Worksheets be damned

I don't know where math anxiety comes from in our house, but it may have something to do with worksheets. My kids, especially the older one, think of worksheets as gratuitous torture which force them to do mental contortions just for the heck of it (I think the unbridled use of Saxon worksheets in my son's third grade classroom was responsible). For my part, I have been conditioned over the years to think of worksheets as a good way to get a handle on math facts and operations.

Everyone in our house has a pretty decent math sense. Which is not the same as knowing their math facts. Though, is knowing math facts a good way to learn to love math? What if math facts could come gradually through the love of math?

As adults, we know that facility with math facts helps us at the bank, the gas station, at the store, and in the kitchen. To kids, it must seem that math facts only help you do math problems. It's hard to see how they can help you solve any other kind of problem. And I've discovered that, more than anything, my kids, and many other kids I've observed, want to solve problems.

So, here's a problem for you (straight from Marilyn Burns' I Hate Mathematics):
How many popcorn kernels can fit in a mailbox?

This problem captures the kids' attention immediately for two reasons: it is completely silly ("Are we really going to stuff popcorn into a mailbox?!"), and it requires making popcorn ("Can I, can I?").

After the popcorn was popped, I found a smallish lightbulb box and asked the kids if they had any ideas about how to guess the number of pieces of popcorn that would fit in it without counting every one. Nadia's plan was to figure out how many were in one layer at the bottom of the box, then count how many layers the whole box could accommodate, and add them all up. Peter liked the idea of measuring the average kernel, then measuring the sides of the box, and mathematically (!) figuring out how many kernels the box could accommodate. Both perfectly good solutions, both arrived at independently, and not a worksheet in sight.

We considered both solutions, decided on Nadia's for the time being, and established that the box would hold about 412 kernels of corn. Now the problem was to translate the contents of the box into the contents of the  mailbox. Peter suggested that one way to tackle it was to see how many layers of boxes would fit in a mailbox, how many boxes were in each layer, and multiply it out. Not a bad plan. We went to check it out. Just in case, I brought along a tape measure.

First, we measured the mailbox using our small box. We omitted the curvy top of the mailbox, because it was non-conforming, and also, if we really stuffed popcorn in there, then it wouldn't open. We discussed the fact that so far we have been using non-standard units of measure: kernels of corn and lightbulb boxes.

For comparison, I suggested we should also take standard measurements, and that's where the tape measure came into play.

Back at home, we tabulated our findings, and came up with the following results:

• Using the non-standard units, the mailbox could hold about 101.25 lightbulb boxes.
• If each lightbulb box held 412 kernels, that the mailbox could hold 41,725.
• Using the standard units, the mailbox had the volume of 135,675 cm3, while the lightbulb box had the volume of 1,200 cm3.
• The mailbox volume was 113 times that of the smaller box.
• Thus, by this method, the mailbox would hold 46,556 pieces of popcorn.

So, if you really want to turn your mailman's day into a nightmare, you need about 50,000 corn kernels, which translates to roughly 75 bags of corn, at maybe 50 cents each, or between $35-40. Is it worth it?

Comments

[Lori]

is it worth it? of course it is!

your math sounds like lots more fun than the algebra class. first- it involves scootering, measuring tapes and popcorn. second because there isn't a very rushed time frame, unless you consider "all afternoon" a time frame.

[Justyna]

Yes, funny you should mention "all afternoon", I have another post on my mind just on that topic.