Category Archives: Geometry

Three Good Things (I’m an overachiever)

At the moment (as in, this week) three things are going really well in my classes. I considered writing about one of them, but I’m an overachiever so I’m going to write about all three.

Also, my masters degree is going fine. Being an overachiever helps with that too.

Problem Solving with In-N-Out

On Friday, the kids started the In-N-Out problem (see link for Robert Kaplinsky’s take) and we finished it yesterday. I love this problem. This year, I hung up my group-sized (2ft by 2ft) whiteboards at the beginning of the year, put the kids into random groups (different groups on the two different days actually) and told them to get cracking.

They did great. They discussed with each other (as much as freshmen who aren’t used to collaborating on things could be expected to), they wrote their ideas, some of them labeled their work really well, and some of them looked around the room from time to time to get ideas or see if they were on the right track.

Today, since they finished the problem yesterday, I used it as an example in each class to move into discussing slope/rate of change and the y-intercept in an equation. When I brought it up, the kids told me they really enjoyed working on it and requested more problems like that.

So now I have to find more problems that are good for vertical non-permanent surfaces, and preferably are related to standards that I actually have to cover in Algebra 1.

This is an amazing problem to have. I am so excited right now. I told the kids that I had a great time watching them solve the problem, and it’s true. I had so much fun. I definitely want to do stuff like this more often, and would be very into the idea of moving toward a much more problem-based curriculum.


Yesterday I also had my formal evaluation, during one of these Algebra 1 classes. My administrator sat in my room and listened to the kids solve this problem, which is not exactly an EEI-structured lesson format but I don’t care. It’s so much fun. And it’s so great to do for an evaluation where the biggest thing they are judging me on is student engagement because I probably had nearly 100% engagement, nearly 100% of the time.

The administrator told me a funny story afterward, and is planning to put this quote in the write-up of the formal evaluation. Apparently the group he was sitting nearest had a student who just kept insisting “It’s 90 cents. It’s 90 cents.” Another student in the group kept asking him how he knew. (!!!) He just kept insisting that it was just right and couldn’t explain his answer, and she finally told him, “You know that when she [meaning me] comes over here, she’s going to ask us! You have to be able to explain it!”

Woo hoo!

I nearly jumped for joy in front of my administrator when he told me that. This is amazing – we’re seven weeks in and some of them already know that being able to explain it is more important than the right answer (as least, it is to me).

This is a great sign, and I’m so excited about what this means for the rest of the year.

KenKen Puzzles

Clearly my theme for this blog post is about explaining reasoning, because this point is also going to touch on that.

So I do a bellwork routine, where we do the same type of bellwork question every week. Mondays are visual patterns, Tuesdays are estimation questions, Wednesdays are Which one doesn’t belong, Thursdays are a writing assignment because our school is doing a writing initiative this year, and Fridays are KenKen puzzles.

Mondays and Fridays are my favorite. I’ll probably swap out the estimation and WODB days for other things as the year goes on, but I usually keep the patterns for the entire year. This year I think I’ll keep the KenKen puzzle all year, because it’s going REALLY well.

I do this bellwork routine in Algebra 1 and Geometry, and since I had a handful of the Geometry kids in my Algebra 1 class last year, the Geometry class has been trained very quickly and very well. They can do harder patterns and are ready for harder KenKen puzzles than the Algebra 1.

The Algebra 1 kids are definitely picking it up, and getting the hang of how to fill in cells, what’s helpful and what’s not helpful, and how to think about the clues. We moved up from 3×3 to 4×4 a couple of weeks ago, and I bet they’ll be ready for 5×5 after fall break. (6×6 will be longer because moving up to an even number is harder than moving up to an odd number.) Every week, I make them do as much as they can on their own, and then we go over the puzzle as a class. I ask the class “What do we know now?” after each step and write down pretty much whatever they tell me. I spend a lot of time paraphrasing and restating what kids tell me, because I want to focus on the logic of the puzzle.

So the KenKen puzzles are going well, but some really cool things happened on Friday.

First, Algebra 1 – I had kids raising their hands and participating in the KenKen discussion who have NEVER raised their hands in my class before. They can tell me what goes in a cell and how they know. At this point, pretty much all I have to say is “Ok, how do you know?” the entire time. They are really getting into it.

Now Geometry is a whole different ballgame. On Friday, we’d been doing proofs for about a week. They’ve done examples of proofs, they’ve used to explore proofs in a structured environment, they’ve written reasons for proofs that have all the statements written, and they’ve attempted writing their own proofs.

On Friday, we went over the KenKen puzzle on the board, solved the whole thing, and I stopped them. “You guys. Everyone. Did you hear what you just did?” They all stare at me. “Did you hear what just happened as you solved that KenKen puzzle?” Now they’re really staring at me like I’m a crazy person. They’re probably sitting there like, yeah, we solved the puzzle, just like we do every week. So I said, “You just did a proof.”

Now they’re 100% positive I’m crazy.

I said, “For every cell in that puzzle, you made a claim, and you justified it. You told me what should go in that cell, and you told me why. That’s a proof. You just did a proof to solve the puzzle.”

Blew their minds. It was amazing. It took a solid few minutes to calm them down again, but the sudden realization of the connection between proofs (which they currently hate) and something that they are generally enjoying was totally worth it.

Also, I enjoy blowing the minds of high school students. It’s a major part of the reason why I teach.