One way to break up the routine in math class is to have the students get up and experience some of the concepts in their bodies. This is of course helpful to kids who like to move, but it helps everyone make connections and remember things. It can also give a useful reference point when teaching a new concept.
Of course, such activities are intended to supplement, not replace other work. Moreover, you should not expect miracles from them: while they add a lot to your program, they are most effective if combined with discussion, reflection, and work on paper.
Here are links to a number of kinesthetic activities for secondary school math.
- The Radian Dance (by Kim Seashore, inspired by Lew Douglas)
- Angles in parallelograms, in regular polygons
- Cartesian graphing of functions
- Circles, bisectors, and more: Distance
- Rate of change: Function Diagrams
- Pascal's Triangle with pennies
- Introduction to Complex Numbers
I have used most of them when I taught high school, and collected some more since then. Many should work in middle school.