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:

Students wrote down their two guesses and we recorded ’em.

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”*

Kinda cheesy….

Oh gosh….

But it seemed to help in understanding the difference between AND and OR.