Open Ended Math Problems

Group work can be an excellent source of exploration and learning, but sometimes it can be difficult to tap into in the subject of mathematics.  One of the reasons why is because many mathematics questions are set up to be closed ended.  You find the one right answer and you check it and you're finished.  Here's an example of changing closed ended to open ended.

Which of the following numbers are prime? 7, 57, 67, 117

Fred thinks that 57 and 67 are prime because they both end in 7, which is a prime number. Dick says he is wrong. Who is correct and why?

Source: http://books.heinemann.com/math/construct.cfm

As you can see with the open ended question, the restraint to one answer is removed.  Also, more information can be given and more critical thinking can be asked by using the question on the right.  I could say 77 is not prime, but it ends in 7, therefore Fred is wrong.  Or I could say 57 can be divided by 3 evenly so it's not prime.  These are not the only rational answers to the question on the right.

Further opening it up could be a question like "What prime numbers end in 7?"  By asking this question, I removed another limitation, this time I removed the upper bound on prime numbers.  Daring students could find primes that are beyond our usual scope of 1-100.