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

Announcements:

Long term SMILE staff member Lee Slick [Morgan Park HS] was hospitalized for observation and tests after experiencing cardio-vascular symptoms recently. He is expected to return home shortly, and can be contacted through email at slicfre@iit.edu.
The SMART program will have two independent sessions during the period 09 - 20 July 2001. These sessions will be held from 9 -12 am and 1 - 4 pm, respectively, during weekdays for that period. Please be sure to sign up for one of these sessions if you would like to participate. Sign-up sheets are available in current SMILE and SMART classes, or you may contact IIT Staff Members directly. Note that there will be no SMILE program for Summer 2001.
A special guest, Shyla McGill of Columbia College, will come to the Elementary Math-Science SMILE B meeting on 24 April 2001 to describe and explain her program of Hands-on Mathematics Instruction for students with weak math skills
Columbia College is sponsoring Physical Science Workshops for teachers of Grades 7, 8, and 9 the Summer of 2001 through the Institute for Science Education and Science Communication. For details call (312) 344-7544.

Section A: [K-5]

Barbara Hill (Fernwood School 1-5 Special Education) Handout: Geometry in Pictures, Pillows, and Places
placed transparent sheets with images of two dimensional [rectangle, triangle, square, circle], as well as some three dimensional geometrical objects [tetrahedron, cone, cube, sphere, prism, and cylinder] on the table. In addition she gave us a big sheet of cardboard stock [about 20 cm ´ 50 cm] and a plastic metric ruler. Then we began to work on her 5 week lesson plan on Pictures, Pillows, and Places.

Week #1: Barbara gives the directions, then models what her students should do. Everybody picks a shape, and draws it carefully onto the cardboard. Then, they go around and find an image or object with that special shape.
Week #2: Students look for various shapes in their local environment.
Week #3: Students investigate volume and surface areas by measuring pillows of various shapes.
Week #4: Students study slides of Chicago Architecture and look for various shapes. [See the recent SMART program lesson The Virtual Math Trail by Bernadette Dvorscak: http://www.iit.edu/~smart/dvorber/lesson1.htm.]
Week #5: Students make drawings of the various shapes, find the corresponding real objects, arrange for musical accompaniment, and do a "walkabout" carrying their special shapes. They then stand together holding their special objects, and photos are made.

We posed for Barbara for our group photograph, but unfortunately there was no film in her camera! What a shame!

Joyce McCoy (Spencer School Head Start 3-5 year olds) Preparation of a Windsock
put the following ingredients on the table:

glue
decorated paper
sheets of colored paper
crayons
Bo-a-Pot kit (plastic bags with colored yarn and various pretty streamers

We came up to the table and made our own Windsocks. Very good, Joyce. For additional information see the websites, A Variety of Ways to Make a Windsock, http://www.track0.com/canteach/elementary/earthspace16.html and Wind: http://eduscapes.com/42explore/wind.htm.

Cynthia Southern (Spencer School Kindergarten)
Handout: Where's the Mathematics? (The Super Source, Cuisinaire 1996). She had us make planar geometric figures using rubber bands on a square lattice with a 5 ´ 5 array of smooth plastic "nails" sticking through it. The device, called a Geoboard, can be used to make triangles, rectangles, and squares of various sizes and shapes, to illustrate concepts of geometry at an elementary, constructive level. Students construct the figures, cut out paper models the same size and shape as the figures, and consider questions like these

What is the difference in a square and a rectangle?
Are diamonds the same as squares?
When are two figures geometrically similar?
When are two figures the same?

At first students are apt to make figures with the sides parallel to those of the Geoboard, but they will learn to make other shapes. Very good, Cynthia! For additional ideas concerning Manipulative Mathematics, see the website http://nlvm.usu.edu/en/nav/vlibrary.html.

Notes taken by Earl Zwicker

Section B: [4-8]

Earnest Garrison (Jones Academic Magnet HS) Electromagnetism
He showed how to unify the presenting of the topics of Electricity and Magnetism using phenomenological exercises, rather than following the traditional approach of separating these topics:

First he passed around a pair of small but strong magnets (5 mm diameter; cylindrical), and showed that these magnets were strong enough to hold one another in place by attraction through the wooden desk tops [about 3 cm thick]. The magnets, which were made of a Neodymium alloy, are much more powerful than the ALNICO [Aluminum, Nickel, Copper] magnets in vogue years ago.
Then he showed and passed around a sealed transparent vessel containing mineral oil fluid, with iron filings in suspension. The vessel had a small [1 cm diameter] cylindrical tunnel through its center, into which we inserted an iron rod with a strong magnet stuck on its end. This produced a magnetic field inside the fluid, and when we shook the vessel the iron filings aligned with the field, clustering around the inside tube. Thus, with no muss and no fuss we could use iron filings to show the field directions in three dimensional space, without getting iron filings all over the room and all over ourselves. The filings line up with the field for the same reason that a compass points North. A commercial product, a Magnetic Field Observation Box [P8-8001 $92.00] is available from Arbor Scientific: [http://www.arborsci.com/]. Here is a picture:
Roy Coleman [Morgan Park HS] remarked that there is a magnet at the Physics Department of Lake Forest College, which had the usual North-South configuration, until it was accidentally dropped on the floor. It was then found to have the very peculiar configuration of South-North-South. Believe it or not!
Earnest then got out a set of Christmas Lights, and showed that when one light on the chain was removed, all the lights went out. The observation that either they all work or else none of them work is an indication that the lights were connected in series in the string.
Earnest took two identical lights consisting of small bulbs in sockets with wires to external terminals.
1. He hooked one of the lights to a 6 Volt battery, and we saw that it burned brightly.
2. He attached the two bulbs in series to the battery. We noted that the bulbs were less bright, and decided that this happened because there were only 3 Volts across each battery.
3. He attached the two bulbs in parallel across the battery. The bulbs were much brighter --- in fact, they were each as bright as in the first case. We felt that there were 6 Volts across each bulb, and that they should each "feel" the full electric potential of the battery.

To unify the subjects of electricity and magnetism, he made an electromagnet by wrapping a copper wire [with thin plastic insulating coating] many times around a common iron nail [10d, if you're big on English Units] and attaching the wire ends to the 6 Volt battery. We used several of these electromagnets to pick up paper clips. We counted the number of turns of wire, and compared the number of (iron) paper clips picked up and held with the number of turns. Here are typical data:

Number of Turns of Copper Wire	Number of Paper Clips Held
70	12
127	19

We concluded that, the more turns of wire around the nail, the stronger the magnetic field, and the more paper clips held up. Very interesting, Earnest!

Earnest led a discussion about the difference in a big battery and a small battery. He asked whether the bulb burns brighter with a big battery than with a small one. We decided that the Voltage produced by the battery determined how brightly the bulb would burn, whereas the size of the battery might determine its capacity, and thus determine how long the light would burn before the battery was discharged.

Porter Johnson asked what was the difference between these standard types of 1.5 Volt batteries:

AAAA, AAA, AA, A, B, C, D In particular [1]What's inside these batteries? and [2] How come they all produce the same voltage? He explained that inside a 1.5 Volt (Leclanche) dry cell battery there is a Zinc anode, a Manganese Dioxide cathode, and an aqueous ammonium or zinc chloride electrolyte that is "gelled" by addition of an inert metal oxide. Details are described at the URL http://www.powerstream.com/BatteryFAQ.html#lec. The same voltage is produced in all dry cell batteries because they all are driven by the same chemical reactions. These reactions are complicated, but for full discharge of the battery can be considered approximately to be the following: Zn + MnO₂ +2 H₂O + ZnCl₂ Û 2 MnOOH + 2 Zn(OH)Cl A 6 Volt dry cell battery contains four independent 1.5 Volt dry cell batteries that are hooked in series. [For comparison, the basic 12 Volt automobile battery actually contains 6 independent lead-sulfuric acid wet cells hooked in series, each producing about 2 Volts.] Here are some additional sources of information about batteries:

Internal Structure of Dry Cell Battery: http://www.edinformatics.com/inventions_inventors/battery.htm
Principles of Battery Operation: http://www.britannica.com/ and search for 'battery operation'.
Battery Information V1.00: http://www.repairfaq.org/ELE/F_Battery_info.html.
http://www.depweb.state.pa.us/landrecwaste/cwp/view.asp?a=1238&q=463452, Pennsylvania Municipal Waste Study, concerning battery safety: "There has recently been increasing interest in Pennsylvania and other states regarding household batteries' contribution to municipal waste. Several states have instituted legislative controls on the manufacture, sale, use, recycling and disposal of batteries. Batteries are the principal source of certain heavy metals found in municipal solid waste. There are opportunities to reduce and recycle the metals of concern."

Valvasti Williams Jr (Bass School) How do you make a motor or generator?
Val began by reciting the familiar mantra of Zoris Soderberg [Clark School]; namely, 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

He took a dry cell battery, two paper clips, two wire leads, a wooden dowel rod [cylindrical, with diameter » 1 cm and length » 10 cm], a rubber band, a small permanent magnet, a small Styrofoam™ board, and a 1 -2 meter length of fairly stiff copper wire with plastic insulated coating. We wound the wire around the dowel to form a circular coil of » 20 turns. We suspended the wire coil over the magnet so that it rotated freely about the axis formed by its straightened ends, using the paper clips. The plastic coating was scraped from one side of the wire, so that, as the wire loop rotated it alternately made and broke electrical contact with the paper clips. The paper clips were attached to the battery electrodes using the two wire leads and rubber bands. The system looked like this:

Source: http://www.hometrainingtools.com/build-motor-project/a/1605/
The purpose of the half-stripped wire was for the current in the wire to be shut alternately on and off as the loop rotated, serving as a commutator. We made a very nice electric motor using this technique, and were able to get the get the motor running continuously after a little practice. Just as an electric motor [such as the starter motor in an automobile] converts electrical energy into mechanical energy, an electric generator [such as an automobile generator or alternator] converts mechanical energy into electrical energy.

Notes taken by Porter Johnson