Math Circle 11.18.2014


(November 18, 2014)  Right away I got out the book “I Love You as Much,” which we were using as an infinity discussion prompt last week.  One of my two assistants, J, read it aloud to the group.  When we got to the page about the “endless blue sky,” N declared, “That’s a lie!  The blue sky isn’t endless!”  He began a brief conversation (continued from last week) about whether the sky – and infinity – are circular or linear.

Then came the line about “as much as the desert is dry.”  “How dry is it?” I asked.  Most answers involved the number one hundred (100 feet, 100, etc.)  I suspect the kids meant 100% but didn’t have the concept of percent under their belts yet.  “Is it totally dry?” I asked.  Most said yes, but both S and L, who I think have been to the desert, explained to the others that the plants hold water and if you cut open a cactus you’d find some.

In response to “as much as the grain in the mill” came many different numbers, some large, some small.  Somehow we got into a conversation about how high it’s possible to count.  Kids were shouting out conjectures to me without regard to each other.  So we started counting.  Aloud.  Very loudly.  In unison.  In rhythm.  It felt like a mathematical tribal chant.  Very powerful.  Then the counting dwindled somewhere between 50 and 100, but some kids continued to count under their breath into the next activity.



Not everyone was totally settled, so I decided to do a math-related mindfulness activity,* the Human Knot.  In this activity, the kids stand in a circle and hold hands with non-adjacent others.  Then they try to untie themselves so that the people with whom they are holding hands end up as their neighbors.  It is a mindfulness activity because deep attention is required for everyone to end up with 2 non-adjacent hand-holders and because the whole self is involved.  It is a math activity because of the distinction between adjacent and non-adjacent, and also because of the implied idea that things that can be done can be undone.  But can everything be undone?  Does every function have an inverse?  We did the human knot 3 times, exploring these questions without explicitly stating them.



As soon as she arrived today, R was asked me, “Are we going to play Math Red Light Green Light?”  (Drat, I was hoping that name wouldn’t stick.)  Finally we were ready to go outside and brave the freezing temperature.  I intentionally led the kids to a gravel path so that they couldn’t use chalk to draw halfway-point reference lines.  It didn’t even come up.  “I know where my halfway point is!” shouted everyone throughout the game.    Unfortunately we had the same problem as last time in the endgame, only worse:

  • 3 kids jumped onto J’s feet at the end, instead of progressing just half way.  Then 2 of them ran off to play in the trees.
  • 3 kids were so far behind that they weren’t involved in the endgame. They just stood there, waiting patiently for their moment in the sun.

L, one of the kids who jumped forward to the finish, stayed.  “Was that jump halfway from your last position?  I asked him.


“Is it the rest of the way?”
“So are halfway there and the rest of the way there the same thing?” I asked him.

“Yes, they could be the same,” he answered.  Hmmm….  interesting .  I was tempted to delve into further deep discussion about this with L.  But 2 kids were in the trees, three were waiting too far behind to hear this, and one wasn’t participating because he was hungry.  To be continued.
(I did notice later, when looking at the great photos that my other assistant L had taken, why halfway and the rest of the way could be the same thing.  When approaching the finish line, the kids’ feet are long enough to be standing on the halfway point and the finish line at the same time.  Next time we’ll do something about that.)



I read the first chapter plus one page of The Cat in Numberland to the kids.  This book is about infinity, particularly mathematician David Hilbert’s famous paradox of the Grand Hotel.  While most of the math in this really fun book is probably inaccessible to kids this young, enough of it is, and they can latch on to that which they can wrap their minds around.  These kids loved it.  They had fun with the presentation of odd and even numbers.  They interrupted the storytelling to point to each other and categorize people’s ages as “even” or “almost even.”  Anyone age 4 or 6 was “even.”  Anyone 5 was “almost even.”  (Is it a crime to be odd?)  M said, “I’m six and a half.”  Not everyone agreed whether she was even or almost even.  Then they asked my age.  “That’s too old to tell,” said N.



We looked at some patterns with colored cubes.  I layed out cubes in certain orders and asked the kids to predict the next color and decide which rows of blocks were patterns.  It got harder as we went.  Everyone enjoyed.  I asked for definitions of the word “pattern.”

Then we finished up revisiting a logic puzzle from last year’s math circle, The Very Clever Prince.  (Back by popular demand – the kids have been talking about it since last week, and those who were in math circle last year have been thinking about it since last year.)  I’ll write more on that another time.

Many thanks to my helpers J and L.  Looking forward to next session!


*The kids had an excess of energy today.  They needed help keeping their hands and bodies to themselves.  I integrated some mindfulness practices to gather and focus this energy.  I’ve written extensively before about the value of such practices to mathematical inquiry, so I won’t explain that here.  (Email me if you’d like some more info on that.)  But I will tell you what we did:

  • I did not let the kids into the room we use for math circle until it was exactly time to begin.  I wanted to delineate math circle time from free time.  To get into one classroom to the other, one must past through 2 doors.  I asked the students to wait until J called their name, then inhale as they walked through the first door, exhale through the second, then quietly find a seat around the table.
  • At the table, I played a note on a triangle. “Some say that the sound this makes never stops.    If you think it does stop, put your head down when you stop hearing the sound.”  Some kids were able to sense the sound in their feet.  This generated a conversation about singing bowls, which 2 of the kids were familiar with.

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