- A composition is when transformations are “put together”. In this lesson, we will be putting together transla-
tions, reflections and rotations. - Glide Reflection- a composition of a reflection and a translation. The translation is in a direction parallel to
the line of reflection. - Expand Example 1- Before moving to the matrix, have the students draw out this glide reflection. This will
give them a hands- on way to see the two images without first moving to the matrices. This will keep it in a
visual way, before moving to an arithmetic way. - Once students have practices drawing in the glide reflection, move to using the matrix to figure out the same
information. At this point, you can refer back to the text. - The technology integration in this chapter is also a great way to provide students with a visual and hands- on
way of working with the material. - Provide time for feedback, discussion and questions after completing the work with technology.
- Intelligences- linguistic, logical- mathematical, bodily- kinesthetic, visual spatial, interpersonal.
III.SpecialNeeds/Modifications
- Review translations, reflections and rotations.
- Review matrices.
- Review the matrix for a 180◦rotation−
[
1 0
0 − 1
]
- Review the matrix for a 90◦rotation−
[
0 1
−1 0
]
IV.AlternativeAssessment
- Allow plenty of time for the students to ask questions during this lesson.
- Spend time on reviewing previously learned skills (ie. How to multiply a matrix) if necessary.
Tessellations
I.SectionObjectives
- Understand the meaning of tessellation.
- Determine whether or not a given shape will tessellate.
- Identify the regular polygons that will tessellate.
- Draw your own tessellation.
II.MultipleIntelligences
- This is a fun lesson and students usually love working with tessellations.
- Provide students with some information on tessellations and then have them work on two activities.
- The first activity, you will need to prepare.
- Students will work in groups, so you will need a few polygons/shapes for each group. If you can provide
different polygons/shapes for each group- great. - Give each group their polygons and tell them that they will need to prove whether each one tessellates or not.
- Students need to demonstrate that it has no gaps, no overlapping shapes, that the entire plane is covered in all
directions. - Also have students demonstrate that it surrounds a point.
- Allow students time for this exploration and then have students share their work.
4.12. Transformations