Elementary Mathematics-Science SMILE Meeting
08 May 2001
Notes Prepared by Porter Johnson

Section A: [K-5]

Betty Marshall [Gregory School, 4th grade] Handout: Glue Goo, developed by Lynn Higgins [708] 447-6339
put the following items on the front table:

• 20 Mule Team Laundry Booster™
• Elmer's Glue A™
• water in containers
• Sealable plastic bags
• Empty containers
• food coloring bottle (green)

We mixed 4 parts of thinned glue to 1 part of borax solution, and began to knead a small amount of the mixture in our hands.  After several minutes, we began to get the final form.  We fine-tuned by adding  small amounts of glue or borax, as appropriate.Then, some of us added a small amount of green food coloring to the mixture, so that our mixtures were either green, white, or somewhere in between.  The mixture eventually stuck to itself, and ceased to stick to our hands.  When we threw it onto the table, it would bounce a little, and then quiver.  It could be shaped into a serpentine [snake-like] form, a ball, or whatever.  The material form is called a polymer. Very nice, Betty!

Lori Fugate [Leland School, 2nd Grade] Handout: Dancing Raisins
gave each of us a small box [1/2 ounce] of raisins, and we made estimates as to how many raisins were in the box, and then we counted the number of raisins.  Then we drew a bar graph of the number of people whose box had a certain number of raisins:

```                   Number of Occurrences

_|
_|                   X
_|                   X
_|                   X
10   __|                   X
_|                   X
_|                   X
_|                   X
_|                   X
5   __|                   X
_|    X              X
_|    X              X
_|    X              X
_|    X           X  X  X
|____X________X__X__X__X__________
|  |  |  |  |  |  |  |  |  |  |
|              |              |
25             30
Number of Raisins
```

Next we considered what happens to the raisins when we mix them with 7-UP™

Raisins sink since they are more dense than water.  However, the 7-UP™ contains bubbles of CO2 that are less dense than water.  These bubbles collect on the raisins, causing them to float.  When they reach the surface, the bubbles pop and the raisins sink to the bottom again.  The cycle is repeated.  It works best with regular 7-UP™, rather than the diet variety.  Also, it helps to shake up the 7-UP™  can before pouring it into the glass.

Thanks, Lori!

Jeanine Frazier [Pullman School] Volume
placed the following items on the front table

• several gallon plastic jugs, filled with water
• 5 empty quart plastic bottles
• 5 empty pint milk cartons
• 4 plastic measuring cups

Scattered on the table, there were many sheets of paper with questions on them.  For example:

• How many quarts are there in a gallon?
• What is 4 pints, in gallons?
• How many pint in a gallon?
• How many cups in a half-pint?

We worked in groups of 2 or 3 to find the answers to these questions.  Good work, Jeanine!

Notes taken by Earl Zwicker

Section B: [4-8]

Marva Anyanwu [Green School, K-8 Science Teacher] Aerodynamics
divided us into groups and set up each group to construct a wind tunnel, using the following materials:

• 2 liter plastic pop bottle
• 2 paper clips
• plastic drinking straw
• scissors
• duct tape
• manila file folder
• air-filled composite targets of various shapes
• air source [hair dryer or fan]

We built the wind tunnel by completing the following tasks:

• remove base from plastic bottle by soaking it overnight
• cut ends off bottle to make a hollow cylinder
• cut circular hole (half-diameter) out of base
• attach outer part of base around one end of cylinder, cutting slices out of the cylinder end and attaching with duct tape
• cut a 1 cm ´ 1 cm hole out of lateral surface of the cylinder half-way down.
• stick paperclip about 1 cm into one end of plastic straw, and attach to straw with duct tape
• use other paper clip to pivot straw at hole about 5 cm from paper clip (which is inside the cylinder), punching a hole in the straw with the paper clip and attaching it to the outside of the cylinder with duct tape
• attach remainder of base to cylinder opposite hole with duct tape, to serve as base
• attach paper protractor to inside of manila file folder, to serve as an indicator of the "tilt angle" of the straw
• attach a  shaped target [triangles, rectangles, circles, about 5 cm on a side] to inside paper clip perpendicular to center line of cylinder
• turn on the air source, and note the "tilt angle" of the straw

The groups observed that the area of the shaped target  was the most important feature, and that with shapes of the same area there was a smaller tilt with triangular shapes than rectangular shapes.

One group observed that, with the fan with a baffle in front, the straw tilted toward the fan when the fan was aimed directly at the target shape, indicating that air was actually flowing toward the fan in that case.  When the fan was "off center" in relation to the target, there was indication of strong flow away from the fan.  Also, the hair dryer produced a steady and uniform blast of air, which became quite warm in a few seconds.

Marva also handed out a sheet describing two additional exercises:

• Dancing Spaghetti:  Put a baking soda solution into a tall jar [2/3 full] and put 15-20 pieces of raw spaghetti of length about 5 mm into the jar.  Then, pour a little vinegar into the jar, and note the bubbles of CO2 that are formed.  If you have enough ingredients present, gas bubbles that attach to spaghetti pieces will lift them to the surface.  Take that, Archimedes!
• The electric Banana:  Suspend a banana by a thread, and rub a hard rubber comb on a piece of wool or fur to generate static electricity.  Bring the fan close to the banana but do not touch it.  Can you  get the banana to rotate because of the charge on the comb by moving the comb around?

Very interesting, Marva!

Roy Coleman [Morgan Park HS] Puzzle
wrote the following pattern on the board:

```      |      |      |      |      |      |      |      |      |
| ____ |      |      | ____ |      | ____ |      |      |
||     ||     ||     |      |     ||     |||     |      |
____ ||____ ||     ||     |      |     ||     |||____ |      |
||     |     |||     ||     ||     |      ||     |  ??  ||
||____ |     |||     ||____ ||     |      ||____ |      ||____
|      |      |      |      |      |      |      |      |
|      |      |      |      |      |      |      |      |
```
What should go in the region in which ?? is located?  The answer is based upon the pattern for displaying numbers on hand-held calculators, which involves a display on which any of seven lines are present. The number 8 involves all seven lines whereas the number 4 has four lines and the number 7 three lines, as shown:
```          ____                           ____
|    |         |    |               |
|____|         |____|               |
|    |              |               |
|____|              |               |

```
Roy's pattern shows a complementary image, in which only the "unlit" lines are shown. Let us put in the lighted lines by using the * symbol:
```      |      |      |      |      |      |      |      |      |
**** | ____ | **** | **** | ____ | **** | ____ | **** | **** | ****
*    *||    *||    *||    *|*    *|*    ||*    |||    *|*    *|*    *
*____*||____*||*****||*****|******|*****||*****|||____*|******|******
*    *||    *|*    |||    *||    *||    *|*    *||    *|*    *||    *
******||____*|*****|||*****||____*||*****|******||____*|******||____*
|      |      |      |      |      |      |      |      |
```
Taking away the | symbols, and then replacing "*" by "|" and "_" in the appropriate places, we obtain the pattern:
``` ____          ____   ____          ____          ____   ____   ____
|    |      |      |      | |    | |      |           | |    | |    |
|    |      |  ____|  ____| |____| |____  |____       | |____| |____|
|    |      | |           |      |      | |    |      | |    |      |
|____|      | |____   ____|      |  ____| |____|      | |____|      |

```

Porter Johnson [IIT] mentioned that the letter sequence o, t, t, f, f, ... is difficult to understand, until you realize that it is "shorthand" for the following:

one, two, three, four, five, ...

Roy Coleman asked  why put the numbers in this order: 8, 5, 4, 9, 1, 7, 6, 3, 2, 0.  The answer: alphabetical order:

eight, five, four, nine, one, seven, six, three, two, zero

Bernina Norton [Abbott School] Fractions with Egg Cartons
Take the bottom half of an egg carton, and divide it into the various parts using 1 cm ´ 10 cm paper strips, being careful not to split any egg locations:

halves (6 / 12), thirds (4 / 12) , fourths (3 / 12), sixths (2 / 12)

Now take colored paper squares [about 3 cm ´ 3 cm] and put them in the egg locations to make the following fractions:

 6/12 4/12 3/12 2/12 Ý ß Ý ß Ý ß Ý ß 1/2 1/3 1/4 1/6

For example, here is the representation of  the fraction 1/2 = 6/12:

 ¨ ¨ ¨ ¨ ¨ ¨

Next she showed us how to teach addition of fractions using three egg cartons. The well-behaved class members got to perform this exercise using Hershey™ Chocolate Bar squares, whereas the rest of us used the paper squares.  For calculating the sum 1/3 + 1/4, we filled 1/3 of the slots [4/12] in the first carton, and 1/4 of the slots [3/12] in the second carton, and then put all of the squares into the third carton [4/12 + 3/12 = 7/12].  Similarly, we used the egg cartons to show that

1/2 + 1/3 = 6/12 + 4/ 12 = 10/12 = 5/6.

Bernina gave us a handout that described making comparisons between fractions, such as 5/6 > 2/3, since 5/6 = 10/12 and 2/3 = 8/12, and 10/12 > 8/12, because there are more squares in the egg carton for 10/12 than for 8/12.

Neat-o!

Notes taken by Porter Johnson