Translation and transformation have continued to prove extremely difficult for my classes. Even my strongest students have been struggling. I'm still trying to work out what is making it so hard to understand (if anyone has insight on this, I'd really love to hear it). I think they are starting to get the hand of it, but for mastery, we'd need at least another full week, and that is time we just don't have - especially for something that is only tangentially in the standards.

I did incorporate the idea of texting in lesson 14, to introduce what I'm calling "translation notation". We're not talking about vectors or anything like that, but I wanted to give them an efficient way to describe the translations and calculate with them. The kids thought it was really funny; I did play it up, calling it "math chisme" (gossip) and pretending I was texting it under my sweatshirt to my friend. You wouldn't want to type out that whole sentence, right?

Anyway, here are the files from this week.

Lesson 12 (Horizontal Shift) Keynote Quicktime

Lesson 13 (Translation and Transformation Practice) No Keynote for this one

Lesson 14 (More Translation and Transformation) Keynote Quicktime

A Geometric Proof of Brooks’s Trisection?

25 minutes ago

## 1 comment:

It's late for this time through, but...

I start without f(x) notation...

Circles and absolute value are great places to begin.

(x - h)^2 + (y - k)^2 = r^2

As you calculate distance to the point, you subtract. Kids know it. I bet even kids not from New York can find the distance from 42nd St to 125th St.

Time playing with circles is time well spent.

Then y = a|x - h| + k

Easy to graph. use y = |x| as reference, then run through, for example

y = 2|x|

y = -|x|

y = ½|x|

y = |x| + 1

y = |x| - 4

y = |x + 2|

y = |x - 3|

Really, more practice is better.

"Discover" the effect of modifying a, h, and k.

and then the hook back to circles:

y - k = a|x - h|

Subtraction is more the normal mode of things.

Then, maybe, y = a[f(x - h)] + k.

But that's fairly abstract notation, and very very hard without a smooth transition.

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