You should be able to do each of the following objectives after completing the corresponding chapter.  This page will be updated frequently thoughout the semester, so please check back often.

Chapter 1 - Squares, Hexagons, and Triangles

• Give a clear statement of a set of legal moves that applies to square, hexagon, and triangle grids and so that shapes will or will not overlap as we expect.  (Tasks 1.1.1, 1.2.1, 1.2.2, 1.3.1)
  
• Write a clear set of rules that allow you to decide if a given shape is a basic unit without applying all legal moves.  (Tasks 1.1.2, 1.2.3, 1.2.4, 1.3.4)
• Decide if a given shape is a basic unit for any of the grids and justify your answer.  (Tasks 1.1.2, 1.2.3, 1.3.2, 1.4.2)
• Give your own examples of basic units.  (Tasks 1.1.2, 1.2.3, 1.3.3, 1.3.1, 1.4.1)
• Describe how to use a given basic unit to create another basic unit.  (Task 1.4.1)

Chapter 2 - The Rigid Motions of the Plane

• List all of the types of basic rigid motions of the plane and identify which preserve orientation and which reverse orientation.
• Given two figures related by reflection, find the axis of reflection, and given an axis of reflection, reflect a figure.
• Given two figures related by rotation, find the rotocenter, and given a rotocenter, direction, and number of degrees, rotate a figure.
• Given two figures related by translation, find the vector of translation, and given a vector, translate a figure.
• Given two figures related by glide reflection, find the axis of reflection and vector of translation, and given an axis and a vector, glide reflect a figure.
• Know and describe what is needed to properly specify each type of rigid motion.
  
• Identify fixed points of a given rigid motion.
  
• Given two figures, decide what type of rigid motion relates them.
• Be able to combine two rigid motions and identify the resulting rigid motion.
  

Chapter 3 - Finite Figures

• Given a finite figure, precisely identify all of its symmetries.
• Precisely identify all of the symmetries of a regular n-gon.
• Identify a combined symmetry of a regular n-gon by recording the effect of performing the symmetries on the vertices of a cut-out regular n-gon (Method 1).
  
• Identify a combined symmetry of a regular n-gon by using diagrams that record the effects of each of the symmetries (Method 2).
  
• Identify a combined symmetry of a regular n-gon by using previous results on combinations of rigid motions (Method 3).
• Identify a combined symmetry of a regular n-gon by using algebraic rules (Method 4).
• Construct and use multiplication tables for symmetries of basic figures.
• Find inverses of symmetries.
• Describe the meaning of the inverse of a symmetry.
• Identify the symmetry type of a given finite figure and draw examples of finite figures with given symmetry type.
  

Chapter 4 - Strip Patterns

• List the types of symmetry a (general) strip pattern could possibly have.
  
• Label amount of translation (t), amount of glide reflection (g), rotocenters, and mirror lines on examples of strips.
• Describe possible relationships between t, g, smallest distance between rotocenters, and distance between vertical mirror lines.
• List symmetries of example strips and create example strips with a given list of symmetries.
• Explain why the presence of certain symmetries of a strip imply other symmetries must occur.
  

• Answer basic questions about the presentation on celtic knotwork.
• Answer basic questions about the presentation on symmetry in architecture.
• Answer basic questions about the presentation on symmetry in biology.
• Answer basic questions about the presentation on symmetry in mineralogy.
  
• Answer basic questions over other assigned readings.
  
• Find basic units when definitions of legal moves are changed.
  
• Provide numbers of faces, edges, and vertices for regular 3-dimensional Platonic solids (regular convex polyhedra).
• State and use Euler's formula relating numbers of faces, edges, and vertices for regular 3-dimensional convex solids.
• Describe rotation axes for the cube.