Many topics in mathematics can be made much clearer when symmetric aspects are made clear or when nice alternative visualizations are possible. When this occurs, it helps both the student and the teacher. We will examine visualization and symmetry in a very general way by means of a set of problems. There is a large amount of potential classroom material here, and almost any small part of it could be used for an entire class session.

Algebra / Arithmetic
Geometry
Problem Solving / General

Multiple Representations
Problem Posing
Problem Sets
Try a Smaller Problem

MP1 - Make sense of problems and persevere in solving them.
MP2 - Reason abstractly and quantitatively.
MP3 - Construct viable arguments and critique others' reasoning.
MP4 - Model with mathematics.
MP5 - Use appropriate tools strategically.
MP6 - Attend to precision.
MP7 - Look for and make use of structure.
MP8 - Look for and express regularity in repeated reasoning.