Elementary Mathematics-Science SMILE Meeting
07 March 2000
Notes Prepared by Earl Zwicker

          OUR NEXT MEETING...
                             ...will be March 21, 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!

          111 LS    A       Cynthia Southern     Cynthia Southern
          (K-5)             Marie Wong           ___________________
                            Joyce McCoy          Joyce McCoy
                            Wanda Pitts          Wanda Pitts
                            Monica Seelman       Monica Seelman

          152 LS    B       Patricia E Phillips  Patricia E Phillips
          (4-8)             Val Williams         Sally Hill
                            Estelvenia Sanders   ___________________
                            Janet Sheard         ___________________

                               SEE YOU THERE!!

          AT OUR LAST MEETINGS (March 7)...
Section A
Winifred Malvin (Carver Primary)
(handout NASA 3-2-1 POP!) put us to work making rockets. We used heavy construction paper; a film canister was the "engine." Form paper into a cylinder for the rocket body, taping the canister into the bottom in the process. Cut and tape on fins and a cone for the nose. Place an alka seltzer tablet into the film can, add water, replace the cap tightly, stand the rocket up. Before long - POP - and the rocket lifts off as the cap is blown off and water and gas are ejected downward! Winifred had Newton's 3 laws beautifully printed on the board, as they apply to the rocket. (eg. First law: The rocket lifts off because it is acted upon by an unbalanced force.) Questions: What affects the height of flight?..the amount of water used? Water temperature? Amount of tablet? Weight of rocket? An exciting and informative experiment!
Ken Schug (IIT) suggested using baking soda wrapped a bit of tissue, place in the film can, add a bit of vinegar and put the cap on quickly. Less expensive than the seltzer tablets.

Margia Artis (Herzl School)
(handouts - The Model Plant, Can You Fool a Plant?) had placed a set of vocabulary words on the board, related to plants: eg. chlorophyll, petal, pollen, taproot, sap, stamen, seed, pistil, cotyledon, etc. We each received a page called a Bingo Grid, which divided the page into 25 squares, 5 squares on a side. And a handful of sunflower seeds. She asked us to write the vocabulary words, at random, onto each square of our Bing Grid. Then she read a definition, and we were to place a seed on the square with the word that fitted the definition. And so it went, until someone hollered BINGO! But then that person had to read the word and state its definition before she was accepted as a legitimate winner. How to make a game out of learning plant parts! We also were invited to the table to fabricate a colorful model of a plant from various materials. Great!

Alma White (Woodson North School)
(handout - Oatmeal Play Clay) invited us to the table where she had flour, oatmeal, water, and some bowls, along with vegetable dyes. Soon we were busy making oatmeal play dough. Many of us tried to form it into the shape of a swan, since Alma had placed a Japanese haiku on the board and challenged us to add to it or subtract from it:

        All swans in a pool           (5 syllables)
        As they go by they look like  (7)
        Bright sunny rainbows         (5)

There was also colorful paper on which many of us drew swans, and our work was shared with all of us later. Alma pointed out (on the board) that the connected activities could involve reading, writing, art-cutting, and even math, geometry, fractions, counting. Really hands-on learning!

Marjorie Fields (Young Elementary)
(handout- Clock Shop) We each received a page with a clock and minute and hour hands to cut out. Also, a paper plate and a fastener. We colored the clock with crayons, the hands and plate too. Then the face of the clock and hands we mounted with the fastener (at the center) of the plate, and we could then indicate the time to the hour and minute. Her very young students would become involved in hands-on learning about how to tell time, and Marjorie provided us information to make games out of it. Wonderful! We should have had more TIME to do these ideas justice.

Allan Evans (Sherwood School/special ed)
handed each of us a packet of M&Ms. He explained that he subbed, and would often come into a class where he would have to improvise and think on his feet. So - he figured teachers would like the M&Ms - but no eating till we're done! And then he asked for ideas on how to use them to get students to learn. "What can we do with them?" he asked. Before we ran completely out of time, he had received more than a dozen suggestions from us, among them: statistics of the distribution of the M&M colors; median, mode, average. Use them as a set of standard weights to weigh objects. Many ideas in a short time!

Section B

John Scavo (Richards Career Academy) handed out copies of Albert Einstein, The Non-Nerd's Scientist of the Century. http://www.time.com/time/time100/poc/magazine/albert_einstein5a.html. He pointed out some of the highlights to us: Interesting Biographical Facts/Timeline: eg. 1895 - failed an exam that could have let him study to be an electrical engineer. etc. And Time Dilation - some equations and discussion. Thanks, John!

Carl Martikean (Wallace HS, Gary)
reviewed some Weird Science with us, that appeared in one movie: A stray planet comes by and eclipses 3 suns at once! How come? And giant bats come out at night! Carl mentioned some movies he thought had good science: Outbreak (about the Ebola Virus) and Dante's Peak (about volcanoes). Thanks, Carl!

Earnest Garrison (Jones Commercial HS) (handout - Evolution: Rap It Up! ) http://www.accessexcellence.org/AE/AEPC/WWC/1995/evolution.html. It involves relating to students and their interests by using a CD of the rap group Salt-N-Pepa that includes their hit, None of Your Business. A set of words is provided dealing with evolution, and they are read in rap rhythm to that tune. Fun and interesting!

Porter Johnson (IIT)
presented exercises on codebreaking and construction of a regular icosahedron. The recent book on codebreaking, Between Silk and Cyanide: A Codemaker's War 1941-1945 by Leon Marks [ISBN 0-684-86422-3] describes the making of codes and communications with allied agents in Nazi-held territories. Their coordinated activities were said by General Eisenhower to have shortened the war by 3 months. Marks was inspired by the short story The Gold Bug by Edgar Allen Poe.

Now, here is your very own coded message.

  1. Zpxvx jg ywx myvw xhxva cjwlzx.
  2. Ix pqhx wyzpjwn zy rxqv xbuxsz rxqv jzgxkr.
  3. Qgd wyz ipqz aylv uylwzva uqw fy ryv ayl. Qgd ipqz ayl uqw fy ryv aylv uylwzva.
  4. Ayl uqw ymgxvhx q kyz ma olgz kyydjwn.
  5. Njhx cx kjmxvza yv njhx cx fxqzp.
  6. Gpx iqkdg jw mxqlza, kjdx zpx wjnpz.
  7. J pqhx q fvxqc.
  8. Q pylgx fjhjfxf qnqjwgz jzgxkr uqwwyz gzqwf.
  9. Zpxvx jg wyzpjwn wxi lwfxv zpx glw.
  10. J vym mqwdg mxuqlgx zpqz jg ipxvx zpx cywxa jg.
  11. J qc wyz q uvyyd.
  12. Gsxqd gyrzka, mlz uqvva q mjn gzjud.
  13. Zy mx yv wyz zy mx; zpqz jg zpx tlxgzjyw.
  14. Fqwux kjdx q mlzzxvrka; gzjwn kjdx q mxx.
  15. Zpx myyd yr wqzlvx jg ivjzzxw jw zpx kqwnlqnx yr cqzpxcqzjug.
  16. Xlvxdq.
Actually, this message is encoded in the simplest of all codes, the "transposition code", in which the letters are simply transposed with one other. The message is easily deciphered by counting the number of times that each letter appears. For this message, the number of occurrences are given here:

Frequencies of Occurrence of Letters

A 15B 01C 08D 13E 00 F 10
G 16H 07I 07J 33K 12 L 20
M 15N 11O 01P 22Q 40 R 10
S 02T 01U 13V 27W 34 X 60
Y 39Z 49--------------- -----

The key to deciphering the message is the apparently meaningless phrase ETAOIN SHRDLU, which represent the twelve most common letters in English, arranged in decreasing order of occurrence. Thus, the most frequently occurring letter in a message is likely to be E, and so forth. You don't learn anything about cryptography unless you try to decode the message, but the answers are given below.

  1. There is one born every minute.
  2. We have nothing to fear except fear itself.
  3. Ask not what your country can do for you. Ask what you can do for your country.
  4. You can observe a lot by just looking.
  5. Give me liberty or give me death.
  6. She walks in beauty, like the night.
  7. I have a dream.
  8. A house divided against itself cannot stand.
  9. There is nothing new under the sun.
  10. I rob banks because that is where the money is.
  11. I am not a crook.
  12. Speak softly, but carry a big stick.
  13. To be or not to be; that is the question.
  14. Dance like a butterfly; sting like a bee.
  15. The book of nature is written in the language of mathematics.
  16. Eureka.

It is a good "multi-cultural exercise" to remember who said each of these things.

Transposition Key

x to +e to xz to et to z
q to ta to qy to ao to y
j to oi to jw to in to w
g to ns to gp to sh to p
v to hr to vf to rd to f
k to dl to ku to lc to u
m to cb to m+ to b------

ICOSAHEDRON. An icosahedron [greek] is a solid with 20 planar faces. The regular icosahedron is one of the five Platonic Solids:

Here is the template, with gluing tabs marked by C, which you can simply enlarge and then cut out and glue along the edges to make a regular icosahedron.
         /\        /\        /\        /\        /\
        /  \      /  \      /  \      /  \      /  \
      C/    \   C/    \   C/    \   C/    \   C/    \
      /      \  /      \  /      \  /      \  /      \
    /\        /\        /\        /\        /\        /
   /  \      /  \      /  \      /  \      /  \      /
 C/    \    /    \    /    \    /    \    /    \    /
 /      \  /      \  /      \  /      \  /      \  /
\        /\        /\        /\        /\        /
 \      /  \      /  \      /  \      /  \      /
C \    /   C\    /   C\    /   C\    /   C\    /
   \  /      \  /      \  /      \  /      \  /
    \/        \/        \/        \/        \/

                                Future Meetings
          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
                            ________________     _________________
                            ________________     _________________

          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       ___________________
                            __________________   ___________________
                            __________________   ___________________

                                PAST MEETINGS
          Feb 8     A       Frana Allen          Frana Allen
                            Barbara Lorde        Barbara Lorde
                            Jean Essig           Jean Essig
                            Earnie Garrison
                    B       Barbara Pawela       Barbara Pawela
                            Zoris Soderberg
                            John Scavo
                            Earnie Garrison

          Feb 22    A       Erma Lee             Erma Lee
                            Shirley Hatcher      Shirley Hatcher
                            Glenda Ellis         Glenda Ellis
                            Beverly Merchant     Beverly Merchant
                            Camille Gales        Camille Gales
                    B       Therese Donatello    Therese Donatello
                            Charlene Smith       Ed Scanlon
                            Ed Scanlon
                            Ernest Garrison

          Mar 7     A       Allen Evans          Allen Evans
                            Winifred Malvin      Winifred Malvin
                            Alma White           Alma White
                            Margia Artis         Margia Artis
                            Marjorie Fields      Marjorie Fields
                    B       Earnest Garrison     Earnest Garrison
                            John Scavo           Charlene Smith
                            Carl Martikean       Estelvenia Sanders
                            Porter Johnson