Hexagons: The First Day

The first day back from break can be a little rough.

Trying something new you’ve never done before can be a little rough.

Doing both at the same time?

Can be a magical roller-coaster of the good, the bad, and the who-even-knows-how-that-went.

On Monday I introduced the hexagons. Not having planned ahead enough to create a wooden set on the school’s laser cutter, I resorted to good old-fashioned cardstock.


I used the cards to separate kids into random groups and then each group named and defined their hexagon. This is the part that didn’t go so awesomely. Funny thing is, kids don’t know what a “definition” is. So, what they did was:

  1. Ask me if I wanted a definition of hexagon. [Thank you, but no.]
  2. Write a list of every single characteristic of their hexagon they could think of.

Not exactly what I had in mind…

But I went with it. Students wrote up their characteristics on chart paper and posted their “definitions” around the room. Then I had everyone do a Post-It activity where they drew a hexagon based on the written description. Another flaw: everyone said they remembered what the hexagons looked like from the grouping shuffle at the beginning of class, so there wasn’t much gained from this part of the class. Oh well.

Next step was to create Venn diagrams of each group’s hexagon and the hexagon to their left. The goal was to discover if it was possible to create a hexagon that fit into the intersection of the two circles. I don’t think any group was able to do this based on their definitions. We repeated with the group to the right. Same story.

That’s when things started to pick up.

I grabbed a marker and set up shop at the hexagon in the front of the room, the Pakman (aside: this group took freaking forever to come up with a name for their hexagon). I asked if there was any way to simplify their list of categories into one succinct description that contained the essential characteristics of a Pakman without additional or redundant information.


After some debate and discussion we settled on the idea that a Pakman’s essential element was that it was a hexagon composed of two congruent parallelograms.

I ended the class by asking:



And, just like the class itself, this will be continued tomorrow…

I Notice Awesomeness

…because there really is no way to have too many posts about the “I Notice/I Wonder” process.

My Math 3A (geometry) students had never done an I Notice/I Wonder before. That is the beauty of this process–it’s practically bullet-proof.

Here’s what they noticed and wondered about the side-length ratios of a 30-60-90 triangle that we played around with in GSP:







In which I write a blog post comprised primarily of tweets from other people. I think normally we call this “being lazy.”


At Asilomar this year I gave a talk on math electives, which was kind of fun:


Also I Ignited…[Alternative Title: Help–I’m On Fire!]

Embedded image permalink

But unfortunately my Ignite talk didn’t include any unicorns.

Instead, I talked about raising the value of mistake-making in the math classroom:

Some people were kind enough to tell me I did okay (even without the unicorns).

Holy crap, there were a lot of people…

Embedded image permalink

All in all, it was a fun time. See you next year!



Review Days

As some of you already know, my school operates on a trimester system. So while most of you are looking forward to Thanksgiving turkey and trips to see family and then coming back to finish out the semester, I am gearing up for finals this week. We don’t have a special schedule or anything, but I am giving finals at the end of the week, hence the title of this post. [Note: I am still doing all that looking-forward-to-Thanksgiving stuff.]

Last Thursday/Friday was my first day for review in Math 2 (one of my classes doesn’t meet on Thursday; the other doesn’t meet on Friday). I have a typical, fairly boring, packet of review problems that I was planning on handing out to students so they could do some diagnostics and figure out what they needed to work on for the next few days.

Then the Xerox machine decided to go on strike.

It was bad, people. It was very bad.

Finally, after both of my classes had met *ahem*, the Xerox machine decided it was okay and I was able to print off my review packets. I passed them out in class today. But I have skipped over an important step in my story. The chronology of this blog-post is out of whack!

What did I do with my bonus 80 minutes for which I had nothing planned, you ask?

I did concept maps:





I don’t have pictures of this part, but my genius move was, after students had worked on the whiteboard concept maps, I had them make a “final draft” on chart paper…but I had them revise a different group’s map. I couldn’t think of a good third-round that would enable them to have hand’s on for all three maps, but 2 is better than 1.

While this definitely didn’t take the whole block, it did take a good chunk of time and it helped students to focus on what concepts were in each unit so they could develop their own study guides. I wrote on the agenda that it was “Choose Your Own Adventure: Study Guide Edition.” No one commented on the reference, so I assume this generation of students all had horribly deprived childhoods. All in all, it worked out to be a pretty productive review day. And I don’t particularly like review days, so that’s saying something.



Inspiration from & Annoyance with Google Images

There should be a way to “report” images on Google, because this is not a rhombus:




And this one really isn’t a rhombus:

However, this is super cool:

And it gave me the idea, what if you had students write definitions of a shape on Google forms and then threw the text into a Wordle. Then you could go back and look at them together and see what jumps out.

Open House

Open House was today. Every year each full-time teacher has to go to one open house to help out the Admissions department. We teach two mini-lessons to eighth graders and sometimes we serve on the faculty panel afterwards. It takes a couple of hours on Sunday afternoon. It’s like everything we do for Admissions, actually pretty good once you’re in it, but it feels like a big huge pain in the you-know-what hauling yourself to school on a weekend.

It didn’t help that on Saturday morning I woke up convinced that it was a workday. I lay in bed pondering how much time I had left before the alarm clock went off. I don’t really know how long it took me to realize that the alarm wasn’t going to go off–because it was Saturday! It was quite the relief to discover that I didn’t need to get out of bed before the sun was up for a change, but by that point I was already pretty much awake anyways, so I wound up getting up pretty early. Not that this is all that strange for me. I seem to be consitutionally incapable of sleeping in.

Today’s open house was kind of funny. I had two sessions of mini-class and then stayed for the faculty panel afterwards as the math team representative. My first class had 30 students! This was bizarrely large. I had been expecting many students, as our open houses tend to be over-full, but I’d been warned to expect around 25. There were not enough chairs in the classroom for all the kids that came in–something which I am upset with the Admissions team about; that is something they should be on top of. Amidst the mass of students was a girl who mid-way through the lesson called me over and said that she’d already visited my class and that her dad knew me. She told me “hi” from him. Super sweet.

Then, my second class only had thirteen kids in it! This would be less annoying, except for the fact that the students literally just go as a group from one class to the next. So, the 30 + 13 was really a group of 43 that got split–NOT in half–and switched places with one another. Not sure why the groups couldn’t have been 21/22 rather than huge and little. I was good though. I didn’t launch into my vituperative spiel with the Admissions team before I left school this evening. I am smart enough to know that it was not the right time.

My tiny second class included a sibling of a former student and someone whose bar mitzvah I went to last year. That one was a first. Mainly because I don’t go to very many bar mitzvahs these days. I’m calling this the “open house trifecta.” Because, well, why not?

Faculty panel was what it usually is. Answering questions from parents, all of which are pretty typical. There are two rounds. Much like my mini-lesson classes, the first group was much larger than the second. Interestingly enough we also got through many more questions in the first round. I think this was due to the experiment the Admissions team had us run. The usual format for parent questions is that they write them down on an index card and hand them in. Then the panel moderator sorts them by similar question types and asks the panel a selection from the bunch. We did that for the first go-round. In the second, parents just raised their hands to ask their questions. I think we only got through three questions in the second group. Which is kind of crazy. We don’t have that much time, but we should be able to get through more than that. I think the Admissions team wanted to counter the possible perception that we were cherry-picking questions to ask the panel, but they didn’t really consider the fact that some parents take 2-3 minutes to ask their question. And when you only have half and hour (less time, really, after introductions and such) that is a huge percentage of the panel time. Summarizing several questions, like our moderator tends to do, goes a lot more quickly. I think that was an unexpected consequence for this experiment.

In any event, I am off the hook until next year. I can’t say that I’m disappointed not to have to come in again on the weekend for a while. But it was kind of fun once things got going.

Your Mission, Should You Choose to Accept It…

(Which of course you will, because you are my student and I have assigned this to you…)

Estimation Mission


This is only one part of the wall–it extends from the first floor up through the ceiling of the third floor.

And since I teach in a private school, and therefore am not bound to the Common Core, none of my students are doing any of the following:

SMP 1-Making sense of problems and persevering in solving them


SMP 3-Constructing viable arguments and critiquing the reasoning of others


SMP 5-Using appropriate tools strategically


SMP 6-Attending to precision


SMP 7-Looking for and making use of structure

"How many little circles are there?"

“How many little circles are there?”

Kind of a double-meaning on that last one…making use of structure. Hah!

But seriously, although I don’t “need” to use the Common Core in my classroom, I choose to because I think these are good practices, and I support this movement to re-imagine what the math classroom should look like.