- Topic: Multiplication, Story Problems. Book: The Book of Perfectly Perilous Math by Connelly. Chapter 1: The Pit and the Pendulum. In this chapter you are tied to a table as a sharp pendulum swings back and forth, lowering with each swing. Meanwhile a rat is one minute away from gnawing through the ropes that hold you. Will you escape before the pendulum kills you?
- Topic: Pendulums. Each kid had a spoon pendulum. We experimented with how many times the pendulum would swing back and forth in a certain amount of time.
- All 5 pendulums were the same length, but dropped from different heights.
- 5 different length pendulum.
- One pendulum that we all counted together, with different length strings.
- Topic: Logic, Story Problems. Chapter 13: The Rope Bridge, from the Perfectly Perilous book. Zombies are twenty minutes away from you. You and four friends have to cross a rope bridge. Two people can go at a time, and you have to share one flashlight. Each person takes a different amount of time to cross: 1, 2, 3, and 8 minutes. Can you all cross in time?
- Topic: Combinations. How many different jack-o-lanterns can you make with a set of eyes, nose, and mouth? There are 2 different eyes, 1 nose, and 2 mouths. Each feature can be right side up or upside down.
How did it go?
We had all 5 kids this week. Halloween was yesterday so we had spooky, Halloween themed activities.
The Pit and the Pendulum
The kids instantly loved this book. They wanted to look at all the chapters at once, and were excited (and slightly scared) by the short stories. The book says the pendulum swings back and forth every 7 seconds, and drops one inch per second. The pendulum is 15 inches above you. How long till it hits you? The kids quickly figured out that the answer would be 15 X 7. One girl computed this using long-hand multiplication. I had the other kids check her work by computing: 10*7 + 5*7, which they could all do.
So the pendulum would drop in 105 seconds, but the rat will untie you in 60 seconds, leaving 45 seconds to escape.
I gave each kids a pendulum spoon. I wanted each pendulum to be 12 inches long so I had a measuring tape. All the kids wanted to measure their own pendulum, which slowed us down. Eventually, they were all set. Everyone released their spoon at the same time, and counted their swings for 20 seconds. Three kids got 20 swings, and two got 18 swings, so it was pretty close.
Next each kid chose a different length of pendulum. We had some more trouble because at first everyone wanted a long pendulum, and then as soon as I convinced a couple kids to use a short one, then everyone wanted a short one. Finally I got 2 kids with long strings, and 3 with short ones. We tried to time them for 20 more seconds, but spoons were hitting each other, and everyone was laughing and forgetting to count.
I corralled everyone together again, and we used just one pendulum and counted it together, with a long, medium and short string. We did the long string twice to make sure our result was repeatable. We found that in 10 seconds, the long pendulum swung 6 times, the medium 8 times, and the short 12 times.
I asked why that might be. One girl suggested that different parts of the rope may be pulling on the longer pendulum. My daughter suggested that the longer pendulum travels further on each swing.
The Rope Bridge
Again, the kids loved the themes in this book. They all wanted to draw and talk about zombies, and also to solve the problem to see if the kids lived. Two kids quickly came up with the same idea: the fastest person should go with a friend across the bridge, and then run back with the flashlight to get the next person.
Everyone liked that plan, but one girl was worried it would be too slow. So, we worked it out together. First the 1 minute and the 8 minute person crossed. There were some interesting ideas about how long it would take them to get across. Someone said it would take 9 minutes. Someone else said it should take 1 minute, because the fast person could carry the slow one on their back. We finally decided it should take 8 minutes, becuase the 1 minute would have to slow down to the speed of the slower person.
We worked out it should take: 8 + 1 + 3 + 1 + 2 = 15 minutes to cross, which gave us one extra minute before the helicopter arrived to rescue us from the zombies.
My daughter was really excited to do this one, because the older circle doesn’t work with pictures and glue sticks very often any more. This time, I decided not to sort the pumpkins for the kids. I would make them decide if there were any duplicates.
At first everyone just made pumpkins, but it quickly became difficult to tell if the pumpkin was new. A couple kids volunteered to sort the pumpkins. One kid wanted to sort them first by whether the nose was up or down. Another kid wanted to make rows for each kind of eye.
We ended up making rows for each eye, but then the kids couldn’t figure out how to sort within each row. My daughter wanted to make the columns have the same nose and mouth, but many pumpkins were missing, and there were many duplicates which complicated it.
Also, having 3 kids try to sort at once, without a clear strategy was pretty chaotic. The first kid independently tried to come up with a strategy by drawing different types of pumpkins on her paper. The second kid drifted between the sorting and the pumpkin making without really being engaged. The third made pumpkin after pumpkin without checking if there were duplicates. The fourth delivered pumpkins to the floor where we were sorting. My daughter and I tried somewhat unsuccessfully to sort the pumpkins together. Then we ran out of time.
So…we don’t know how many different pumpkins we made! Follow up work for next time.