This was a tough lesson, and there is no way that I can expect kids to have this figured out in a day.
I began with a review of the four basic transformations, once again writing them all on the board – mentioning that we’ve done translations and now we’re going to do reflections. To begin, I had a linear/piecewise generic function on the screen using Sketchpad. I had the students tell me what each point’s coordinates were (this was not done well on the previous day’s quiz), and using the text function wrote them on the graph. Then I reflected the function over the x-axis (after asking what quadrant the image would be in) and we wrote down the coordinates of the images and compared them. On the board, I wrote that a reflection over the x-axis made (x,y) → (x,-y).
Next I selected the points of the function in Sketchpad and told the program to print the coordinates for me to save time. I then reflected the graph over the y-axis and wrote the rule down. I also did the same thing for reflection over the line y = x. The students had a difficult time noticing that the original image, which was entirely in the first quadrant would remain in the first quadrant when flipped over the line y = x. But once it was on the screen and I pointed out where each point was going, they seemed to get it. One kid in one class asked what would happen if I reflected the graph over both the x- and y-axis, which I did. I also pointed out, using Sketchpad, that it was the same thing as a 180 degree rotation, which I showed by having Sketchpad to a 175, 176, 177, 178, 179 and 180 degree rotation in succession, which the kids thought was cool.
When I was done, we had a table like this on the board, which I had them write down.
Once that was complete, I turned the screen off and began plotting functions, then once the equation was hidden away, I’d turn the screen back on so that they could try to look at a function and figure out its equation.
For each one (I only could do three in each class because it is very time consuming) I’d have the students write out the descriptions (in words), the coordinates in (x, y) form, and the equation.
I didn’t get to do too many and it was apparent that many kids were not getting it, so I’ll have to do lots more examples tomorrow. But, I did assign homework, #1 – 3, 5, and 7, which I can use for more examples tomorrow.
