Ratio and Proportion

By Neil Seeley

Resources Needed: VW Bug model, butcher paper with life-size bug drawn on it (divided into four sections of profile), Exact measurement of the width of the bug, five computers with internet access, school blueprints, overhead projector with LCD display for Power Point slides.

Exposition:

1. Introduce the concept that an adjustment in the length of lines does not produce the same proportion in adjustments of area and volume. In other words, linear proportionality does not convert directly to two dimensional or three-dimensional proportionality.
2. Scaling is an integral part of every day life and it is simply a matter of ration and proportion. Do engineers work with life-size drawings of the edifices they build?
3. Building of any type requires scaling. Later you'll find we use a type of scaling in math when creating graphing grids.

4. With students in five groups, each group with a computer, have them locate the math forum web site and find the first "pie" problem. Have them read through the problem and look at the solutions that appear just below the question. Each group is to come up with one improvement for each of the given solutions. Then they are to write 3 to 5 sentences about which solution they think is best. They, of course, must explain why they chose the one they did.
5. Have the students locate one of the real world pages where ratio and proportion are used in scaling. Have the youngest person in the group be the reporter. Going clockwise around the group select the reader, recorder, encourager and internet surfer. Go around to each group and ask them which profession that uses ratio and proportion they would like to present to the rest of the class. Make sure that each group is presenting something different. Give each group five minutes to determine what information they will present and how they will do so.

You are given a VW Bug model to 1/ 24 scale. Is finding how much smaller the model is from the real thing a matter of linear proportionality, two-dimensional, or three-dimensional proportionality? Refer to the Power-Point slide about the various proportionalities.

Four of the five groups are given one of four sections of the profile of the bug on butcher paper. The fifth group is merely to calculate how many of the models are contained within the given width of the life-size Bug. That fifth group will also tabulate the results on the overhead. As a class with you at the head, come up with an estimate for how many models will fit inside a real bug.

Math Forum. (2000). Problems of the Week. http://forum.swarthmore.edu/

Lanius,C. (2000). Build Golden Rectangles. http://math.rice.edu/~lanius/Geom/golden.html

YES Mag. (2000). Activities – Geared Toward Engineering. http://www.new-sng.com/heykids.htm

Math Forum. (2000). Pyramid Building. http://forum.swarthmore.edu/sum95/math_and/spreadsheets/intro.html

Breedlove, Becky. (1996). House Building. http://edweb.sdsu.edu/courses/EDTEC596/Project1/DesignAHouse.html