Ring-a-Ding Numeration

We started this meeting with a notice and wonder with this image of the numbers 1 through 6 in a numeration system created by professor emeritus at Smith College Jim Henle. The system (a piece of mathematical art!) is called Ring-a-Ding Numeration. The rings are the circles and the dings are the dots.

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Number Visuals

The session opened with a wonder and notice of this image:

Participants noticed that the number of dots in each figure is increasing by one as you look left to right in each row. One person said they see certain groupings of dots repeated in other groupings. Another noticed that the dots are arranged in a circle for some numbers and someone else wondered if that was because those numbers are prime.

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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.

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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?

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A pile of coconuts

Sophie led us through the following problem from the Museum of Math’s weekly puzzle during COVID. Sign up for emails from MoMath.

PUZZLE: Coconut Classic
Five men and a monkey, marooned on an island, collect a pile of coconuts to be divided equally the next morning. During the night, however, one of the men decides he’d rather take his share now. He tosses one coconut to the monkey and removes exactly 1/5 of the remaining coconuts for himself. A second man does the same thing, then the third, fourth, and fifth. The following morning the men wake up together, toss one more coconut to the monkey, and divide the rest equally.

What’s the least original number of coconuts needed to make this whole scenario possible?

Mind-Benders for the Quarantined! (Museum of Math, NYC)

We had a lot of interesting ideas and shared a few strategies, but we didn’t get to a solution.

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Rainbow Squares


We started with a quick game of online Simon Says.

It was okay, but a little clunky. Usha suggested a different kind of activity where video on means yes and video off means no. Read a series of statements. Here are a few I brainstormed: Winter is my favorite season of the year. I love ice cream. I am excited to be back in school. I want to go to college. (You probably have better examples.) End with a statement everyone can say yes to…

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Sums of Consecutive Numbers (follow-up)

In this meeting, we explored the sums of consecutive numbers (inspired by a CAMI meeting led by Usha Kotelawala in June 2017). The meeting is also based on a two-day lesson I led with the support of other teachers during summer 2020 problem-solving meetings with CUNY adult education students.

Before the meeting, I shared this post on the CAMI email list:

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