Elementary Mathematics-Science SMILE Meeting
06 March 2001
Notes Prepared by Porter Johnson

Section A: [K-5]

Winifred Malvin (Carter School) Handouts: Oxygen; Products of Combustion
On the desk she put an assortment of jars, bottles, pie plates, candles, and matches. She placed a burning candle on a pie plate with a high flange that contained water to a depth of a few cm. Then, she put a jar over the burning candle. The candle burned for a while, and then went out. As we watched, the water level in the jar began to rise.

What happened?
Why did the water level rise in the jar?

The burning candle, which contains hydrocarbons, produces carbon dioxide CO₂ and water vapor H₂0, while consuming oxygen O₂. The water vapor tends to condense rather rapidly onto the walls, and condensation is visible. The water level rises as the volume of the gas decreases because there is a decrease in the gas pressure inside. This occurs in part because of condensation of water vapor, and in part because of the decrease in temperature after the flame dies down. We all went to the table and repeated the experiment. One of us tried it with burning paper, and found the same effect. One gets the same by-products from burning paper: water and carbon dioxide.

CO₂	Carbon Dioxide Gas
H₂0	Water (liquid or vapor)
O₂	Oxygen Gas
Vapor	Gas
Gravity	(keeps things on the ground)

Margia Artis (Wentworth School, 6th Grade) Handout: The Big Bubble Battle from The Education Center, Inc
remarked that she could always learn something in SMILE to take back to her students. She poured a 4 ounce (100 ml) bottle containing Solution C into a pie pan, and repeated the exercise with Solution A and Solution B. Here is a description of the solutions

Name	Description
Solution A	1 part Joy™ Dishwashing Liquid 3 parts distilled water
Solution B	1 part Joy™ Dishwashing Liquid 3 parts distilled water 1 part glycerin
Solution C	Miracle Bubbler™ commercially available bubble solution

We had a great deal of fun making bubbles and keeping them afloat. If time had allowed, we each would have predicted which solution would allow us to make the longest-lasting bubble, and then tested the hypotheses. Note that glycerin is typically added to bubble solutions because it keeps water from evaporating, resulting in longer-lasting bubbles.

Glenda Ellis ( Williams School) Handout: Right or Wrong
Jeremiah, a hapless student visitor, agreed to try to identify small chunks of food from their taste alone, without seeing what he ate (that is, while seated and blindfolded). The question was whether he could tell the difference in a potato and an apple. Here are the results

When he held his nose he identified the apple as a peach.
When we put an onion under his nose, he identified the potato as an apple.

Everybody came up to the table to do their own taste/smell experiment with the food chunks and with a partner. We tried to confuse the partner's taste by putting an onion under the nose.

Marie Wong (Warren School)

Handout: Gummy Bears (Aims Education Foundation 1987)
She passed out plastic bags containing Gummy Bears, and we estimated the number of GB's in our bags. A typical estimate was 14, and the bags contained 21 GB's on the average. We then counted the number of red, green, orange, yellow, and white GB's. Here are typical numbers:

	**
	**		**
**	**		**	**
**	**		**	**
**	**	**	**	**
**	**	**	**	**
RED	GREEN	ORANGE	YELLOW	WHITE

4 red ... 6 green ... 2 orange ... 5 yellow ... 4 white
We laid them out on a "sorting sheet", and made a bar graph with the GB's. Then, we colored in the bar graph with crayons of the same color, and ate the GB's.

Handouts: Help for Humpty [The Education Center Inc, 2001] and 'Tis the Season for Eggs [http://www.themailboxcompanion.com]
On the table she placed tacky glue, Elmer's White Glue™, and colored paper strips of different lengths. We used these ingredients to decorate the body parts on a cut-out sheet to make "addition people. Each body part [face, 2 legs, 2 arms, hat, bow tie] contained a different addition fact resulting in the number 7, such as 3 + 4 or 5 + 2, and the body contained the number 7 itself. the patterns were traced on different colors of construction paper, cut out, and assembled with glue by everybody. The faces were colored with crayons. Verrry interesting!

Notes taken by Earl Zwicker

Section B: [4-8]

Sally Hill (Clemente Park HS) M&M's Activities
Sally passed out small bags of M&M's to each of us, and asked us to estimate [guess!] how many pieces of candy were inside our bag. In addition, we guessed the colors from the six colors shown on the package:

Blue, Brown, Green, Orange, Red, and Yellow

The average number in the package of ordinary M&M's was near 25, and the most common color seemed to be brown. It was suggested that brown ones were easier to make, since the interior is made of brown chocolate, with a colored sugar coating.

Sally also handed out special Valentine's Day bags of M&M's. We decided that they were special because there were fewer of them in the bag (22 versus 25) and because they cost more! We recorded data in the following format [data taken by Porter Johnson are shown]:

Color	Ordinary M&M's	Valentines M&M's
Blue	5	2
Brown	5	9
Green	5	5
Orange	6	0
Red	3	5
Yellow	4	1
All	24	22

For chocoholics everywhere, Porter Johnson recommended the new film Chocolat [http://www.ram.org/ramblings/movies/chocolat.html and http://www.movielocity.com/m/r.cgi?ID=331], as well the M&M's website, http://www.m-ms.com, for information and good ideas for games. The M&M's Virtual Factory Tour is opened with the following profound assertions:

Billions and billions of years ago, life as we know it arose from this primordial chocolate ooze...
Actually, the story of M&M's^® began thousands of years ago - the Mayan and Aztec civilizations of Central America used to make a drink from the beans of the cacao tree. Spanish colonists brought the drink back to Europe in 1528, but it wasn't until over 300 years later that a method was found to produce solid chocolate.

Zoris Soderberg (Clark School)
She once again emphasized the K-Method for Effective Teaching:

Keep it Simple [as simple as possible]
Keep it Graphic [as graphic as possible]
Keep it Relevant
Keep it Safe
Keep it Fun

How do we know there is air in this room? She took a plastic [water/cola] bottle of volume about 250 cm³, and put the plastic cap-- upside down -- on the top of the bottle. Then she carefully picked up the bottle and held it in her hands for a few minutes. The air inside the bottle became warmer, and we could see the cap move a little bit, as air inside the bottle expanded and some of it left the bottle. Thus, she demonstrated that the bottle contained air.

How do we know that Oxygen is the active ingredient in air? She put a powder inside test tubes, gave one to each of us, and also gave us a wooden splint [coffee stirrer]. Then she poured a clear liquid into each test tube, and it began to interact with the powder already there, producing bubbles and foam. Then we each lit our splints and blew them out, quickly inserting the splint with glowing embers into our test tube. To our delight, we saw the embers on the splint burst into flame inside the test tube, indicating that oxygen was being produced in the reaction.

What happened? The powder was obtained from a package of cooking yeasts, and the liquid was Hydrogen Peroxide, H₂0₂. The enzymes in the yeast served to catalyze the chemical reaction that produced free Oxygen -- 0₂:

2 H₂0₂ ® 2 H₂O + 0₂

There was discussion as to whether the yeasts had to be alive to catalyze this reaction. The feeling was that they probably should be, although the chemical reaction is different from that in baking bread. In the latter, one catalyzes glucose C₆H₁₂0₆ to produce ethyl alcohol C₂H₅OH and carbon dioxide CO₂:

C₆H₁₂0₆ ® 2 C₂H₅OH + 2 C0₂

This chemical reaction is the same as than in brewing ethyl alcohol from mash. Most of the ethyl alcohol evaporates during the baking process, but bread does contain a small residual amount of ethyl alcohol.

For the coup de grace, she put a full package of cooking yeast into a large jar [liter/quart], and added about 50 ml of Hydrogen Peroxide. Then, she held a piece of steel wool inside the jar, and put the glowing splint inside, as before. The steel wool burst into flame and burned to glowing embers in the oxygen-enriched atmosphere. Why did that happen? Very impressive, Zoris.

Don Kanner (Lane Tech HS) Sound
He introduced the following terms relating to sound waves:

f	Frequency (number of oscillations per second)
l	Wavelength (peak-to-peak distance)
v	Wave speed
v = f ´ l	Connection of speed, frequency, and wavelength

He illustrated the relation v = f ´ l by taking a plastic straw and blowing on the ends of it to produce sound. He was able to get a good sound out of a straw [it sounded somewhat like a Kazoo] by rubbing it flat on one end, cutting a little off that end, and then cutting small notches on both sides to make a "V" with point facing toward the mouth. In effect, he was able to create a double reed for the straw, like an oboe. As he shortened the straw by cutting off the other end with scissors, the pitch [frequency] of the sound increased. Why? The velocity of sound, v, is about 330 meters/sec. When the straw is shortened, the wavelength l of the sound produced, being comparable to the length of the straw, decreases. Thus, the frequency f increases, since v does not change. It must be true! Don recommended visualizing it with the following formula:

v = f ´ l = f ´ l = f ´ l

He illustrated the point another way by blowing over the lip of a partially filled plastic bottle [250 cm³] producing a fairly low pitched sound. Then, he drank some of the fluid in the bottle, and blew again. The pitch was definitely lower. Since he had made the region of air in the bottle larger, sound was produced at a larger wavelength, and the frequency or pitch was reduced. Simple, non?

The shape of musical instruments determines the amount and pitch of sound that comes out of them. Don illustrated this in several ways:

He took a very long straw [actually, several straws connected], to illustrate that the resulting sound was low-pitched, as in a tuba. He showed that the sound did not change when he bent the straws and wrapped them around his head; the only important consideration being the length of the straws. The same is true of musical instruments, such as the trumpet, French horn, and Sousaphone.
He cut off the top 8 cm (3 in) of a plastic coke bottle (to form a bell or bellows), and punched a small hole in the cap so that the round end of a straw would fit tightly into the hole. We were surprised that the sound was much louder [and more like an English horn] because of the presence of the bellows on the end. Because of the bellows, more sound was transmitted into the air, and the tone became somewhat richer.
He then notched a small hole in the side of the straw, and played it while placing his finger over the hole. When he removed his finger from the hole the pitch went higher. He was able to produce sounds of a different pitch (frequency), using the same mechanism as in a clarinet, saxophone, or fluto-phone.
Finally, he put a bigger straw over the smaller notched straw, and played as he moved the straw up and down, thus illustrating the action of a trombone.

His presentation is based upon the 1989 Royal Institution [London] Christmas Lecture Video entitled What is Music?, given by Professor Charles Taylor. For additional references on musical acoustics see the websites http://www.phys.unsw.edu.au/music/ and http://www.acoustics.org/press/137th/rossing1.html.

Porter Johnson then told a Physics Joke:

Q: What does a 500 pound canary say?
A: Chirp!!! (very low-pitched, because of the size of the bird.)

Marva Anyanwu (Wendell Green) Handout: Floating in Space (Scholastic Inc 2001)
She mentioned that the International Space Station [ISS] has been occupied by astronauts since November 1999, in an environment of Weightlessness, or Micro-gravity. To illustrate the effect of this apparent weightlessness, she took a transparent plastic jar, cut a large rubber band, and suspended it inside the jar, after placing a small amount of putty on its end. The rubber band was held in place at its top end as she tightened the the lid of the jar on it. The rubber band was stretched by the weight of the putty at its free end. Then, she dropped the plastic jar.

Q: What happens to the rubber band as the jar falls?
A: It shortens and the putty floats! The weight of the putty no longer stretched the band as it falls.

This experiment illustrates weightlessness in the ISS. Gravity still exists there, and is nearly as strong as on earth, but because the spacecraft is "falling in its orbit", the inhabitants experience weightlessness. We listed other examples of weightlessness:

Roller Coasters at amusement parks.
Falling in an elevator.
Going over an incline in an automobile.
Hitting an air pocket in an airplane.

Porter Johnson expanded upon the issue of apparent weightlessness on the space station. If you climbed up a tower [or a bean stalk] and jumped off, you would fall to the ground, even if the tower were hundreds of miles high. The space station doesn't fall straight down, because it is moving around the earth with speeds of about 8 kilometers/sec [5 miles/sec]. The space station is continually falling [accelerating] toward the center of the earth (as required by the force of gravity and Newton's Second Law: F = m a ), its sideways motion takes it away from the earth at the same rate that it falls. The result is a circular orbit about the earth.

Notes taken by Porter Johnson