Sophie Griffith

A Chess Puzzle

Inspired by the hit TV show The Queen’s Gambit, we tackled a chess puzzle in February’s evening meeting. Sophie shared a problem from one of Alex Bellos’s recent Monday Math Puzzles. Here it is:

Before we went into our breakout rooms, we spent a bit of time clarifying the ways that a Queen can move on the board, and making sure we agreed about which squares were “unattacked” or “safe.” (We had some debate about the square that the Queen is sitting on. In the end, we decided that this was not a safe square.)

Check out the Jamboard to see some of the work we did (or don’t, if you don’t want any spoilers!) One question we found intriguing was, “how do you know when you’ve found the best answer?”

Since then, many of us have been playing chess on chess.com. We’re even thinking about starting a CAMI chess club. Want to play? Send us a message and we’ll loop you in.

Why are maintenance covers round?

In the December evening meeting, Amy Vickers led us through a new exploration that was loosely inspired by last month’s meeting on some circles.

As a warm-up, Amy presented us with this question: Why might a manhole cover (or, in the gender-neutral, maintenance cover) be round? One of the central ideas that came up in the resulting discussion was that a circle won’t fall through its own hole, no matter which way you turn it. It has a constant diameter, or constant width.

A Pattern With Circles

In CAMI Meetings and in class with students, we often want a prompt to get students generating their own mathematical questions to answer, rather than giving them a predetermined math problem that everyone needs to solve. In the November evening meeting, we started off by considering some prompts and sentence starters to get students asking questions that will lead to math explorations.

Here are a sentence-starters that we came up with:

How many…?
How many ways…?
Is this always true?
Could this pattern continue?
Would it be possible to…
What would happen if…?

And a few questions we can ask to get students thinking mathematically:

Why would I show you this?
What’s the point?
What do you see that relates to math?
How do you see this?

What questions do you ask students to get them thinking? What kinds of questions do you want them to ask themselves?

Exploding Dots

Sophie gave us an introduction to the strange world of Exploding Dots, which can be used to represent all kinds of math. We started with place value.

In July’s evening CAMI meeting, we met an interesting machine, the “two one” machine, written like this: 1<–2 machine.

Here’s how the machine works:

We can add dots to the box on the far right – as many as we want! Whenever there are two dots in the same box…

…they EXPLODE!

Continue reading “Exploding Dots”