# The Parallelogram and the Pendulum (Age 8)

## The Activities

1. Topics: Logic:  Still More Stories to Solve, by G. Shannon.  We read and discussed the first two stories.
2. Topics: Spatial Reasoning, Tangrams:  We did the same set of tangrams from a few weeks ago (letters, numbers, and things from Cinderella).
3. Topics: Physics, Experiments:  Inspired by the Galileo chapter of Mathematicians are People Too from a few weeks ago, I hung a makeshift pendulum from the ceiling — a roll of tape suspended from an 8′ thread, hanging from a sticky hook attached to the ceiling.  I had pre-marked the 2′, 4′, 6′, and 8′ points away from the center of the roll of tape.  We released the pendulum twice at each length, varying the height that we released it at, and timed how long it took to go 20 swings.
4. Topics: Sorting, Patterns:  We have a card game called Blink — basically a racing version of Uno.  Each card has some number of symbols 1-5, one of six colors, and one of six shapes.  There are 180 possible combinations, but only 60 cards in the deck.  After we figured out there should be 180, I asked the kids to find out which ones are missing.

## How Did It Go?

We sat on the floor this week to make room for the pendulum; this tends to make them a little crazier since they can easily roll around on the floor.

#### Still More Stories to Solve

I wasn’t crazy about the first puzzle, but the second one, about two brothers having a contest to see whose horse would get somewhere LAST, was nice.  The kids figured it out with some hints.

#### Tangrams

Corey and I discovered that I’m better at Tangrams than she is :), so unlike last time, where Corey AND the kids were stuck I was able to help them solve the puzzles.  The main thing I tried to teach them was to figure out where the big triangles go first; it’ll be interesting to see if next time we do Tangrams they remember this.

#### Timing a Pendulum

As you can see from the chart above, we had really reproducible results.  I believe we were actually only counting 19 swings (we started on 1 as we let go and then stopped when we said 20, when we should have let it swing again).  Anyway, I had incorrectly remembered from physics long ago that the time was linearly proportional to the length of the pendulum, so I was initially worried about the timings we were getting — but once they were all in, it become obvious (to me, not the kids) that the time is proportional to the square root of the length.  I asked how long the pendulum should be to get 15 seconds; and also, how long would a 32′ pendulum take.  They were comfortable assuming a linear relationship, but when I pointed out that 8′ was four times 2′ while 60 s was only two times 30 s, they couldn’t really use that information — one kid did guess 1/2 foot for the 15 seconds question, but they didn’t stick to their answer so I think it was just a guess.

One thing that worked out well is that the pieces of tape served as resting spots for the thread so that it would stay at the right length (I didn’t cut the string, we had looped it over the hook like a pulley).  If I hadn’t had the tape sticking out, it would have been hard to maintain a constant length.