I'm not quite sure what I've taken on.
Thirteen kids aged 7 through 13 squeezed around my dining room table and looked at me with varying degrees of anticipation.
"I don't want this to be about rules." I ventured.
Running a math club for homeschoolers has been something I've been thinking about for several months. And now, it has officially begun. I imagine that a classroom teacher stands in front of her group of kids with a fairly firm idea of what she wishes to accomplish and how that's going to happen. I don't have a teacher's training, and had no such preconceived notions. I wanted merely to present what I hoped was a fun idea, and let the kids run with it. Yet now, running was something I was a little afraid of. There were, after all, thirteen of them.
Here was the problem:
You may use: one bag of popped corn, an empty box, a tape measure (optional), a calculator, plus paper, pencil and a friend.
The problem immediately had to get modified due to abundant rain, and a large quantity of squishy mud around my van. I desperately wanted that mud to stay outside. After a short deliberation, we decided to use various rooms around the house instead. I divided the kids into mixed-age groups, and set them loose.
Initially, they needed a little prompting. How would you go about figuring out how much popcorn will fill your box? Could you do it without counting the kernels? Could you do it without actually filling the box?
And they were off.
At first, four groups of kids crouched of the living room floor deliberating and scribbling in their notebooks. Then, for two hours, chaos reigned. Each team picked a different room to measure, and one team picked the fireplace. There were kids inside the fireplace. Others stood on the bathtub and the toilet. Still others climbed beds and each other's shoulders before they figured out they could measure the height of a ceiling with a stiff tape measure without actually climbing to reach it. Popcorn disappeared from bowls as great quantities of it were consumed or scattered on the floor in the course of the project. Calls for help were heard from one part of the house to the other. Younger kids needed explanations of what bigger kids were doing. Bigger kids needed conversion factors. Liam entertained everyone with stories of a monthlong ski trip from which he had just returned against his will.
But, in general, everyone seemed on board with solving the problem. Peter drew 3-d cubes and penciled in numbers along the sides. In between ski stories, Liam measured several corn kernels, and calculated their average size. Zola multiplied numbers into the tens of thousands longhand, oblivious to the presence of several calculators in the room. Zeb figured out that two boxes fit in a foot, and measured the room using boxes. Nadia wrote long paragraphs documenting every step of the process. Louise and Eric meticulously converted feet into inches and then into boxes. Mattie had a little trouble with writing some numbers, but seemed to intuitively grasp the concept of volume.
In the end, it was estimated that about 149,000 kernels would fill my fireplace, just over one million would be needed for the bathroom, and about three million for each of the bedrooms. As a bonus problem, we figured out that if we wanted to play a joke on Peter and literally fill his room with popcorn, it would cost us about $5,600. There were no takers.
Here are a few things I would consider for future math club meetings:
- Briefly introducing the basic concept of what we are doing. I wanted this to be as far from a "lecture" as possible, but a short demonstration of calculating volume with a few simple cubes might have been helpful.
- Having kids work in same-age groups. The idea of dividing them into mixed-age groups was, of course, to keep everyone involved, and to balance out different levels of ability. This notion of "balance" may be somewhat flawed. Younger kids may understand something conceptually, but are frustrated by the inability to express it in mathematical terms. However, they may be able to express it through pictures or narrative. Older kids who have the facility of using mathematical notations may find it more satisfying to use these shortcuts. I dunno. Different activities may lend themselves to different approaches.
- Allowing kids to choose to what degree they want to participate in the project. Kids have different attention spans. Many of the participants seemed quite eager to get down to the business of solving the problem, while others wanted to go exploring. I think that's fine, as long as they respect the essential integrity of my house. I prefer to have kids voluntarily engage in an activity. Perhaps if those who are genuinely engaged appear to be having a good time, the more reluctant ones will come around on their own.
I consider this our warm-up project. The kids almost certainly had fun. They probably learned something from the process as well, though perhaps it was not what I would have intended. Who knows. But, as usual, I myself learned a few things, and walked away with a lot of questions.
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