Elementary Mathematics-Science SMILE Meeting
14 November 2000
Notes prepared by Earl Zwicker

Note: The academic year write-ups for the current semester (and several previous semesters) appear at the web location http://www.iit.edu/~johnson/acysmile.html. At the end of the semester they will also appear on the SMILE website, http://www.iit.edu/~smile/.

SECTION A (K-5)

Angie Morris (Burnham School)
presented us with the "Elevator Problem." (handout) The problem can be presented at many different levels and with various approaches. She treated us as she might 8th graders, by giving us the following problem: 

"Suzie got into an elevator. She went down 5 floors, up 6 floors, down 7 floors.
She was then on the second floor. Where did she get on?"
Angie asked us to work on a solution with a partner. Steps she would take:
Make sure we understand the problem (read it aloud; have students read it aloud; discuss)
Compare and discuss (students see the variety of solutions available)
Sum up by teacher (review)
Have students write down what they have learned
Extension - What if Suzie got off on a different floor? - How does this affect the answer?
Angie would point out that there is more than one way to solve this problem. And students get to make up their own elevator problem - a real test of understanding! Thanks, Angie! (Oh! The answer is - 8th floor!)

Rae Lynn Schneider (Williams School)
involved us in an activity usable in a range of primary grades: Learning to Cut. Handout:
Fiskars™ Inc, c/o Education Dept. T&T
7811 W Stewart Ave
Wausau, WI 54401
(715) 842-2091
Rae saw that we each got a piece of colorful poster paper (12" x 18") and a pair of Fiskars™  scissors, which had colorful, plastic-coated handles. They cost $1.50 - $2.50, depending on where you buy them. (After we had been busy cutting awhile, she passed around a "fake" look-alike pair costing much less; but it cut very poorly.) Rae had us fold the paper, and then cut a large square using folds as guide. Then she modeled for us what to do. Cut a circle out of the square. (Her technique was good and practiced, and the circle appeared to be nearly perfect!) Following her example, most of us did fairly well also. Then she cut into the edge of the circle at a small angle, and spiraled the cut around and around toward the center. This generated a dandy spiral which behaved like a paper spring! When allowed to collapse on the table, it again appeared as a circle. The handout was detailed and complete, including safety, beginners, how to select a good pair of scissors (without naming Fiskars!), developing cutting activities (scribbling, cut a line, cut to a target, cut curves, cut and change directions, cut different shapes). Advanced cutters dealt with many topics, including different materials: wax paper, aluminum foil, felt, fabric, etc. A great way for students to develop hand skills, and to become creative. Thanks, Rae! She made us into a bunch of "cut-ups!"

Chandra Price (Burnham School)
involved us first in an interesting number "tricks." One of them was: Pick any three digit number with the first and last digits differing by at least two. Reverse the order of the digits. Subtract the smaller number from the larger to get the difference. Now reverse the order of the digits in the difference. Add these two numbers (the difference and its reversed digits). What do you get? (1089) Try it again with another three digit number to see if you get the same result. Neat! You had to be there to get still another number trick - both were handouts from Chandra.

Chandra next gave us handouts about the flora and fauna of Hawaii. "What kinds of animals are found in different part of Hawaii?" was her question to us. She gave us four pages showing diagrams of the various creatures, and maps showing Average Rainfall, Hawaiian Ecological Zones, and a page with an outline describing how to investigate Bird Adaptation. On the table for all to see, she had many transparent blue plastic cups partly filled with various bird foodstuff (actually some raisins, seeds, etc), and some styrofoam cups partly filled with water. In our group, one of us received a wooden fork, another a clothespin, and another a straw. These tools represented various shaped bird beaks. And then each of us had to use their "beak" to pick out some of the "food," and to "drink" some of the water. We learned how specialized beaks can be! See http://www.jason.org to learn more about the Jason Project. As usual, Chandra gave us much to learn and think about.

Rita Ford (Altgeld Elementary - Special Ed)
works with intermediate and primary children. We each received a plastic bag containing colorful construction paper, a film can (black, opaque), and a page of instructions describing how to make a "pop up rocket." Rita does not lecture - it doesn't work. She goes over certain terms via questions: What are rockets? Where do they go? For what are they used? Gravity: Students jump up, but gravity pulls them down. Gravity pulls you down on the scales so it reads your weight, which is how hard the force of gravity is pulling down on you. Then she gets students working in small groups to make a rocket. Eye protection is a must! (Make the body of the rocket by wrapping the construction paper around the film can to form a cylinder. Form a conical nose cone and tape it on, along with fins. Add baking soda and a little vinegar to the can and quickly cap it and stand on the ground - and POP!! - it jumps up into the air. (Always done outdoors with students.) We made some and had fun seeing whose rocket went highest. Why did it? What factors control this? And students investigate to find answers. A great way to learn, Rita! Thanks!

Tanisha Kwaaning (Pullman School, 4th & 5th Grade split)
gave us a handout describing Act It Out, Draw It Out. It is a way to learn strategies for solving word problems. Another page contained 8 examples of word problems to practice on with groups of students. But she models it first so they have an idea how it might work, and that is what she did with us: A parking lot with spaces numbered 1 - 16 is full. All of the cars in the even numbered spaces leave. Then every third car of those remaining leaves. And finally, half the remaining cars leave. How many cars remain in the parking lot?

So - Tanisha had 16 of us line up in front. Then they counted off 1 through 16. Then she had the even numbered people take their seats. Then every third person took her/his seat. And then half the remaining people take their seats. And we simply counted the number remaining to get the answer! Great! One could also draw successive pictures to show the process, and arrive at an answer as well, which is best done after the modeling exercise.

She told us that it works at all grade levels, and students really get involved and learn. Wonderful ideas, Tanisha!

Jeanine Frazier (Pullman School, 3rd grade)
(handout - Number Sense) used charts with 4 columns: thousands, hundreds, tens, ones (place value charts) - and rubber-banded groups of ten popsicle sticks - to teach us double digit subtraction. She wrote on the board:

                     minuend          addend
                     subtrahend       addend
                     difference       sum
Then she had us work through the specific example
                    54
                   -35
using 5 groups of ten sticks in the tens column, and 4 single sticks in the ones column. We could not take away 5 sticks from 4 sticks, so we regrouped and renamed (borrowed - but the preferred terms now are regroup and rename). i.e.. We took a group of ten sticks from the tens column and and put it in the ones column (regrouped). Then we broke it apart into single sticks in the ones column - (renamed), giving us 14 sticks in the ones column. Now we could subtract the 5 sticks from the 14 sticks, leaving us with 9 sticks in the ones column, and 4 groups of ten sticks in the tens column. The result was the difference represented by those sticks: 49 Beautiful! Jeanine's handout described these ideas with simple elegance. And students learned the technical math terms - minuend, subtrahend, etc. - to meet questions on tests. Similar procedure to teach addition. A really phenomenological way to learn math concepts! Great, Jeanine!

PS - Virgina O'Brien (Higgins School)
completed her birdhouse with guidance from Lee Slick (Morgan Park HS). It was really spectacular! Now she will be able to tell us her experiences feeding birds this winter.

Notes taken by Earl Zwicker

Section B: (4-8)

Jannyce Omueti (Cook School - counselor)
subjected us to a handout on Chaotic Computing. (AIMS Education Foundation 1987) http://ww.aimsedu.org/  This brought home the effect of distractions on study habits. For example, little brothers/sisters making noise is a distraction. The TV set is a distraction. In order to test this hypothesis, we worked in groups. The handout provided Table 1 and Table 2 and a long list of numbers. Each table had four headings:

Time Begun          Time Finished         Time Taken             Number Correct

We had to do 20 additions and subtractions of numbers with no distractions, and find how long it took and number correct. This was then repeated with a different set of 20 additions and subtractions, but a partner provided distraction by reading from the list of numbers as we worked. We saw that the time to complete the work increased by half (from 2 minutes to 3 minutes), while number correct was about the same. This varied from person to person, but the conclusion was clear: distraction makes a big difference! This was a most interesting experiment for us to do. Thanks, Jannyce!


Bernadette Dvorscak (Williams & St James Schools)
had us cut out rectangles from "grid paper" to do multiplication by rectangles. Associated with each rectangle was an area, so that a rectangle which was 1 ´ 1 had an area of 1, a rectangle 1 ´ 2 had an area of 2, etc. Our results:

arearectanglesarearectangles
11 ´ 16 1 ´ 6 , 2 ´ 3
21 ´ 27 1 ´ 7
31 ´ 381 ´ 8 , 2 ´ 4
41 ´ 4 , 2 ´ 2 91 ´ 9 , 3 ´ 3
51 ´ 510 1 ´ 10 , 2 ´ 5
............
201 ´20 , 2 ´ 10 , 4 ´ 5
We noted that primes had only one array, and perfect squares had square numbers. Next, we placed rectangles out on the upper left corner of a clean sheet, and wrote in the area in the lower right corner. E.g.,
                                _ _
                    _ _ _       _ _      _ _
                    _ _ 6  ,    _ 6  ,   _ 4  , etc.

The result was a multiplication table:

                    1  2  3  4   5  6
                    2  4  6  8  10 12
                    3  6  9  12 15 18
                    4  8  12 16 20 24
                    5    etc.
Cool, Bernadette!

John Scavo (Evergreen Park HS)
gave us a handout: How Long Do Batteries Last? It listed Equipment, Hypothesis 1, Hypothesis 2, Procedure, and a table to enter values for the variables: battery name, cost, weight, time. Which battery lasted longest? (Duracel™ , Energizer™, Panasonic™ ) Which proved the best value? Matching pairs of batteries are placed in identical flashlights, which are turned on at the same time. When the batteries begin to fail, the time is recorded. Graphs of time vs mass and time vs cost are made. A dandy way for students to learn both the practice of science and how batteries compare. John also gave us copies of articles on Helicobacter pylori (a primary cause of ulcers), ocean warming, discovery of a planet orbiting Epsilon Eridani. All interesting stuff, John!

Therese Donatello (St Edwards)
shared a game which illustrates energy concepts. Handouts:

Energy Source, Relay Race, and Energy Pantomime (1998)
The Need Project
http://www.need.org/
102 Elden St, Suite 15
Herndon, VA 20170
Tel: (703) 471-6263
Good for all ages, little preparation and takes about 20 minutes each. Gets audience moving, looking, thinking and acting. Breaks audience into several smaller groups. Mixes audience randomly or by ages, as desired. Includes list/diagrams of energy sources and users. Requires paper and pencils. Gives rules for playing. Builds ideas of what energy is and how it is generated and used. Thanks, Therese!

Marva Anyanwu (Green School)
did the Eye Spy Test with us. (handout - a model of a science project) This illustrates scientific method, and involves making observations in teams, and distinguishing independent and dependent variables. We knew we could depend on you, Marva!

Notes taken by Porter Johnson.