First I had students try to make a triangle with three line segments which could NOT create a triangle. They concluded that it was impossible because two of the line segments were not long enough. Then I had students make a triangle with three line segments that were sufficient for creating a triangle.

I then wanted students to record a hypothesis for evaluating any three line segments' ability to form a triangle. This was really tough for students. They were able to describe why three segments could or could not form a triangle, but they had trouble generalizing their findings.

I want to keep working at making my students think about math in a broader sense. They are used to solving problems (as long as the problems are set up in a familiar format), but are not able to apply what they know to scenarios beyond what they are familiar with. My hope is that if I continue to challenge them to think beyond the box, they will begin to learn to see the big picture of what math is

*really*about.