Today in Geometry things were insane. We spent most of the day working through a couple proofs, things moved very slow. After class I didn’t feel too great about how things went. The proofs were sloppy (on my end) and it felt like students were taking a 360-nose-dive.
I know exactly why the day took a turn for the worse. I didn’t even buy what I was teaching. The way I worked through one proof followed the textbook’s logic. I would NEVER have worked through it that way. But, with the influence of the textbook (which isn’t a bad way, just different) I convinced myself to teach against my gut. I feel better about things now that I recognize this issue.
Anyways, Algebra was awesome today! Courtesy of Estimation180
I started by throwing this up on the board:
I asked students to word it as a range of numbers BETWEEN two values; which I would change next year. You can always add more structure later on. I showed them the answer then we moved on to this one:
After their guesses were recorded, we wrote a. and b. as inequalities and recorded guesses.
This was exactly how students worded things. Pretty cool to see the concept emerging without any promoting on my end.
At this point I used Jared’s as an example and introduced a little more structure: 320 < x < 450
We looked at the answer then watched the video on how many scoops it would take to fill the jar. I asked students to write this as “x placed between two numbers”
In every single class there was an inequality that was either < 15 or 15 <, it was fun to see students call each other out for being wrong by not including the 15 and fixing their estimates.
After this point I introduced some more structure and vocabulary, we first talked about what a graph of Aubrey’s estimate would look like then graphed it.
After, students practiced graphing and solving a few and we talked about the difference behind what we mean when we use AND or OR in a normal conversation;
“Eric invited me over for dinner tonight, he said that would would be having dinner and dessert, what should I expect to have?”
“He also let me in on what we are having; mac and cheese or lasagna, what should I expect to eat”
But it seemed to help in understanding the difference between AND and OR.