Elementary Mathematics-Science SMILE Meeting
21 March 2000
Notes Prepared by Porter Johnson

          OUR NEXT MEETING...
...will be April 04, 2000
4:15 p.m.

Section A (K-5) meets in 111 LS
Section B (4-8) meets in 152 LS

Be sure to sign up for a presentation if you haven't
already done so!


Apr 4 A Christine Scott Ben Butler Jr
Lilla Green Kenneth Onumah
Shirley Cesair Carolyn McGee
Carolyn McGee Iona Greenfield
Ben Butler Jr

B Janet Sheard Janet Sheard
Earnie Garrison Charlene K. Smith
________________ _________________
_??? OTHERS ???_ _________________



Announcements by Porter Johnson

Section A
Wanda Pitts (Douglas Academy; Third Grade)
  1. Making a "Rippling Rainbow":
    What will happen if you drop 10 drops of red food coloring into a jar of H20? Watch the diffusion of food coloring throughout the liqud.
  2. Place 2 cups of uncooked rice into a quart jar, and put in a large marble (or ping-pong ball). After putting the marble in, put on the lid and turn upside down. The marble will be at the bottom. Give the jar a few vertical shakes, and note the marble comes to the top of the jar. Why?? As you shake the jar, the rice will fill in the spaces. The marble is too large to do this, so that it will work its way to the top. Question: Is this why the large cashew nuts are at the top of the box when you open it, even they are also the most dense of nuts? Amazing!

Marie Wong (Warren School; First Grade)
Guessing the number of jelly beans in the bag:
The actual number was 355, and the closest guess was 350. [How, other than by pure luck, can you get this close?] Do this exercise with a class, and list the guesses in order from the least to the greatest, to study their distribution.

In the second activity each person was given a bag of jelly beans. First they estimated the total number of beans, as well as the number of beans of each color. Then, the beans were sorted by colors and counted. Next, a graph of estimated and actual numbers were plotted for each color and for the total [bar graphs]. Finally, everybody gets to eat the beans. All five senses are thus brought into this exercise. Delicious!

Ernest Garrison (Jones Commercial HS)
Polymers, continued He mixed chemicals obtained from Flinn Scientific to make a type of "polyurethane foam". He added one teaspoon of a monomer foam called Part A to one teaspoon of the other monomer foam called Part B, and then stirred the mixture for a few minutes. The resultant "compound??"expanded, gave off heat, and in its final form it felt firm, resembling styrofoam. Check the website for Flinn Scientific: http://www.flinnsci.com/.

Cynthia Southern (Spencer School; Kindergarten)
She showed a picture of Michael Jordan's hand, and had us estimate how many great northern white beams it would require to cover that hand. Then, we placed the beans on his hand, and we compared our estimates with the number required, which was about 120. Michael has big hands!

RaeLynn Schneider (Williams School)
Stored Energy

Monica Seelman (St James School; Williams School)
Sister Monica demonstrated paper folding. We made a polyhedron [a solid with many faces, each of which is a plane polygon] with f =24 faces, e =36 edges, and v = 14 vertices [corners]. This count is consistent with Euler's theorem:

f + v = e + 2


24 + 14 = 36 + 2

This solid is called a Tesselated Octahedron.

See you next time!

Section B:

Pat Phillips (Arai Middle School)
Lesson on Probability (handout) It has been possible to get a Pokemon Card with a McDonald's Happy Meal. Let us say that there are 6 different kinds of cards, and that each is equally likely; i.e., each occurs with probability 1/6. How many Happy Meals must you order to get a full set of six cards? We did a Monte Carlo Simulation of the process, by putting two copies of each card [12 cards in all ] into a box, and drawing cards randomly from the box, recording the card name, and putting that card back each time. We were divided into groups for this process, and each group did three trials. Here are the data for one of the groups of number of "hits" for each card and "total number drawn" to get a full set of 6 cards:

Card Face Trial #1 Trial #2 Trial #3
Charizard 1 2 4
Blastoise 1 1 4
Mentuo 1 1 1
Alakazam 3 1 3
Dragonite 3 1 1
Clefairy 1 1 1
----------- --- --- ---
Total Number of Draws 10 7 14

This group averaged 10.3 draws in order to get a complete set of cards, whereas the other groups averaged 17.3, 18.0, and 11.0 draws, corresponding to a class average of about 14.2 draws. We were thus close to the average over many trials, which is said to be about 14.5 draws.

One may determine and discuss the mean, mode, and median of the trials. This exercise involves the application of notions of probability in our everyday lives, for such things as batting and shooting averages in sports, life insurance, quality control in industry, opinion polls, raffle tickets, etc. This activity is consistent with the NCTM [National Council of Mathematics Teachers] standards and the requirement to include "probability" in the teaching of mathematics. Also "math" is linked with "reading", as well as "sports", "politics" , and "consumerism".

Porter Johnson mentioned that such Monte Carlo Techniques are very frequently used in science and engineering to get good estimates on numbers that are too difficult to calculate by "brute force". The name was chosen based upon experiences by Stanislaw Ulam, a scientist on the Manhattan Project in World War II, who became severely ill just after the war, requiring several months of recuperation. He began to play the card game SOLITAIRE, and began to wonder what the odds of winning would be. He modified the usual rules to require that "every move that is not forbidden is compulsory", just like in the US Army, so that the outcome of each game would be determined merely by the order of the cards in the deck. The total number of different orderings of a deck with 52 cards is 52 factorial, = 52 !, or

1 x 2 x 3 x . . . x 50 x 51 x 52 = 8.066 x 1067

The odds [which may be about 1/3 for the most liberal of rules] are "borderline impossible" to calculate, but you can play a few games to get a qualitative estimate of them, and if you play many, many games the estimate improves. Roughly speaking, with N trials, the accuracy is of order 1 /Ö N, so that, for example, in an "opinion poll" 625 people must be asked to get 4 % accuracy, since

1 /Ö625 = 1/25 = .04 = 4 % .

According to the pollsters, their opinion polls are far more reliable as an indication of public sentiment than the actual elections, since about half of the eligible voters do not vote, and as a result the actual election is considered to be statistically biased, whereas the polls are not!

Val Williams, Jr (Perkins Bass School, Band Instructor)
Science through Music
How do the various types of music affect our central nervous system? We know that music has a profound effect upon our emotions [music soothes the savage breast; or is it "beast" ], and there is some evidence and a popular consensus that you "think better" with the right background music. That is, babies who listen to Mozart and such learn to talk more quickly, etc.

How do we test this hypothesis? He developed a modest experiment, based upon the battery-operated board game Operation: Skill Game. While wearing earphones, his trusty assistant Jeremiah played the game. Over one minute intervals we recorded

while Jermiah was subjected to various types of music in the earphones. Here are the data:

Music Type Success Count Failure Count
No Sound at all 4 4
Rhythmic Blues 7 12
Soul Music 4 10
Classical 2 0
Rap 6 3

One might be tempted to conclude the following:

Next, Val gave the following mantra for good teaching---it should be all of these things:

Finally, he and his assistant performed the science-based "soft rap" song Evolution, as given on the website http://www.accessexcellence.org/AE/AEPC/WWC/1995/evolution.html. This song has the same cadence as the classic "rap" work None of your Business by Salt-N-Pepa. Very interesting, and also "catchy"! This is a science exercise that should have special appeal to our students!

Estelvenia Sanders (Jones Commercial HS)
Science in Sign: Part XVIII
She gave us signs for the following things:

Bowl (hands holding bowl) Water (3 fingers up)
Sprinkle (fingers sprinkling) Drop (1 finger down)
Dishwashing liquid (s-o-a-p water) Pepper (2 fingers on 2 fingers)
full (hand off hand) "full of it" (pointer on neck)
watching (2 fingers out) observing (both hands out)
Procedure (hands rolling over hands) ...etc...

First, she did several experiments with water:

Procedure ---> Outcome
Put in cinnamon ---> it sinks
Put in black pepper ---> it floats
...then add soap ---> ...pepper runs to edge
Put in gumbo seasoning ---> it floats
...then add soap ---> ...it runs to edge
Put in season salt ---> it floats
...then add soap ---> ...it runs to edge

Next she asked why a solidly frozen plastic water bottle took all day to melt, if then. Points to consider:

Finally, she posed the mathematics question: How do you find the area of a triangle if you know the sides to be (a, b, c)? The answer by PJ: First, calculate the semi-perimeter
s = [ a + b + c ] /2

The parameter s, as the name suggests, is the triangle perimeter divided by 2. Then calculate the area A according to the formula

A = Ö [s x (s - a) x (s - b) x (s - c)]

That's all there is to it!

Barbara Pawela (SMILE Staff Member; CPS Retired)
The Clanging Soda Pop Cans (handout) to illustrate Bernoulli's Principle.
Take two empty soda pop cans and lay out about two dozen drinking straws in parallel [like railroad cross-ties] on a level table.

The Bernoulli Principle states that the pressure is reduced where air is moving over a surface at high velocity; the higher the velocity the lower the pressure. This principle is related to the flight of airplanes, although it does not tell the whole story.

See You next time!

                                Future Meetings

Apr 25 A Sophia Watson Sophia Watson
Virginia O'Brien
Iona Greenfield Claudette Rogers
Virginia O'Brien ___________________
Iona Greenfield ___________________

B Brian Cagle Brian Cagle
Pearline Scott Pearline Scott
Kim Baker Kim Baker
__________________ ___________________

May 8 A Barbara Baker Barbara Baker
Chandra Price Chandra Price
__________________ ___________________
__________________ ___________________

B Brian Cagle ___________________
Mikhail Siddiq ___________________
__________________ ___________________
__________________ ___________________