Vertical learning can transform a math classroom.  When students get out of their chairs and work on non-permanent surfaces, they start to communicate and think more effectively.

The following set of 80 problems are examples of activities I use to engage student thinking.  The problems allow students to approach math from more than one perspective.  As my school year progressed, I would randomly use different problems to review concepts taught earlier in the semester.  These problems and this approach to math was inspired by the book Building Thinking Classrooms by Peter Liljedahl.