Hi Adam, I take your point that the quadratic formula can be presented in a way that does not inspire understanding or affection. And it sounds like that's how it was taught to you. So let me try to make a better case for it. Here's how I discussed it in my book The Joy of x. (1/9)

I had enough fun with the middle school problem that I wanted to solve the other two!

I enjoyed your commentary on CU. I’ve also found number lines to be somewhat hit or miss. My preservice teachers have, however, connected fairly well with using integer chips to understand computation with negative numbers.

I enjoyed the consideration retrieval practice and spiral review.

I have quite a few squares memorized, 20x20 among them, which is 400. Then, I have one too many 20s, so 400-20=380. ♾️

And now I realized I read that wrong. For some reason I read the message of “kids who do well are less likely to get caught than kids who struggle”. Oops.

I like this comparison as it can explain some breaks that great teams get—refs are predisposed to expect good things out of elite players. It’s frustrating, but more representative of incompetence and human error than conspiracy.

In this case, I think the metaphor is the school system rigging the cheating. Unless you think the Chiefs pay off the refs? Again, enjoy the win! Winning is fun, and we’ll probably get a rematch that should be just as entertaining.

Enjoy the win! I’m pretty skeptical of conspiratorial thinking that a small market team is going to have games rigged for them. I recall a huge play overturned on a penalty last year against the Bills (and it was rightfully a penalty then, too).