Applied Mathematics - University of Washington AMATH University of Washington

SIAM Student Chapter

Activity Overview:

Autumn 2010: Sharks and Minnows, Measuring Gravity, Math in Art, Estimation Station.

Winter 2011: Measuring Height with Lasers, Acid/Base Epidemiology, Grocery Store Math.

Sharks and Minnows

Goal: Introduce the basic mathematical concepts behind perdator/prey interactions. Sharks and minnows is the most lecture-style activity of this math fair but still requires participation by the students. Equipment: Sharks and minnows Python program, projector, and paper to record populations at various times during the simulation.

We created a the Sharks and minnows program as a stochastic simulation of predator-prey interactions that the students can observe on a projector. The instructor can pause the playback at 4 points during the simulation, and asked the students to estimate the number of minnows (red dots) and sharks (blue dots).

(The Python program above is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.)

Measuring Gravity

Goal: Introduce students to some basic physics principles and allow them to participate in a science experiment. Equipment: 5 ft ramp at a steep incline (we used PVC pipe with a large bucket at the end), large marble, stopwatch, worksheet.

Each ramp is supervised by a volunteer. Students roll the large marble down the ramp, using the stopwatch to time the drop from the top of the ramp until the student hears the marble hit the bucket. After performing the experiment three times, recording their data on the worksheet, they use a calculator to complete the worksheet and approximate gravity using the equation d = (1/2)*g*(t^2). Have each group of students record their approximation on the histogram; this led to great conversations about where there might be error in the experiment and how we could get more accurate data.

Math In Art

Goal: Through arts and crafts activities, talk to students about geometry and symmetry. Equipment: copies of tetrahedron and dodecahedron templates, scissors, tape, blank colored paper, markers, crayons.

Here we have two activities where the students decorate, then cut-out and tape together a geometrical solid. At this table volunteers talked with students about geometric shapes (equilateral triangles, petagons, vertices, Platonic solids, etc.). In the other activity, students make paper snowflakes by cutting out only a single kind of shape (triangle, circle, rectangle, etc). We asked our students to think about what kind of shapes will emerge when they unfold their snowflake. Volunteers talked about symmetry and geometric shapes.

Estimation Station

Goal: Show students two different techniques on estimation using applications in ecology and map making. Equipment: Plastic Pit Balls, animal stickers, paper cutouts of Washington state, digital scale that measures to .01 g, calculators.

The first activity simulates the capture and recapture method used to estimate large animal populations. Place approximately 100 plastic pit balls in a large canvas bag. Have each kid "capture" a plastic pit ball out of the bag and "tag" it with a sticker. (We used various animal stickers.) Replace all the balls in the bag then have each student "recapture" by taking out another ball. Count the number of balls in the "recapture" that are tagged with the animal sticker. Using ratios we can estimate the total number of balls in the bag.

In the second activity, students estimate the area of Washington State by weighing a paper map printed on an entire piece of paper. Students weigh both the cutout and a small square of known area (made using the map scale for the map of the state) on the scale. Using ratios, students estimate the area of the state by dividing the weight of the state by the weight of the small square, and multiplying by the area the small square represents.

Measuring Height with Lasers

Goal: Using similar triangles and lasers, students estimate the height of objects. (Preferably tall things that they cant reach the top of!) Equipment: laser, meter stick, measuring tape, worksheet, calculator.

Placing the end of the laser on the floor, students angle the laser until the dot is on the top of object to be measured. (To make it easier, we built small tripods out of PCV pipe, and mounted low-power laser pointers to one leg) The volunteer places the meter stick between the laser and the object until the laser hits the stick. Students measure the distance from the laser to the meter stick, the laser to the object, and how high up the meter stick the laser point hit. Using similar triangles, students use ratios to calculate the height of the object. To build good safety skills we also made the students stay behind the laser while it was on.

Acid/Base Epidemiology

Goal: In a large-scale experiment, students simulate the spread of disease (such as the flu) as well as receive a brief introduction to chemical ph. Equipment: clear plastic ups, water, vinegar, droppers, red cabbage juice.

Pour a small amount of water into a large clear plastic cup. "Infect" a few of the cups with a approximately a teaspoon of vinegar. Give each student a cup and instruct them to have 4 "mixings". Each "mixing" consists of a pair of students combining their chemicals into one glass to mix them, and then pour half of the mixture back into the first cup. After the mixings, have the volunteers drop approximately a tablespoon of cabbage juice into the cups. The cups that have any vinegar will turn pink while the plan water will be purple. We found the cabbage juice to be remarkable sensitive to the presence of acid. Count the number of "infected" cups. Repeat the experiment a few times, varying the number of original infected cups, and see if the students can guess the consequences!

Grocery Store Math

Goal: Using everyday grocery items, students use the Nutritional Facts on the items to find the grams of sugar and apply unit conversion to be able to measure out sugar using measuring spoons. Then compare the amount sugar in different items, and discuss which options are more healthy, and which are less healthy. Equipment: single serving grocery items including some fresh produce, sugar, measuring spoons, worksheet.

Ask students to choose any item from the "grocery store" where they will find a variety of single serving items. Introduce them to the Nutritional Facts panel and have them find the grams in sugar a serving. Ask the students to convert the amount from grams to teaspoons and have them measure out the appropriate amount of sugar into a small cup. Have them return the grocery store item and the measured sugar to the "grocery store". In the followup conversation ask students if any of the results are surprising, point out that although some of the produce has substantial sugar there are other ways to measure "healthy food". Also point out that students can do the same thing when they are at the store by looking at the Nutritional Facts; this is a good example of doing "math in the real world".

Department of Applied Mathematics, University of Washington, Guggenheim Hall #414, Box 352420, Seattle, WA 98195-2420 USA
Email 'info' (at amath.washington.edu) Phone 206-543-5493 Fax 206-685-1440