Compositions, Not Just a Notebook

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Objective

SWBAT define compositions of transformations and identify these in M.C. Escher’s work.

Big Idea

Students will be introduced to compositions of functions by looking at MC Escher’s famous tessellations drawings. This lesson will then specifically explore glide reflections and give students an opportunity to review transformations including reflections

Do Now and MC Escher Video

20 minutes

Do Now:  In the Do Now, students will review how to translate points along a vector.  This is a great opportunity for teachers to review the definition of translation and also how vectors are used with this transformation.  The second Do Now question asks students to identify the transformations in a picture with more than one movement.  This second question will help to lead students into today’s new topic, compositions!      

 

Teachers can also review the agenda and objective for this lesson.

 

Teachers will then introduce students to M.C. Escher, a famous artist who focused on creating tessellations.  There are two videos, one of Escher’s life (http://www.youtube.com/watch?v=gSvE-2ZzFOw&safe=active) and another website which includes a host of Escher’s works (http://gogeometry.com/escher/m_c_escher_impossible_slideshow.html).   This is a great lesson for visual learners and students who are artists.  I usually ask students to first look for any transformations and then to try to determine multiple transformations within each tessellation.  It may be worthwhile to pause on a specific piece to ask students to describe the movements, which are composed of the artwork.  Teachers may want to prompt students with review questions like,

-  Do the figures change shape in these tessellations?

-  How many shapes are there in this piece? 

-  How do the shapes change in this piece? 

-  What is unique about Escher’s work?

-  Can you name the transformations that we see?  Does one transformation appear to do done first or second? 

Exploration and Class Notes

25 minutes

Activity/Homework and Exit Ticket

20 minutes

After completing in class examples, students should be encouraged to work in pairs or small groups on practice questions and a worksheet with examples, which can be found in student notes.   Teachers can circulate and answer student questions.  After giving students 10-15 minutes to work on this assignment, teachers can ask students to put their work on the board and then review these questions with the entire class.  This is a great opportunity for teachers to reinforce vocabulary and also ask students some important summary questions like,

- How are tessellations and transformations connected?  How are they different?

- What real-world applications are there for compositions of transformations or tessellations? 

- When you complete a composition of transformations, what are the steps? (it’s great to review that we always do the second transformation first!)

- Describe a glide reflection or ask students to sketch a glide reflection on their paper.

 

The Exit Ticket for this lesson reviews how a triangle in one quadrant would move based on a composition of transformations.