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.
Here are just a few of our noticings and wonderings:
I notice …
- 1, 2, and 4 only have one dot, but 3, 5, and 6 have 2.
- In 4, the circles are a little bigger. In 6, the inner circle is off-center and smaller.
- The number of items in the box corresponds to the number for the numbers 1,2, and 3.
I wonder …
- If the size of the rings and the location of the ding matter.
- Is this a positional number system? or another kind?
- I wonder what #7 would be.
People had a lot more to notice and wonder about (I haven’t included the rest of our noticings and wonderings so that you have space to notice and wonder yourself!) and conversation moved naturally into trying to figure out the rules of the system. To facilitate this, I shared this link where you can put in your own number and see what the system produces. (Refresh the page when you want to look at a new number.)
When our group felt like they had a pretty good handle on how the system works, we explored two more pages that show how to add and multiply numbers in the Ring-a-Ding system. On each page, you enter the numbers you want to see added or multiplied and then watch the magic happen!
We had a lot of fun exploring how different numbers added and multiplied and making and checking predictions.
Here is the main Ring-a-Ding Numeration page. Warning – there are some spoilers – don’t visit the page until you have investigated all you care to on your own.
Want to see some of the work we did? Check out our Jamboard.
Is Ring-a-Ding Numeration useful or important? I don’t know, but it sure is fun to play with. For more on having fun with mathematical objects … or even falling in love with them, check out Jim Henle’s TEDx talk Math is for Our Pleasure.
