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Mathline

Math in the Park or City (Grades 6-8)

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cityMathematics is everywhere! The following questions relate to things you might see in the world around you in a city or in a park. Keep your eyes open.

Mathematics and Bricks

Bricks are useful and durable building blocks. They also offer an opportunity to explore mathematics.

1. As you travel around, watch for different shapes of bricks. Most bricks are what shape?

2. Why do you think bricks are this shape?

3. If you keep your eyes open, you will probably be able to find bricks that are not rectangles. Side walks and patios are good places to look. What shapes are the bricks? Do they still tessellate?

4. See if you can find a place where rings of bricks are laid in a circular pattern. Good places to look are around statues and fountains. How does the number of bricks in each ring change as the rings get larger? Try to come up with a rule to describe the pattern.

A Mathematical Look at Fountains and Pools

5. Once you find a fountain or pool, try to figure out how much water it contains. Using what you know about calculating volumes and measurement skills, estimate how many cubic feet of water are in the pool or fountain.

6. One cubic foot of water contains 7.48 gallons of water. That is a lot of water! Calculate how many gallons of water it takes to fill the fountain or pool.

7. How much does the water in the pool weigh? Water is a pretty heavy liquid, which explains why most people float in water instead of sink. It turns out that 1 gallon of water weighs approximately 8.57 pounds. How much does the water in the pool or fountain weigh?

Shadows and Heights

With the help of a couple of meter sticks or yardsticks, you can figure out the height of some tall objects like a tree or flagpole. There is a direct relationship between the height of an object and the length of its shadow. This relationship is the same for all things if the measurements are taken at the same time of day, which means the sun is in the same spot.

8. Find something tall so that you can measure its height. It should be something like a tree or flagpole that casts a shadow and that you can actually measure from its base. A fountain would be more difficult since you don't want to be at the base of the fountain.

9. On flat ground, place one measuring stick point straight up. Measure the length of the shadow.

10. Figure out what number you would need to multiply the length of the shadow by to generate the length of the measuring stick. Call this number the shadow factor.

11. Measure the length of the shadow of the tree or flagpole. Multiply the length of the shadow by the shadow factor you calculated in Question 10. This will give you a good estimate of the height of the tree or flagpole.

12. Note that the shadow factor changes as the sun moves. When is the shadow factor very small?

13. When is the shadow factor very large?

14. Can the shadow factor ever equal 1? If so, when?