Download and open in PowerPoint only.  The files will not work correctly in Google Slides. 

CHAPTER 1 

Strongly encourage students to stay on top of the vocabulary.  Visual aids are very helpful: cardboard polygons and stars, a Plexiglas "plane" (on which you can draw with a dry erase marker), a wooden dowel (for a pointer and a reflection line), a picture of a right hand copied into an overhead transparency sheet.

PowerPoint can help students decide whether an object is oriented. Switch from presentation mode to editing mode, double-click an object, duplicate the object via copy-and-paste, and then choose "Flip Horizontally" to flip the duplicate.  Does the flipped copy look essentially different from the original?

CHAPTER 2 

Take time to have students construct the Cayley table for a square (with the handout below printed two-sided in color with the first page cropped to make it a double-sided gnome-square). 

Pause during the slide lecture to discuss the proofs of one or two of the key theorems mentioned : the Sudoku Theorem, the Zero-or-Equal Theorem, the Rigid-Motion-Detector Theorem.

Avoid over-emphasizing the abstract.  Keep the focus not on general groups but on symmetry groups, and the beautiful things we learn about symmetry with this new point of view.  For example, students might have conjectured the Zero-or-Equal Theorem in Chapter 1, but one needs the group viewpoint of Chapter 2 in order to prove it.

CHAPTER 3

 Devote time to the border pattern handout below (with a second copy printed on transparency or performing rotations and reflections).  This handout could lead to a discussion of parts of the proof of the classification theorem that the book relegates to the exercises.  I do not spend much time discussing wallpaper patterns, but I recommend the iOrnament app for creating and studying them.  The Symmetry Quilt below includes 16 of the wallpaper pattern types (with the 17th on the quilt's backing).  Have students classify the symmetry type of each of the quilt's 16 blocks (ignoring color).

CHAPTER 4 

Avoid over-emphasizing the abstract; in particular, avoid function notation.  For a class of humanities majors, I recommend NOT writing things like "f(x)*f(y) = f(x*y)".

CHAPTER 5

For generated subgroups of cyclic groups, have 10 students stand in a circle passing a ball by 1s and by 2s and so on. Then add an 11th student and then a 12th.

One way to minimize abstraction is to skip the section about product groups, in which case you must later skip the final section of Chapter 7.

CHAPTER 6  

A set of refrigerator magnet letters is an indispensable visual aid.  Take time to have students construct the Cayley table for P3 with the handout below (using magnet letters or the cut-out letter strips below).

Students can self-discover the concept of even/odd.  Ask them to generate EADCFB with swaps, and report the number of swaps required.  They will notice that all reported numbers are even.  Follow up with CADEFB, which is odd.

CHAPTER 7 

Visual aids are crucial.  Zometools are great for building hollow edge models of the tetrahedron, cube and dodecahedron, through which it is easy to stick a dowel to represent a rotation axis.

Bring many 3D objects to class, and discuss where they fit in the classification flowchart.

Origami can enrich this chapter in many ways.  Search for "Sonobe origami" on YouTube. Learn by video how to fold the sonobe unit, which you can easily teach to your class.  Assemble 6 or 12 or 30 sonobe units together into a beautiful polyhedron.  A single sonobe unit is chiral, so the most common mistake is to accidentally fold some left and some right hand versions, which will not compatibly assemble together.  This can lead to a fruitful discussion of chirality.

Rachel Hall created beautiful wonderland-themed templates for the tetrahedron, cube and dodecahedron.    They are found below, together with worksheets that lead students to self-discover the proper symmetry groups of these objects.

I also identifying the symmetry types of the 3D objects built from Matt DeVos' templates. 

Perform a web search "Archemedian solid template" or "Catalan solid template" to find templates out of which you can create interesting 3D objects.    Distribute objects to students and ask them to count the symmetries of each.  

CHAPTER 8 

Physical models of the Platonic solids are crucial.   I recommend Magformers to quickly snap them together.

Most classrooms are shaped roughly like a cube.  It is entertaining to build the room's dual with streamers and tape. Or to save time,  simply mark the dual's vertices on the classroom walls, and simply ask students to imagine the dual's edges.

Hoberman makes toys that nicely illustrate the three dualities: "Switch Pitch" for the tetrhaderon's self-duality, "Flip Out" for the cube-octahedron duality, and "Super Flip Out" for the dodecahedron-icosahedron duality.

Euler's formula for the sphere can be introduced by passing out balloons to all of the students.  White board markers work well for drawing graphs on balloons. Also draw a graph on (a small portion of) an inflatable inner tube, and cut out its faces with scissors to help students see why the "surrounding ocean" face is not a deformed polygon.

CHAPTER 9  

This chapter can be covered quickly as a one-day special topic.  I bring to class a mop bucket full of soap solution and Zometools polyhedra to dip.

CHAPTERS 10, 11 and 12 

 I don't typically have enough time to cover these chapters, but PowerPoint presentations are included for instructors who wish to include these chapters.