out (like dice) and counted the M&M’s with the M showing (heads up). The candy pieces that landed with the M up were put back into the cup, which was shaken and tossed once more. Again, about half of them remained. We continued the process. Here are the data recorded in tabular form for the groups:

M&M's Toss
Trial Number  Group #1 Group #2 Group #3
1 53 55 54
2 29 25 21
3 14 08 16
4 05 08 07
5 00 04 02
6 - 02 01
7 - 01 00
8 - 00 -
One might expect the number remaining after n tosses, Yn, to decrease exponentially with n according to the formula
Yn = Y1 (1 - r)n   ...   with    r = 1/2.

She drew a graph of the number of M&M’s remaining versus the number of tosses, obtaining a profile that looked roughly exponential. She estimated the parameter r by using the formula Y2 = Y1 (1 - r), or

r = 1 - Y2 /Y1

We obtained r = 0.45, 0.55, and 0.57 for the three cases -- the extrapolated numbers using these values of r being fairly close to the actual results.

For more candy games see the M&M's website:  http://us.mms.com/us/fungames/games/. A good Phenomenological lesson -- edible too! Thanks, Nneka.