I just found MathsChallenge.net thanks to a link at Maria’s Homeschool Math Site.
Unfortunately, it doesn’t seem to be getting updated anymore, but the “latest” page linked above contains 20 nice-looking problems, most of which have a number-theory slant to them. For example:
- If all the counting numbers from 1 to 1000 were written out how many digits would be written down?
- Show that two consecutive primes cannot have a sum that is double a prime.
- Prove that the difference between the expressions
and
is a multiple of six.
- Prove that the last digit of an even perfect number will be 6 or 8.
and 
is a multiple of six.The problems are rated for difficulty on a scale of 1 through 4. (I’ve provided one example of each level above.) Solutions are also provided.
Since most of the problems ask the student to “prove” something, which is not something most middle schoolers are familiar with, the problems may have to be re-worked somewhat to make good investigations for middle schoolers. However, these all seem to be excellent jumping off points!
