Looking for…

I mentioned a couple of times that I was a “Mentor teacher” this past year, and I got my official letter last week that I will be again this year. The definition is a little different than what you’re thinking of–basically a cooperating teacher for an alternative certification program that lasts for a full school year.

In less than a month, I will be assigned two Residents, who will be paired with me for the school year, to learn to be a teacher, run a classroom, deliver instruction and more. Every Monday through Thursday, they go where I go (Fridays they take their grad school classes).

Last year I had two residents, one of whom was awesome–I’ve shared some of his great  work on here and the other…had some struggles. She ultimately left the program (and had anyone involved had more experience, myself included, the whole thing would likely have been much smoother). My load last year was hard. Really hard actually, although it took me months to realize that I wasn’t struggling only because I was adjusting to the whole “having two people with you every second” thing but also because teaching three completely different preps is just HARD.

For me, the part where they were different was the tough part, but my content itself was no picnic. I taught one section of AP Statistics (and primarily reserved that one for myself) and three sections of Honors Advanced Algebra–tough content, fast pace. When my resident struggled, the coaches kept asking how much of it was my (difficult) content.


Does it matter? I get where they need to know if she can’t teach or if she just can’t teach _____. But that’s what I had to teach; I couldn’t very well have her try something totally different instead of what my students should be learning.

All this is to say, this year I have TWO sections of AP, and while we are never allowed to choose our residents, I’ve been asked for my feedback about what the coaches should look for when I’m matched. And I’m CLUELESS.

I need someone who can admit that they don’t know or understand something (instead of teaching Stats wrong)

…but not someone who already knows Stats (awesome, but not likely to happen)

I need someone who can…work hard? Teach three preps?

I don’t think smart is nearly as big of a deal as willing to figure it out and be able to explain it to the students, but how do you vet that? I will still teach the really tricky stuff, like hypothesis testing, myself–so they don’t need to be able to pick up on everything.

See? Lost 😦

Any ideas? What are some qualities that make someone likely to be able to handle my AP classes? What kind of background should I look for? Please help me!


Rate of Change Cards


This is a classic–five years ago, at my past school, Drew & I sat around (with a few other colleagues, I don’t recall which ones) at our monthly meeting and talked about graphing, coming up soon in our Algebra 1 classes.

“They just can’t calculate slope from a table.”

“Well, my kids don’t seem to connect what the numbers mean to the rate of change. They don’t get what it means.”

“I wish they could just explain it in a sentence.”

And so on. We had some common concerns, but other things were more specific/personal pet peeves. We focused in on our students understanding of slope as a rate of change and some of the things we wanted them to be able to do:

  • Calculate slope from a table
  • Assign units to slope
  • Describe the rate of change in a sentence

In retrospect, this lesson was probably also the start of my obsession with word problems and understanding what a problem actually means.

We decided that we wanted our students to be able to put together those pieces and then scaffolded the problems. There are three sets of cards, and we did each set on a different color (so we could easily see where each group was). To make sure students were finding what we were asking for, each group got an answer blank. With the students in groups of 4, we handed out the answer blank and then the first set of cards. Each student was told to take 1 (they are numbered 1-4) so that they could take a little more ownership–this would probably be a great place for each group member to have a role, but I’m not that good.

1. Ms. Cutter lives 75 blocks from Solorio and bikes to school.

Use the table to find her biking speed and

time required to ride to school.

























Here’s the first problem. Stop it. Now.

I don’t care what the answer is, and I didn’t ask you for it. (This is actually worse with teachers than with students–teachers have no interest in following my directions because they don’t want to think about rate of change this way either, or at least not the ones I’ve presented to!) We wrote it like this because what the problem is asking shouldn’t always change our approach–jumping straight to an answer can take away understanding what you’re actually doing.

We start with determining which variable is independent/dependent and x/y, and then label the top and bottom of the fraction–units only, no numbers. Then we find the rate of change from the table (yes, my bike is jet-propelled–it makes a funny joke so I’ve never changed it.) Set 1 all has an intercept of 0, so these aren’t too tough. As soon as most of the class has the rate, fill that in on your fraction as well. The last thing we need to do is state the rate of change as a sentence. Nothing fancy, “She bikes five blocks in one minute” “Every minute she goes five blocks” or whatever. But say what it means.

Finish up Set 1, and start on Set 2.

5. Ms. Cutter bikes to Marquette Park to see the

tennis team and then bikes home.

Use the table to model her trip.

minutes after tennis

total blocks traveled























Same as the first, but now we’ve got an intercept. We’re still focused on the rate of change, so we start with our units again, but then discuss (first in groups then as a class) what has changed and how to handle it. You can use starting point or intercept here, but we want to get across that we can’t un-ride or un-carry or un-paint. It’s happened already, so it won’t be affected by anything else. The only change here is to fill in that starting point as well, although it doesn’t need to carry over to the sentence.

It’s getting a little bit harder now, and if you have a single period class, you’re also out of time now. Hand out some tables and have students find the rate of change and state it in a sentence for homework to reinforce what you’ve done today. On to Set 3–the students are realizing this was not nearly as easy as we thought but are also starting to understand what the rate is, how to find it and what it means.

The only new part of Set 3 is writing a function for the situation, which you can also skip and come back to later (I would still do the rest of the card).

I think this is a good framework. But I haven’t had the opportunity to discuss it with anyone in the five years since we wrote it, and I haven’t revised it either. I’d love to hear what changes you would make or how you would tweak it to make it even better. I would appreciate any feedback or suggestions you have in the comments. And if anyone is interested in the follow up lesson after this, I’d be happy to post about that later.

I’m going to be out of the country for a week, so I’m not ignoring your comments if I haven’t replied. I really would love to hear what people would do with this lesson.