Monday, May 07, 2007

Who is smarter than a fifth grader?

My 5th grade daughter just competed in the Santa Cruz Math Contest, and had to answer these questions:
10. Find the surface area of a plate with the radius of 6 inn. Use 3.14 for pi.
11. A Ferris wheel at the boardwalk has a diameter of 50 meters. Find its circumference. Use 3.14 for pi.
19. What is the sum of the first ten prime numbers?

Answers: about 113 in2, 314 m, 101.
I am afraid that I would not have won. Problem 11 is just wrong. If the radius were 50 then the circumference would be 314, but as it is, the correct answer is pi times the diameter, or 157 m.

You can only get the approved answer to problem 19 if you count 1 as a prime number. But it is not. It seems to satisfy the definition for primes, but it is excluded in order to simplify mathematical statements such as the unique prime factorization theorem. If 1 were a prime, then prime factorizations would no longer be unique as you could include or not include factors of 1.

The difficulty with problem 10 is that it uses the term "surface area", instead of just "area". The term "surface area" suggests that the plate should be considered a 3-dimensional object, and that the areas of both sides should be added together. The given answer is just the area of one side.

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