Minimizing Products
Two integers, x and y, have a sum of S. What are the values of the integers if you want to have the least possible product? Give your answer in terms of x.

Extensions 
Restrict the values of x and y to the positive integers. Investigate the least and greatest possible product for any given pair of positive integers. Justify your conclusions.

Related External Resources 
Assorted problems
Assorted problems of the day from Highland Middle School.
Can this be done?
Determine the largest sixdigit number that can be written following two simple rules.
Integer addition
Interactive math lesson on the addition of integers.
Submit your idea for an investigation to InterMath.
