Math and Poetry

The Mostly-Annual PDS Math Contest (TM) is drawing to a close. This year, the challenge is to submit a poem about your favorite number, or your favorite number sentence. Entries are pouring in. 7 and 9 seem to be popular choices, as are the ol' reliable 1 + 1 = 2 and 2 x 2 = 4, but we have some, um, more creative favorite numbers and sentences as well...All will be revealed shortly.

In the meantime, another thought about poetry and math. Some people claim that the two disciplines are unrelated. How very wrong they are! Here's an example from just last week of how an understanding of poetry can help children improve their math skills. Yes! Srsly!

Background: We asked first graders to solve a word problem that involved finding the sum of three addends--5, 7, and 5, in this case--and to EXPLAIN how they got the answer (a big step for children that age). Most of the children wrote something like "I added 5+5=10 because it's a doubles fact and I know that 10+7 is 17." Short and sweet. Some used their fingers to help, or drew sketches as evidence. BUT one young lady had a very different approach:

"I remember when we were studying haikus. Haikus go 5, 7, 5 [that's the number of syllables per line--SC]. I counted how many altogether in a haiku and it was 17. So I know 17 is right."

Another example of the interdisciplinary learning PDS does so well...:)

Pi Day

One of the great mathematical holidays of the year is Pi Day, which occurs every March 14. (It may be the only mathematical holiday of the year, in fact, but never mind.) The third and fourth grade classes celebrated Pi Day this year by deriving this number--or as close as we could get.

We began by distinguishing, of course, between pi (the number) and pie (the food). Several students said they'd heard of pi (the number). All students said they'd heard of pie (the food). Once we had that out of the way, we introduced the concept of DIAMETER (distance across a circle, through the center) and CIRCUMFERENCE (the distance around a circle). "Okay, here's the question," I said. "Are these distances related? If you know the diameter of a circle, can you use that to calculate the circumference without measuring?"

To explore, we had pairs of students use tape measures to determine the diameter and circumference of various circular objects in their classrooms--clocks, round tables, woven mats, stools, and more, rounded to the nearest whole centimeter. Here's a sampling of their results:

Bowl d = 9 cm C = 28 cm

Stool d = 21 cm C = 66 cm

Wheel d = 13 cm C = 45 cm

Garbage can d = 49 cm C = 150 cm

"Any patterns in the data?" I asked. Ye-es, the students said tentatively; the circumference is always more than the diameter. "By a lot, or by a little?" I queried. By a lot, they agreed. Usually, one cautious soul hastened to add. "So maybe if I add the same number to each diameter, I'll get the circumference," I suggested. "What number would I have to add to get the circumference? Talk with a partner and see what you come up with."

They considered the question and then they shook their heads. The numbers didn't work. You need to add a small number to the diameter of something small, like a magnifying glass, they pointed out, but you have to add 100 or even more to the diameter of something big. Clearly, addition was NOT the way to go.

If addition didn't work, the obvious answer was multiplication, and the students quickly moved in that direction. (Multiplicative thinking at work! Hurray!) "The circumference is, like, double the diameter," one student suggested. "More than double," a classmate countered. "Triple the diameter," said someone else. We tripled a few diameters using mental arithmetic. "When you triple it," someone concluded, "you get just a little bit less than the circumference." "Usually," piped up our cautious friend from before. "Oh, I know!" shouted an excited third grader. "You triple the diameter and then you add one! Oh, wait a minute--"

This, as it turned out, was a job for a calculator. We keyed in circumferences and divided by the diameter, then recorded the ratio (a new word for most students) on the board, cutting the endless stream of decimals to two places. 3.33, 3.00, 2.97, 3.24... "They're mostly around 3," students noted. I nodded. "We can't measure exactly with our tape measures," I explained, "but if we could, we'd discover that the ratio is always the same--a little over 3. This number is pi. The digits of pi go on forever, but are there any guesses about what pi would be if we just used two decimal places?" There were plenty of guesses, of course, there always are, but one exceptionally observant fourth grader had a reason for her answer. 3.14, she said, for why else would Pi day be March 14?

Why else, indeed?!

A footnote: This year, Congress passed a resolution officially declaring March 14 to be Pi Day; the resolution was also an attempt to highlight the importance of math education. Incredibly enough, ten representatives voted against the resolution. It's fun to speculate why. Perhaps they have had bad experiences in the past with irrational numbers, or maybe they think the value of pi should be determined by the open market, not the government--oh, wait... More information about the bill can be found here.

(Photo credits to Jan Campbell, and to Ellen DeLong's camera.)