Joss Ives ask for a list of my Math Circle activities for young children. What Joss asks for, Joss gets, so here is a blog post on the activities. Also, my wife wants a list of the activities we did in January and February, so I get to kill two birds with one stone with this post (Note: my usual communication with my wife is not via this blog).

Procedure: We meet once per month in a room at the public library. I usually run two 30-minute sessions, with three to seven kids attending each session. Their parents are rarely in the room, although it happens on occasion.

I stole most of these ideas, mainly from Math from Three to Seven by Alexander Zvonkin and Math Circles for Elementary Students by Natasha Rozhkovskaya. I also steal ideas from Talking Math with Your Kids by Christopher Danielson. I am trying to cite every place where I stole ideas, but I am sure I am forgetting. Please contact me if I should be giving you credit.

Disclosure: I have met Christopher and I am friends with Natasha, but no one has paid me to link to anything in this blog post (or any others).

Here are the activities.

Day 1

1. I gasked questions like “Are there more geese than birds?” and “Are there more women than moms?” I wanted them to start thinking about set containment.

2. I showed them pictures of, say, a bunch of dolphins (and also cats) that look similar (I drew them). I asked, “Is it true that there exists a dolphin with a ball?” “For all cats, the cat has an umbrella?” The purpose is to get them thinking about quantifiers.

3. I showed them a geoboard. I put a geometric design on the left half, and they had to do the mirror image on the right half.

Day 2

I taught them to use Base Ten blocks with the help of a puppet named Yachel. I told them that Yachel is afraid of the number “ten,” so he does not to see ten of anything. The kids organized the Base Ten blocks into groups of ten so that there would be only one big group, rather than ten small groups (so Yachel wasn’t afraid). They kept doing this until all of the blocks were organized. In the end, I asked them to guess how many blocks there were (something like 1287), and I showed them that they can actually tell exactly how many of them there are by just counting how many big groups of each type they made.

I don’t know how much the kids learned about the Base Ten number system, but Yachel was a *huge* hit; my kids still treat him like he is one of the family.

Day 3

I read them a book called something like *5 Cats*, in which the cats categorize their family members into different groups (3 are male and 2 are female; 1 is black, 2 are white, and 1 is calico; etc). I brought hula hoops, and then I asked questions so that the kids could sort themselves (“Stand in that hula hoop if you are wearing something blue today.”). This was a bit of a flop.

Day 4 (March 2016)

This was a Pi Day celebration. I found a bunch of circular lids of different sizes, and cut up a bunch of pipe-cleaners so that they were the length of the diameters of the lids. Then I hot-glued googly eyes on them, and called them “Diameter Worms.” I made up a story about how Diameter Worms find circles to live in, just like hermit crabs. The Diameter Worms need to have a circle that is exactly the right size for it. Then I asked them to figure out how many Diameter Worms can lie end-to-end around the outside of their circle home. First, they made a prediction, then they actually wrapped the worms around the home. Of course, everyone learned that “a little more than three worms” could fit around, regardless of the size.

I don’t know how much they learned about pi, but it started a Diameter Worm craze in my son that lasted for several months.

Day 5

1. More work on subsets and quantifiers, as we did in Day 1.

2. I did something with 3×3 patterns, but I don’t remember what.

3. I gave students cut-out polygons and scissors, and they had to do certain challenges. For instance, cut quads into 2 triangles, or cut a quadrilateral into 2 quadrilaterals, or cut a quadrilateral into a triangle and pentagon.)

Day 6 (11/2016)

1. We did Danielson’s Which one doesn’t belong?

2. We played Nim on graphs, which is a game developed by Marie Meyer and me for her senior thesis.

Day 7 (12/10/2016)

We played (in an unstructured way) with Base 10 blocks (there were only two kids that week).

Day 8 (January 2017)

1. Danielson’s How many? to get at the idea of units.

2. We talked about “Doot Aliens.” When Doot Alien A touches Doot Alien B’s nose (which makes a “Doot!” sound), both Aliens disappear and some Doot Alien C reappears in its place (A-Doot-B always results in the same C, although B-Doot-A might not result in C). There are Ghost Aliens such that A-Doot-Ghost yields A, as does Ghost-Doot-A. I asked them: “What happens when one Ghost touches another Ghost’s nose?” They didn’t come up with the answer, but a couple of them have asked me about Doot Aliens (without me prompting) since then.

3. I gave them a bunch of statements like, “The sky is blue” and “There are seven people in the room,” and I asked them whether each statement was true or false. Then I asked about “This sentence is false.”

4. More of Danielson’s Which one doesn’t belong?

Day 9 (February 2017)

One-cut hearts to celebrate Valentine’s Day (plus, one-cut stars to celebrate Betsy Ross).

Day 10 (March 2017)

I am working a new Pi Day activity, but I haven’t thought of it yet.