What are Transformations?

In the eighth grade Common Core standards, students are introduced to geometric transformations. To identify (and activate) their prior knowledge, I give a Pre-Assessment as a Do Now. Since students are asked to identify and describe transformations of points in Part A, there may be different answers. This helps me see how students think about transformations. Part B asks students questions about specific transformations. I take their papers away after 10 minutes, even if they haven’t answered every question. Incomplete pre-assessments can also help me identify students’ knowledge and skills.

I teach the unit on transformations in the context of Alice’s Adventures in Wonderland and Through the Looking Glass by Lewis Carroll. Lewis Carroll, born Charles Lutwidge Dodgson, was a mathematics professor at Oxford University.  Lots of mathematics is embedded in his stories. 

For this Mini-Lesson, I have created a presentation with guided notes for students to complete. As a general introduction to transformations, I use pictures and quotes from Alice’s Adventures in Wonderland. I give students information about Lewis Carroll and we discuss why the book is appropriate to use in a unit on transformations. We then discuss the Caterpillar’s quote, “So you think you’re change, do you?” as a bridge to defining the term “transformation.”

As we go through the presentation, students match the pictures from the presentation with the pictures on the sheet “Transformation Note-Taking Guide.” They then write the name of the transformation shown in the picture. When we get to specifically defining the various transformations, we discuss and develop descriptions before I show them the actual definitions. Depending on how well developed their descriptions are, I may not even show my definitions.

After students have filled out the sheet, I have them annotate the pictures on the sheet by labeling the pre-images, images, line of reflection, angle of rotation, center of rotation, etc. where appropriate.

The What Are Transformations Presentation notebook file is animated and you can see this in my video. For example if you click on the word bubbles, information appears and if you click on the images in the “Rotations” page, they spin around. The PowerPoint Presentation contains all of the same information without the animations but you could add those in if you download the file.

In the Activity students work on a sheet that asks them to identify various transformations. It is similar to the pre-assessment, but instead of just looking at points, students are looking at triangles.

Sometimes the Mini-Lesson runs longer than I expect. If necessary, I have the students work on questions 9 and 10 and complete the rest for homework. After about 8 minutes, I choose students to give their examples of transformations in the real world. We also discuss their responses to question 10. It is here where students construct viable arguments and critique the reasoning of others (MP3).  The answer I am looking for is “Mohammed is correct because dilations are the only transformations where the size changes.” This leads into the lesson summary. However, if students give a different, answer, I accept it as long as their justification is valid.  

At the end of the lesson, I introduce students to isometries, which we will expand on in later lessons. I show students the slide, “What Are Transformations Exit Ticket Presentation,” and then hand out the exit ticket. Students fill in the blanks with information from the slide and then they answer the question, “What is an isometry?” based on the information from the slide.  I collect the exit ticket, check the students’ responses, and return the slips to them to glue in their notebooks.

Students who have not finished the worksheet from the practice section can complete it for homework.