Elementary Mathematics-Science SMILE Meeting
24 April 2001
Notes Prepared by Porter Johnson
Section A: [K-5]

Mary Scott [Williams School] Handout: Jelly Bean Investigation [The Education Center, 2000]
Led us through an exploration of properties of jelly beans using our five senses.  We put our reactions to these statements inside question boxes, as shown:

 It feels ... It looks .. It sounds ... It smells ... It tastes ... smooth round like an egg  a stone like pebbles marbles rattles dice fruity each color has own smell grape, orange, ... sugary crunchy good

Then we wrote a verbal description of our investigation of a particular jelly bean, and drew a picture. Example:
The jelly bean was blue. It tasted like grapes, and smelled like grapes. It was sugary and crunchy, too. They sounded like dice.
Very nice, Mary!

Virginia O'Brien [Higgins Academy; Kindergarten] Handouts: [1] Magnetic Train [Science Horizons] and [2] Mighty Magnet  from Mostly Magnets [AIMS activities Grades 2-8, Aims Education Foundation 1991 Gretchen Winkleman, editor; ISBN 1-881431-29-0].

On the table at the front of the room, she placed various objects: horseshoe magnet, ceramic coffee cup, ballpoint pen, soap bar, paper clips, glue bottle, paper plates, piece of fabric, tin can, aluminum foil, glass jar, crayons, wooden ruler. Then, using a small disk-shaped magnet (about 2 cm diameter), she stuck a colorfully decorated paper plate on the board as an example for us to make a Magnetic Train. The circular rim of the plate had a series of equally a spaced radial lines drawn on it to represent the ties of a railroad track. colorful "scenery" was drawn inside the plate, surrounded by the "track". How could we move a "train" around that track? To get some ideas, we went to the table to explore the magnetic properties of the various materials. After making our own "train track" paper plate with the help of crayons, we found that a paper clip placed on the "track" could be moved around the edge of the plate with the aid of a disk magnet held under the plate, and moved around the edge. A neat way to learn something about magnetism, and to end up with a magnetic toy train! Thanks, Virginia!

Renee Robinson [ST Galasius School] Handout:  The Science of Ice Cream/ Kitchen Chemistry
Using basic materials and ingredients [ice, milk, eggs, granulated sugar, rock salt, flavoring, spoons, cups, napkins, and plastic bags] we made ice cream.  Then, role-playing as budding student-scientists, we investigated this ice cream and the commercial product.  Here are the instructions for making ice cream:

Pass out two zip loc bags to students, one small and one large.  Have them fill to 1/2 capacity the large bag with crushed ice and then add in the large bag six (6) tablespoons of rock salt on the ice.

In the small bag, they should put in one (1) tablespoon of sugar, 1/2 teaspoon of vanilla flavoring and 1/2 cup of milk.  Secure the zip loc bag and place the small baggy inside the large bag.   Have the students shake the baggies for 5-10 minutes until the ingredients begin to gel.

They can add cookie crumbs, chocolate syrup, fruit, etc. at this point to the ice cream

For additional information see these websites:

Iona Greenfield [After School Program; K-3] Handout:  Orange You Amazed? [Project AIMS]
There were two bags of oranges on the table; we each got an orange and a paper towel.  We peeled the orange, first estimate the number of orange segments [8], and then counted the number of edible segments [9].  We compared our results with expectations [9 vs 8].  The students were to weigh the ingredients [200 grams], and then wait two days and weigh them again. They could then calculate the moisture lost due to evaporation, and draw graphs.  The orange would lose mass less quickly if left intact. As an extension, they could let the orange pieces continue to dry, and record the total amounts lost to moisture. Or, they could make a solar oven for drying of the orange. In addition they could obtain information on the process of dehydration of oranges; see History of Minute Maid Orange Juice: http://en.wikipedia.org/wiki/Minute_Maid and Space Food and Nutrition: http://www.nasa.gov/pdf/143163main_Space.Food.and.Nutrition.pdf.

Notes taken by Earl Zwicker

Section B: [4-8]

Shyla McGill (Columbia College) Handout: Basic Skills Instructor Book
This book is used for instruction in Middle Mathematics (one 3 hour class per week) for students with weak math skills; usually 9th and 10th graders. Her approach, in its third semester of operations, has been successful. She engages students by visual, "hands on" exercises that involve them in discovering things about mathematics. Shyla presented us several exercises to illustrate the approach:

• Shyla gave each of us about 5 paper strips, and asked us to put them on the board.  First, she grouped the strips by colors and asked the class to answer questions as to the percentage of strips of various colors.  Then, she asked us to calculate the perimeters of the regions bounded by the strips, as well as their areas.  Curiously, you could just add the areas of each strip to get the total, but that did not work with the perimeters.  The students discover this point and become curious about it.
• Next she passed out an envelope, with lines drawn on it like the Union Jack [http://www.jdawiseman.com/papers/union-jack/union-jack.html], the British Flag with its crosses of ST George, ST Andrew, and ST Patrick:
`            ______________________________           |  .           |            .  |           |      .       |       .       |           |           .  |  .            |           |--------------|---------------|           |        .     |    .          |           |    .         |          .    |           |______________|_______________| `
Now, we cut out one of the four crossed regions [along the envelope cap], corresponding to an obtuse triangle. Then, we formed a tetrahedron out of the remaining envelope. We were asked questions concerning the areas of the various triangles, as well as the area of the tetrahedron itself, which consists of 4 triangles. The area of the tetrahedron was shown to be equal to the area of the envelope out of which it was made.
• Next she described an exercise of "tiling" a region of space using the least amount of paper, where you are given whole sheets and allowed to make only one cut. There was a fairly ingenious and exotic solution, which her students worked hard to find!
• The next exercise was to cut a "quarter circle" out of a circle.
• She then described cutting a sheet of paper into "one gram" pieces.
• Finally, she showed the Cuisinaire [ http://www.etacuisenaire.com]Fraction Circular Ring/Decimals, which had the circular perimeter marked into hundredths, rather than in degrees, as in a protractor.   This ring made it simpler to divide circles into fractions.

Shyla talked at length with the group about her experiences.  She can be contacted directly at mailto:smcgill@popmail.colum.edu, or by telephone (H): (773) 581-7757; (W): (312) 344-7548. Thank you for sharing, Shyla!

Christine Etapa [Gunsaulus Academy] Handout: Chemical Changes from Glencoe Life Sciences Lab Manual for 7th Grade.
passed out thermometers, test tubes, graduated cylinders, pieces of liver, and Hydrogen Peroxide [H2O2] to groups of teachers. We added 5 ml of Hydrogen Peroxide to small samples of liver, and recorded the temperature at 30 second intervals for 6 minutes.  The temperature was seen to rise by about 6oC above room temperature, which was about 26oC, and then to decrease back toward room temperature. It was recommended that several trials be performed to accumulate statistics and reduce error, but the reaction was definitely exothermic, i.e. heat was given off.

Christine then gave out pieces of potato, and we repeated the experiment by adding Hydrogen Peroxide to the test tube containing the  potato piece.  This time the temperature seemed to decrease.  It was unclear as to whether this decrease was caused by the evaporation of oxygen from the Hydrogen Peroxide, or whether the reaction with the potato was genuinely endothermic. The temperature decrease was only 2oC in this second reaction.  Very interesting, Christine!

Another thought about liver :  "I hate liver! Liver makes me quiver! Liver makes me curl right up and die (it makes me cry)!"  The song I hate Liver was performed at The Second City [http://www.secondcity.com/] in the 1970's by cast members David Rasche and Jim Stahl, and is frequently played on WFMT Midnight Special  [http://www.midnightspecial.org/] on Saturday nights.  Unfortunately, it has never been released commercially.

Beth Womack [Miles Academy; first grade] Handout Sheet: Fun With Mirrors from Science is Fun, Teacher Created Materials, Inc.
passed out a sheet of alphabet letters and asked us to identify which letters could be converted into other letters using a mirror.  At first, we thought this was a very simple game, but then we discovered that quite a few letters could be produced by placing the mirror in directions other than horizontal and vertical.  For example, we could make an "A" out of an "H" by reflection, by placing the mirror to cover part of the "H", and obtain the following:

`              |              |			          ____|              |               |              | `
Very interesting, Beth!

Marva Anyanwu [Green School] Magic Number  Columns from Blockbuster Science Activities
gave us a handout containing the following columns of numbers:

 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 7 9 4 2 6 5 9 7 4 5 8 9 4 6 2 8 6 9 4 3 5 8 2 5 3 8 5 7 8 4 2 6 9 4 3 5 2 7 6 9 6 3 7 9 9 2 3 7 7 3 6 8 5 6 8 7 7 2 5 9 5 4 7 9

Note that, in each column the sum of the first, second, and fourth numbers is 18; for example, in column #1 we have 7 + 9 + 2 = 18, whereas for column #9, 9 + 4 + 5 = 18.

Now, separate out several of the columns, in any order, and  write them again.  For example, if we write #5, #13, #11, #16, #1, we obtain

 #5 #13 #11 #16 #1 6 9 4 3 7 3 6 8 6 3 7 9 5 4 7 9 7 9 4 2

Now, combine the elements to form the following addition problem:
```
67657
93349
***           46774   ---> 246774 - 2 = 246772
38992
-----
***          246772               it's a match!
```
The sum can be obtained from the number in the third row, simply by putting a "2" in front, as well as subtracting "2" from that number. The answer can be obtained for any number of columns, chosen arbitrarily, using the same procedure. The explanation is that, the sum of the first, third, and fourth numbers is equal to 18 + 180 + 1800 +  ... + 180 ... 0 = 199 ... 98 = 200 ... 00 - 2.  Check it out!

Roy Coleman [Morgan Park HS]
gave us a preview of a presentation for next time, in which he wrote the following pattern on the board:

`      |      |      |      |      |      |      |      |      |         | ____ |      |      | ____ |      | ____ |      |      |      ||     ||     ||     |      |     ||     |||     |      | ____ ||____ ||     ||     |      |     ||     |||____ |      |      ||     |     |||     ||     ||     |      ||     |  ??  ||      ||____ |     |||     ||____ ||     |      ||____ |      ||____      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |`
What should go in the region in which ?? is located?

Fred Farnell (Lane Tech HS; Visitor)
passed out a sheet from the American Chemical Society Office, CHEMLINKS FOR KIDS, which contained the following websites:

Thanks, Fred!

Notes taken by Porter Johnson