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Winners of the September - October 2004 Math Cats Writing Contest:

The contest rules were: __________ Explore "shadow math" and then write about it. Here are some possible ideas to explore: Measure the changes in a shadow several times in one day. You might mark the shadow's position and measure how many degrees the shadow moves in an hour. You might mark the length of the shadow at different times of day. Measure a friend's shadow at different times, or get someone to measure yours. Compare your shadow's length to your own height. When and how can you make the shortest shadow? When and how can you make the longest shadow? Use shadows to help you measure something really big, such as a tree or a building. For instance, in the illustration, the ruler is twice as long as its shadow, so the tree must be roughly twice as tall as its shadow. (If the tree is very full, this might not be very accurate.) Write down what you did and what you found out. You may write in the form of a story or an explanation. We like writing that is clear, lively, and creative. __________ First Place - "Shapes and Proportions" - by Liana Kutos Finalist - "Shadows in Our World" - by Jenna K. Dunay Prizes We're helping a special friend of Math Cats, too! __________ * First Place: Shapes and Proportions - by Liana Kutos age 11, grade 6, Janney Elementary School, Mrs. Barbara Clements's class Washington, D.C., U.S.      To do my shadow experiment I needed these materials: a paper cone, a tin can, a box, a cardboard poster, graph paper, scissors, and tape.      At 4:30 pm., I laid the poster on the side walk. I took the cone, and put it on the edge of the cardboard , and outlined the shadow with marker. I did the same thing with the box and the can. I repeated the experiment at 5:30 pm.      I compared the size of the shadow of the three objects for 4:30 pm and 5:30 pm. Even though the shadows grew much bigger at 5:30pm, the proportions of the objects, when compared to one another, stayed about the same. The depth of the can and the box added to the length of their shadows, but it didn't really affect the proportions. Here is the data:   Actual Size 4:30 shadow 5:30 shadow shadow length, removing depth 4:30 5:30 Cone 6.5" 9.25" 16.75" 9.25" 16.75" Can 4.625" high 3" diameter 7.625" 13.375" 6.625" 12.25" Box 7.75" high, 4.875" wide, 1.875" deep 12.875" 23.25" 11.75" 21.375" I used the graph paper to try to find the areas of the shadows in square inches. I traced the shadow shapes on graph paper and cut out the shapes. Next, I counted the squares to find the area of each shadow in square inches. The proportions of the areas changed from 4:30 p.m. to 5:30 p.m. __________ The judges felt that this entry was the clear winner. In fact, it was the only entry that explored shadow math! There is no second or third place winner this month. There is one other finalist entry. It does not meet all of the contest guidelines, but it is a fine essay about shadows. * Finalist: Shadows in Our World by Jenna K. Dunay age 15, grade 10, Fair Lawn High School, Mrs. Ometz's class Fair Lawn, New Jersey, U.S.      When people perform math, it s always calculating and measuring. Never once do people think to estimate. In fact, I think that estimating is almost non-existent. After all, who wants to know how to estimate when they can learn how to use their graphing calculators in the same amount of time? But the point is that people are almost forgetting that estimation is a way to do math. Estimation is all around us; just nobody cares to take notice.      One way to estimate is to look at a shadow. The shadow can say many things about the actual object. For one, the shadow is always smaller than the point. Ever sit under a tree to cool off on a hot day? Who knew that while you were relaxing that you could estimate the size of the tree?      Shadows are used in many other ways as well. When a carpenter builds a canapé, he or she has to realize where the sun will be at different times of day in order to get a better understanding of how their creation will work.      Furthermore, the shadow can also be quite interesting to watch and study during the course of the day. The shadows of objects change as the sun goes up and down. Also, the shadows rotate around their object, just as the sun rotates around the Earth.      I personally feel that a shadow is a great way to sum up how the world works. Each day, it begins in the same place, and it changes as the day goes on, but in the end, it always makes its way back to where it began. __________ * Prizes The first place prize is a Math Cats T-shirt and a large certificate. The finalist prize is a smaller certificate. ____________________ * We're helping a special friend of Math Cats, too! Wendy of Math Cats is making a donation to the IFOPA in honor of the winner and in honor of Jasmin Floyd, a young friend of Math Cats. You can learn about this worthy cause on the main contest page.

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