Where We've Been: We've just finished our Unit Assessment on Logic and Proof. Students have been introduced to foundational theorems in Geometry, they have participated in inductive and deductive reasoning, and they have written proofs.
Where We're Going: In this unit, Extending Transformations, we'll be establishing rigorous definitions for rigid transformations and we'll be using rigid transformations to establish congruence criteria. So this is an easy-going entry event before we get into the weightier parts the unit.
I start the lesson by showing the Rotational Symmetry Concept Attainment Slideshow.
The slideshow presents a series of symbols that either have or do not have rotational symmetry. The students' job is to figure out the secret ingredient that distinguishes the haves from the have nots. My job is to operate the 'slide projector' and keep my lips zipped. I don't do any "right", "wrong", "hot", "cold", etc. I just let students have time to think and sort it out. I am strategic about how I operate the slides. The flow of the student discussion dictates how I choose to go back through the slides. The students will sometimes request to see certain slides again, which is great. The goal is for the right concept to get out into the classroom and for everyone to agree on it. For more on this, see the Rotational Symmetry Concept Attainment Description Video.
Once that happens, I define some concepts related to rotational symmetry. First, I show the Mathisfun.com Rotational Symmetry Page. The site gives an informal definition of rotational symmetry as follows:
With Rotational Symmetry, the shape or image can be rotated and it still looks the same.
I follow that up with a more formal definition: A plane figure has rotational symmetry if and only if it can be mapped onto itself by a rotation of less than 360 degrees. Next, we look at how the site defines 'order' and we play around with the applet that shows the difference between order 2 symmetry and order 3 symmetry. We also take a look at the examples of order 2, 3, 4, and 8 symmetry.
To see if students have understood the idea of order, I flip back through the Rotational Symmetry Concept Attainment Slideshow to see if students can identify the order for the figures that have rotational symmetry.
When the students have the concepts down, it's time to have some fun creating our own designs. I start by demonstrating how to create designs using the Mathisfun.com Symmetry Artist Tool. [pause for the oohs and ahhs.]
Ok. This part is completely informal. Let's just see what students come up with. All I give them is a sheet of blank paper and directions to create designs with order 2, order 3, and order 5 rotational symmetry. I like to see what they come up with.
I'm not overly critical of the designs when I see them, but I do ask, for example, "How much do I have to rotate this before it maps onto itself?"
I like to run this activity as a whole-class guided practice. This way, I can keep everyone focused and on task. This format also gives me the opportunity to narrate and model the steps when necessary.
For independent practice, students create their own design with order 5 rotational symmetry using the methods they learned in the guided practice section. Students' success will depend on whether they have found regularity and made generalizations about the process for creating a design with any given order of rotational symmetry (MP8). Each student receives the Independent Practice_Rotational Symmetry student resource and tracing paper.
I run this as an in-class activity. See video description here Before students start to create their designs, I have them come to me to get their basic design element and angle of rotation approved. See Enacting the Rotational Symmetry Independent Practice activity for more on this. Also see Student Work_Rotational Symmetry for several examples of the work students produced in this lesson.