Sunday, April 13, 2008
1,2,2,3,3,3,4,4,4,4,... What is the 2008th term? SAT-type Questions vs. Math Contest Problems
Don't forget to submit the name of our Mystery Mathematician. Contest ends around 4-15-08. Thus far, only one correct submission (emailed of course!).
The problem in the title is the math contest version. Knowing the formula for the nth triangular number would be helpful (so might a calculator). Do all middle school and hs students become familiar with triangular and other figurate numbers? Should they? My vote: Yes!
The SAT -type would be:
What is the 56th term of the sequence 1,2,2,3,3,3,4,4,4,4,..., in which each positive integer N occurs N times?
Comment: This is considerably easier than the contest problem as one could do it by listing with or without a calculator. It also may reveal your strong number sense students who will see the idea fairly rapidly. Try it as a warm-up in class!
Another SAT-type (probability, counting) to help students prepare for the May Exam:
Let S be the set of all 3-digit positive integers whose middle digit is zero. If a number is chosen at random from S, what is the probability that the sum of its digits is even?
Note: I wrote this question to demonstrate basic principles of probability and counting. Although one could use the Multiplication Principle (aka, Fundamental Principle of Counting), students should also be encouraged to make an organized list and, by grouping, see why the answer is 1/2.
Posted by Dave Marain at 12:59 PM 7 comments
Labels: counting problems, math contest problems, probability, SAT-type problems, triangular numbers