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 Winnersof theSeptember - October 2004Math CatsWriting Contest:

The contest rules were:
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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.

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First Place - "Shapes and Proportions" - by Liana Kutos

Prize

We're helping a special friend of Math Cats, too!
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* 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:

removing depth

 4:30 5:30
Cone6.5"9.25"16.75"9.25"16.75"
Can4.625" high
3" diameter
7.625"13.375"6.625"12.25"
Box7.75" 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.
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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.

* Prize

The first place prize is a Math Cats T-shirt and a large certificate.
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* 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.