Elementary Mathematics-Science SMILE Meeting
28 November 2000
Notes prepared by Earl Zwicker
http://www.iit.edu/~smile/
SAFETY TIP: Heating Water in a Microwave Oven
I feel that the following is information that any one who uses a microwave oven to heat water should be made aware of. About five days ago, my 26 year old son decided to have a cup of instant coffee. He took a cup of water and put it in the microwave to heat it up (something that he had done numerous times before). I am not sure how long he set the timer for but he told me he wanted to bring the water to a boil. When the timer shut the oven off, he removed the cup from the oven. As he looked into the cup he noted that the water was not boiling but instantly the water in the cup "blew up" into his face. The cup remained intact until he threw it out of his hand but all the water had flown out into his face due to the buildup of energy. His whole face is blistered and he has 1st and 2nd degree burns to his face which may leave scarring. He also may have lost partial sight in his left eye. While at the hospital, the doctor who was attending to him stated that this a fairly common occurrence and water (alone) should never be heated in a microwave oven. If water is heated in this manner, something should be placed in the cup to diffuse the energy such as a wooden stir stick, tea bag, etc. It is, however, a much safer choice to boil the water in a tea kettle. Here is what our science teacher has to say on the matter:

Thanks for the microwave warning. I have seen this happen before. It is caused by a phenomenon known as super heating. It can occur any time water is heated and will particularly occur if the vessel that the water is heated in is new. What happens is that the water heats faster than the vapor bubbles can form. If the cup is very new then it is unlikely to have small surface scratches inside it that provide a place for the bubbles to form. As the bubbles cannot form and release some of the heat that has built up, the liquid does not boil, and the liquid continues to heat up well past its boiling point. What then usually happens is that the liquid is bumped or jarred, which is just enough of a shock to cause the bubbles to rapidly form and expel the hot liquid. The rapid formation of bubbles is also why a carbonated beverage spews when opened after having been shaken.

PLEASE PASS THIS INFORMATION ON TO FRIENDS AND FAMILY!
                      OUR LAST MEETING
                      OF THE SEMESTER...
                             ...will be December 12, 2000
                                        4:15 p.m.
                    Section A (K-5) meets in 111 LS
                    Section B (4-8) meets in 152 LS
                  SECTION   PRESENTATIONS        REFRESHMENTS
          Dec 12    A       Leticia Rodriguez    Nancy Katich
                            Willie Mae Merrick   Monica Ban
                            Pearline Scott       Elizabeth Cowan
                            Virginia O'Brien     Anne Genther
                            Iona Greenfield      Sophia Watson
                            Margie Fields
                            Sophia Watson

                    B       Val Williams         Val Williams
                            Chris Etapa          Chris Etapa
                            Marva Anyanwu

                               SEE YOU THERE!!

SECTION A (K-5)

Francesca Drnek (Brunson School)
started us off with a quiz - What Is Your Banana IQ? - (handout) with a set of 10 True/False statements.  Here are 2 examples.

When we had finished our answers, she gave us a page - The BIG Banana Peel, which asked the question: What part of the banana is edible?, and instructing us: Use your BANANA to find the answer. And she handed out bananas so that each group of two of us received one, along with a colorful plastic balance to make weighings. We had to complete the table on the page by finding 

Francesca drew a copy of the table on the board, and then asked some of us who had completed it at our desks tell her our data, which she then used to fill in the table on board, for all to see.

 So we were able to make a comparison, and she gave us a page with such a table to fill in for Bananas A, B, C, D, E - and find averages of each measured and calculated quantity. A bar graph could be constructed on the bottom half of the page. Finally, she gave us a 4 page copy of information about the Banana Plant. By this time we eagerly read it, and learned the correct answers to the quiz that we had taken at the beginning; The banana is a berry! Bananas do not grow on trees - the banana plant has no trunk but is rather a gigantic herb growing from an underground stem. She then reviewed with us the quiz and which statements were true or false. Wonderful, Francesca! A real phenomenological approach.

Monica Ban (Anthony School)
placed on the table for all to see: a transparent plastic vase (10 3/4 inches high!), a 6 or 4 inch Spathaphyllum Plant (Peace Lily), a plastic bag containing water and a fish! - and other stuff. She gave us a handout: 

The Amazing Betta Vase:! - The Easiest Pet You Have Ever Owned!
which provides all the details. She explained what she was doing as she assembled the parts. Soon she had constructed a vase containing the plant, and we could clearly see its roots nearly filling the upper part of the bulbous bottom of the vase. And the male Betta fish (the Siamese Fighting Fish) was swimming around in the bottom of the vase, beneath the plant's roots! 

The handout provided an Introduction, Objective, Materials, Procedure, Results, and Maintenance Hints.

Monica gave us the  website http://www.gardening.com (Gardening Magazine) as a reference, along with Terry's Aquarium/Pet Co. To top it all off, she had a beautiful Betta Vase as a giveaway to the lucky number-drawer, who happened to be Ken Schug! A great idea to promote student interest in biology and an eco-system (but not necessarily the fairness of lotteries!). Thanks, Monica!

Elizabeth Cowan (Anthony School)
set up a colorful display on the table showing these four books about Magnets, and a variety of magnets and materials to experiment with.

She gave us photocopied pages with these titles:
Magnets (FS-83129 Physical Sciences), which described Concepts ("Magnets are objects that will pick up or attract things containing iron or steel." etc)
Discovery Through Experiments (Magnets Attract, Magnetic Force Passing Through Materials)
Language Arts Connection (Magnets & Their Uses)
Math Connection
Art Connection
Science Connection
Literature Connection

This was followed by pages with experiments to do: Magnets Attract - Question: What are some objects that magnets attract? Materials: magnet, paper clip, key, scissors, rubber band, penny, piece of foil, nickel, toothpick, soda can, nail, chalk, crayon, button, marble, etc. A record sheet followed to record observations for each object: Predict, Record (observed). And then Think & Write: In what way were the objects that the magnet attracted alike? etc. Elizabeth invited us to the table to find the answers for ourselves, and soon we were crowded around, using the materials to do so. We saw objects attracted, repelled, and iron filings on a piece of paper formed a changing pattern when a magnet was held under the paper and moved around. Fascinating! A beautiful way to involve students in their own learning!

Nancy Katich (Burnham/Anthony, K/primary)
did 100th Day Activities with us, and gave out a 2 page write-up. A colorful display of 5 children's books was set up, and other materials set out on the table. She then did a variety of the activities with us, including Watch Cassie Grow. Cassie is a caterpillar, and Nancy had created Cassie on the board for us to see. A series of paper circles (about 4 inch diameter) were stuck to the board in a row. They were a bright green, and the first circle had a face and pipe cleaner antennae. They were consecutively numbered, with the 5th, 15th, etc. circles in white, and the 10th, 20th, etc in orange. Starting with just Cassie's head (first circle with face) on the board, with each passing school day another segment (circle) of Cassie's body would be added. By the 100th day, it would be 100 circles long! - perhaps sometime in January of the school year. And then a big, beautiful paper butterfly would appear on the board! - Cassie had metamorphosed! What a great way for students to learn counting, 5s, 10s, and something about the life cycle of a caterpillar. Examples of activities:

 Nancy showed us examples of many of these completed activities. She asked a colleague, Anne Genther, to come up, and hung a necklace - made by stringing 100 Cheerios O's on a string - around Anne's neck, and then placed a colorful paper crown on her head with the words "100th Day" printed on it. Also listed in the handout were Student Books (15 references), Teachers Resources (5 books). See also the website "100th Day of School": http://users.aol.com/a100th day/links.html. What an exciting set of ideas to stimulate youngsters to learn, and to enjoy learning!

Anne Genther (Burnham/Anthony, K-3)
gave us a handout: Domino Activities, with 12 pages from the following reference:
Math Activities with Dominoes, by Helene Silverman and Sandy Oringel, [Cuiseneaire Company of America 1996] ISBN 1-5745-2027-X.
She listed these objectives, among others:

Activities: Usually done in pairs or small groups, open-ended. Can easily be adopted to the needs of any class. Can be modeled on chalkboard or overhead. etc. She then gave pairs of us a plastic bag containing a set of dominoes, along with a page titled: I'm All Set, with a drawing of two large intersecting circles and a space for a number card associated with each circle. (The instruction page for teachers informed us that the circles form a Venn diagram, and described Task, Set-up, Start-up, Discussion, Wrap-up.) Soon we were busy following Anne's directions. We placed a number card (provided by Anne) in the each of the spaces. (We got a 4 and a 6.) Then we had to place the dominoes with 4's in the 4's circle, the dominoes with 6's in the 6's circle, and the dominoes having both a 4 and a 6 in the common area of the intersecting circles. What a fun way for kids to learn to count, sort, compare, and to recognize patterns! Other activities (we didn't have time to do) were the following: 

 Learning is enjoyable and dynamic with such good ideas! Addition and subtraction math skills may also be developed using dominoes. Thanks, Anne!

Monica Seelman (St. James School)
passed out 4 sheets of paper (11 x 17 sq inches, white) to us, and scissors. She then instructed us how to make a "book." Sure enough! With a very few scissors cuts and a clever assembly idea, we each had constructed a "book" which having 16 pages, and which held together very nicely to form a "book!" A great trick!

Next, Monica gave us a 6 page handout with instructions of how to draw stars: For K-2, the Star Man - a 5 pointed star with face, body, arms and legs. She showed us how to do this at the board. For grades 1-3, make an 8 pointed star beginning with a tic-tac-toe grid. Then came Star Geometry (grades 4-6), and she pointed out a 5-pointed star has a prime number, and 6-pointed is not. This led on all the way up to a 12-pointed star and the rules for forming such a star. The greater the number of points, the closer the resulting star/polygon approaches a circle. Beautiful math ideas from such a humble beginning, Monica! Thanks!

Notes taken by Earl Zwicker

Section B: (4-8)

John Scavo (Evergreen Park HS)
gave us copies of articles from the Sunday 26 November Chicago Sun Times. One, entitled New Find Completes Long-necked Dino, concerned discoveries made on the edge of the Sahara Desert in Niger. A web-site was given: http://www.projectexploration.org. Other articles:

"Are obesity and virus linked?"
"DNA testing could prove links to Lincoln."
"Coronary stent now standard."
Interesting science reading, John. Thanks!

Carl Martikean (Wallace School, Gary)
showed us some interesting ice stuff. He had two containers that looked like they were partly filled with water. He put a piece of ice in one, and it floated. But when he put a piece of ice in the other container, it sank! How come? After some discussion, Carl revealed the answer. The liquid in which the ice sank was isopropyl alcohol, with a density of about 0.80, and not water; density 1.00! He then mentioned that Heet™ (a commercial product to add to auto gasoline tanks in winter) will dissolve a small amount of water in a gasoline tank, preventing the water from freezing and stopping the gas from getting to the engine. Next, Carl had a question for us: If ice is floating in water, and it then melts, does the water level change? Answer: No! But if the ice is held completely submerged under the water, and then melts, the water level will drop. Why? Explanations? (Answers next time?) Good puzzler, Carl!

Emma Norise (Dunbar Career Academy)
gave us a chemistry experiment (3 pages) Is It an Acid, Base, or Neutral Liquid? Emma then passed out equipment so all of us could be involved in doing the experiments. The first step is to make a pH indicator by boiling red cabbage leaves and drawing off the colored liquid. Emma had prepared this for us; we each got some. The pH of a water solution tells us how acid or basic it is. The red cabbage liquid tells us that by its color: pink is acid, dark blue or greenish is base. So we did the experiments and got the results indicated in the table below. 

          substance       acid or base           color

          baking soda       mild base            greenish
          lemon juice       acid                 pinkish
          grapefruit juice  acid                 pinkish
          water             neutral              greenish
          milk of magnesia  mild base            greenish
          vinegar           acid                 pink
We checked IIT water (greenish), and 7-Up (pink/acid). [For more details see the recent smile lesson bc101000.htm and the website http://chemistry.about.com/library/weekly/aa012803a.htm. Good stuff, Emma! Thanks!

Bernina Norton (Abbott School, 6th grade)
showed us some new ideas on math from the Math Fair: Historical Connections in Multiplication (1992 AIMS Education Foundation). [https://openlibrary.org/works/OL8678227W/Historical_Connections_in_Mathematics]  First came the Russian Peasant Method of Multiplication, and Bernina gave us a dandy one page handout showing how to do this. She had us work through some examples on our own; it worked! Here's how:

          To multiply 18 X 25

          Divide by 2 and
          discard           Double this
          remainders        column

             18 -------------   25          Cross out all the rows
                                            which have an even
              9                 50          number on the left.
                                            Then add up all the
              4 -------------  100          remaining numbers on
                                            the right.
              2 -------------  200

              1                400
                             ------- 
                               450  our final answer

Used during the 1800's, and still in use in some parts of Russia. An unusual process to us, but according to Porter Johnson it is closely related to binary arithmetic.  The first factor 18, which can be written as

18 = 16 + 2 = 24 +21,

has the binary representation 100010.  Note that 16 X 25 = 400, and 2 X 25 = 50; we add these answers to get 400 + 50 = 450.

Next, she took us through Lattice Multiplication via another handout, same source. Used by the early Hindus, she had us work through some problems with this method. Here is an example:

76 x 98 = 7448

First form the figure 

                      	_______________
                        |     /|     /|
			|    / |    / |
			|   /  |   /  | 
			|  /   |  /   |
			|_/____|_/____|
                        |     /|     /|
			|    / |    / |
			|   /  |   /  |
			|  /   |  /   |
			|_/____|_/____|
and write the two factors to be multiplied on its top and left sides, as shown: 
                           7      6 
                	_______________
                        |     /|     /|
			|    / |    / |
			|   /  |   /  |
			|  /   |  /   |    9
			|_/____|_/____|
                        |     /|     /|
			|    / |    / |
			|   /  |   /  |  
			|  /   |  /   |    8
			|_/____|_/____|
Now, multiply the each number on top with each number on the right, and put the factors in the corresponding sub-region. For example, 6 X 9 = 54 (top right). 
                           7      6 
                	_______________
                        |     /|     /|
			|    / |   /  |
			| 6 /  | 5/   |
			|  / 3 | /  4 |    9
			|_/____|/_____|
                        |     /|     /|
                        |    / |    / |
                        | 5 /  | 4 /  |  
                        |  / 6 |  /8  |    8
                        |_/____|_/____|
Now, add along the diagonal slices, as shown: 
                          7      6 
                	_______________
                        |     /|    / |
			|    / |   /  |
			| 6 /  | 5/   |
            	  6	|  / 3 | /  4 |    9
			|_/____|/_____|
                        |     /|     /|
			|    / |    / |
			| 5 /  | 4 /  |  
			|  / 6 |  / 8 |    8
		 13	|_/_ __|_/ ___|

              		   14      8
Now, put the numbers in columns and add, as shown: 
    
            8
          14 
         13 
       __6_____
         7448
The answer, 7448 appears.

You will have to study this example to appreciate the method. If you reverse the factors in the multiplication (98 x 76), the same numbers appear (in a different order) in each diagonal slice.  Thus, when you add them, you get the same answer.  Clearly,  you must have 98 X 76= 76 X 98, according to Porter Johnson.  Although this method is a variation of the ordinary method of multiplication, the relation a  X b = b X a  [multiplication is commutative] is more evident in this approach. Cool stuff, Bernina!

Notes taken by Porter Johnson.