# Math Circle Turns Two!

## The Activities

This was the second anniversary of our first math circle, so we decided to revisit some memorable activities from past circles.

1. Book: Brian Wildsmith’s Puzzles by B. Wildsmith.
2. Topic: Conservation of Quantity:  This was one of Piaget’s conservation problems.  I laid out two parallel lines of different colored stones, each with the same number.  I asked which had more, then spread out one of the lines and asked again.  Then I removed a few to make them the same length, spread that one out again, etc.
3. Topic: Conservation of Quantity:  I had some number of blocks, and arranged them in different shapes, including stacking, asking whether there were more or less than before.  I also cheated and (attempted to) remove or add blocks without them noticing.
4. Topic: Logic:  We have some small Wizard of Oz dolls (I believe they originally were prizes in McDonald’s Happy Meals).  The set has Dorothy, Scarecrow, Tin Man, Cowardly Lion, Glinda, Wizard of Oz, Wicked Witch of the West, and Wicked Witch of the East.  In each problem, the characters had a race, and there are clues about what order they finished in.  Note that Glinda is a witch, and I abbreviate WWotW or just West for Wicked Witch of the West.
 Using all but tin man and lion: Wickeds were first and last. The East was next to Glinda. The hats of same color were together (Scarecrow and WWotW). Dorothy held the Scarecrow’s hand. The wizard finished just before Glinda. Using all but tin man and lion: The Wickeds were next to Dorothy on each side. Scarecrow next to Glinda. East finished after Dorothy. The boys were together. Glinda was first. Using all but tin man and lion: Pointy hats finished together (West, Scarecrow, East).  A boy won the race. Dorothy cried because she was last. East pulled Glinda’s hair and finished before her. The two with lightest hair finished together. Someone with black shoes was second. Using all 8: Every other person had a pointy hat. Red shoes won and lost. Boys were together. Witches were together. Scarecrow held hands with the wizard and the lion. Green skin and green pants were together. No hat won the race (Lion or Dorothy). Using all 8: The wizard and the lion are (directly) surrounded by mean witches. Dorothy didn’t win. 2nd place had red shoes. Someone with a dress won. The witches are apart. The WWotE finished right ahead of the wizard. The tin man cried and rusted because he was 2nd to last.

Solution for puzzle #4

5. Topics: Sorting, Numbers:  I gave them a shuffled deck of cards from 1-104 (our deck is from the game Category 5, also available as 6 Nimmt!).  They had to sort the deck as fast as possible, laying it out in a line.

## How Did It Go?

We had four kids this week.

#### Brian Wildsmith’s Puzzles

A nice book with fairly simple puzzles, but with a nice amount of variety.  The kids had no problems at all solving the puzzles.

#### Conservation of Quantity

As expected, both the conservation of quantity activities were trivial for the kids.  They weren’t confused for even a second about which had more, and they pointed out that the spread out line had more spaces between the stones.  They were even less fooled by the blocks activity, rearranging the blocks didn’t trick them, and they actually saw when I tried to cheat.  Even when I managed to get one away without them seeing, they had no doubt that I had stolen it and tried to find it under the table.

#### Wizard of Oz Logic

Last time we did this, some of the kids were pretty good, but not all of them.  This time, all the kids were pretty good at it.  Still, it wasn’t trivial.  Last time, I often directed their attention to particular clues they had already read in order to speed things up (it’s not even clear they would have finished without the hints), this time I only did that a couple times.  Another big difference is that this time, they could read the clues themselves.  They were much better at incorporating clues even when they didn’t uniquely determine anything; for example, if they knew that the wicked witches were on each side, they would go ahead and pick one of the two possibilities, and switch it later if they needed to.

#### Sorting 1-104

This also went better than last time we did it, but not by a lot.  They were able to do the first 60 cards in 10 minutes, and the whole thing in 13:24.  They still had some issues of coordination.  Most of the kids spread out their cards on the ground, but one held her cards in her hand and cycled through them.  At first, they didn’t skip, which slowed them down a lot, but after a while they started skipping, but still usually only one at a time, which slowed them down a lot.  After they got to about 20, someone suggested looking for all the 30’s.  Meanwhile, two of the other kids had started at 50 working upward one at a time.  One funny thing was that the kid who had the pile of 30’s got distracted trying to help those two find the 53.  If they did it again, I think they would be quite a bit faster, since they were quite a bit more robust to missing single cards by the end.