I love teaching transformations. It's so fun to get visual with the students and allow them to see the world around them with new vocabulary and new appreciation.
Take a look around for examples
Transformations are everywhere. I like to ask the students to brainstorm as many reflections and then translation and finally, rotations that they can think of in 5 minutes or less.
Once they do this, we can share on the board all their different answers. As the other students start to answer they can add to their lists. After a bit, as their brains are still processing the new information they just learned from their classmates, I like to add have them add to their list again.
With the challenge of not listing something on somebody else's paper, their answers can get very creative. Usually, too creative, and someone will oversimplify the definition. This is a great time to emphasize common misconceptions and mistakes around transformations.
And if they need more ideas, this video shows so many. While I don't enjoy the music during this video, I really like that it is simply a slideshow of images we can use during class as discussion pieces.
Use technology to encourage curiosity
Let them play
I like to put a shape on the board that has undergone a translation to see if the students can recreate it within the program. We always start with easy ones, making sure students are understanding the formulas and patterns they are seeing.
If the class is doing well we can then start combining transformations to challenge their understanding.
And don't forget to ask...
"How do you make it look like this?"
"Is there another way to do that?"
Check for understanding
Just for fun!
Common Core Standards:
CCSS.MATH.CONTENT.HSG.CO.A.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.