The latest article I have been writing for my website deals with combined inequalities(or compound inequalities). One of the difficulties in teaching this topic is helping students understand conceptually the difference between "and" and "or". I try to accomplish this by developing real world examples. For example I give them the statements such as:
"The sky is blue and the grass is green."
"Peyton Manning is a Colt and a running back."
"Barrack Obama is running for president or he is a math teacher."
I then ask them which of the following are true and why. The goal is to get the students to understand that both statements must be true for an "and" inequality to be true. And that at least one must be true for the "or" inequality to be true.
What are other ways to help students understand combined inequalities?