# Spilled Water and Furry Houses

## The Activities

1. Topic: Factors: Book: One Hundred Hungry Ants by E. Pinczes.
2. Topics: Sets, Attributes: I had a number of groups of four clip-art pictures, download here.  I asked the kids to divide them into two groups based on some attribute (e.g., girls vs. boys).  For each set, we came up with as many ways to group the pictures as possible.
3. Topics: Geometry, Graphs, Map Coloring: I had several different similar pictures of flowers, with clearly defined regions.  The task was to color each flower using as few colors as possible, subject to the rule that no two adjacent regions could have the same color (this is often referred to as the map coloring problem).  Some of the flowers could be done using 3 colors, others required 4.  You can download the pictures here.
4. Topics: Measurement, Conservation of Volume:  I gathered a number of different household containers, such as drinking glasses, tupperware, a champagne glass, etc.  The goal was to compare the relative volumes of each of these containers by pouring water from container to container.
5. Topics: Games, Tower of Hanoi:  We have enough sets of Tower of Hanoi for each kid to have one.  I started them with three rings each and then we tried the four ring version.

## How Did It Go?

We had 4 kids this week.

#### One Hundred Ants

The kids listened intently to this book and noticed that the other animals were stealing the food while the ants were busy making rows.  I didn’t do any follow up discussion about the different ways to make 100.

#### Map Coloring

The kids made rather different amounts of progress on this one.  One kid understood the rules, and I helped them get through all 4 of the pictures.  Another mostly understood the rules but kept accidentally coloring adjacent regions the same color.  Another wanted to keep coloring the first picture with different color schemes.  And the final one wanted to watch everyone else do theirs instead of working on their own.  For the one who made it through all 4, I asked what the difference between the first and last one was (6-petals vs. 5-petals), but their answer was mostly “3 colors worked on this one but not that one.”

#### Relative Volumes

I decided that I would do all the pouring, which in theory could have made it less engaging; as it turned out, the problem was that the kids got TOO excited (my son had to have a timeout partway through because he was dumping water out of the cookie tray I was using to catch any spilled water).  My measurement method was to fill one of the things and then pour it into the other.  They understood the idea that if it overflowed, then the first was bigger.  They were super excited whenever it overflowed, as you might expect.

The kids don’t really understand transitivity, and as a result they didn’t realize that we could come up with a total order over all the items.  A particularly good example of this is that initially, most of the kids thought the champagne glass would be bigger than a drinking glass, because the champagne glass was taller; and later on, many of them still thought the champagne glass would hold more than an even bigger drinking glass.  They certainly gravitated towards preferring the taller thing.  They greatly underestimated the volume of a 5-6″ square, 2″ tall tupperware — they initially thought it was the smallest but it was actually one of the biggest.  At one point, one kid said that the big drinking glass would hold about twice as much as the champagne glass, because about half the champagne glass was just stem — a nice observation (although actually the drinking glass was way more than that, because it was also much wider).

#### Tower of Hanoi

The kids got the rules in a reasonable time; there were a couple of things they tried: holding one ring off to the side while they used their other hand to move another ring; and moving a whole pile of rings at a time.  I started with a 3-ring puzzle, and no one could solve it — no one came up with the hard idea of moving the little ring on top of the 2nd smallest in order to make space for the big one to move.  Interestingly, several of them got the (seemingly equally hard) idea of then needing to move the little one to the empty spot so they could move the middle ring onto the big one.  By the end, most of them had successfully demonstrated the solution to the 3-ring puzzle.  The 4-ring puzzle was quite a bit harder; several kids made it to the point that they had moved the 2nd biggest ring (but not the biggest) — one kid did solve the puzzle but with help from me at several points.  So they definitely have lots of room to improve.