comfortable to explore
All the thinking tasks, the first week stuff, the trailhead statement, the national park backdrop, the hiking metaphors… It’s days like today, it’s lesson like today that make it worth it.
I’ve given the same worksheet on reflections on a graph every year, the first questions asking students to explore the points, and determine the reflection line. They eventually discover the reflection points of the x-axis, y-axis, and y=x. In past years, it took a lot of 1 on 1 help, and kids didn’t really explore it, but rather waited for me to give them the answer.
But not this year.
They fucking went for it.
And when I brought them all together to go over y=x line… Man. I asked them to share out how they described that strange diagonal line that we flipped the shape over. Here were the responses I got:
y+x because it goes over both of them
(0,0) because it goes through the center
the diagonal line where the x and y are the same
a reflection over x, and then y.
Best of all, I had a student in the back of the classroom, with his buddies, not the students I usually see get excited about math, figure out the equation y=x all by himself, remembering y=mx+b, noticing the slope was 1, the y-intercept was 0, and boom. He had the freakin biggest smile on his face when I told him he was right, and his friends were legit stoked for him and dabbed him up.
THAT is what math is all about.
LET the kids explore it first. Don’t give them the map right away.
They just might find the trail all by themselves.