How Many Share Your Birthday?
This afternoon, we celebrated Alex and Eli’s sixth birthday with a Disney-themed Cinco de Mayo party. The kids all wore Mickey Mouse ears, while the parents drank lots of margaritas. Tonight’s “bedtime math” question for my sons was the following:
You celebrated your birthday on May 2. How many other people in the world do you think celebrated their birthday on May 2?
It’s a simple estimation problem for most of us, but ratio is a tough concept for six-year-olds. I wasn’t sure they’d make much progress… especially since the good folks at about.com make this claim:
You currently share your birthday with about 859,178 people who reside in the United States.
This estimate appears to have used 313,600,000 as the U.S. population, which is reasonable, and then divided by 365. My frustration is that they then display the result to six significant figures. That’s problematic for two reasons — first, because their population estimate has only four significant figures, but also because it’s not the case that exactly 1/365 of the population celebrates their birthday on a given day.
But I digress. Sure, I’m frustrated with about.com’s negligence, but I started this post to tell you about our bedtime math problem, and it highlighted why I hate traditional textbook problems even more than I hate bad math in the media.
Alex first suggested that maybe the number of people who have the same birthday could be found by calculating 1/14 of 7 billion. When I asked why he wanted to divide by 14, his response was, “Because it’s a multiple of 7.” When I asked a few more questions to probe his thinking, he changed his mind. “No, wait, maybe it’s 1/35.” This time, he said he wanted to divide by 35 because it was a multiple of 7 and a multiple of 5, and he knew that 7 billion was also a multiple of both 7 and 5.
Then it hit me. He wasn’t trying to solve the problem. He was just trying to make sure the answer was a “nice number,” that is, an integer that preferably would end in a couple of zeroes.
A few more questions, and he finally admitted he knew an estimate could be found by dividing 7 billion by 365. “But that doesn’t work when you divide,” he told me.
I believe this is what happens when kids see too many traditional textbook problems where the answers are neat and clean. They get conditioned to thinking that math is never messy.
[Update: 5/8/13] Just read this on the About page at the Let’s Play Math blog and thought it was worth including here: “Math is like ice cream, with more flavors than you can imagine — and if all your children ever do is textbook math, that’s like feeding them broccoli-flavored ice cream.”
And that couldn’t be further from the truth. Math is unbelievably messy. At least, real math is. Solving real-world problems often means getting a little dirty. You’ll have to roll around in fractions, dig through some decimals, and — Heaven help us! — occasionally tangle with some irrational numbers and extraneous results.
Eli then offered, “If you divide 7 billion by 365, you won’t get an integer.” (He smiled, proud of himself for using the term integer.) “That’s the answer, but I don’t know how to do that.” What he meant is that he couldn’t compute the result in his head; nor would I expect him to. We then found an estimate by building on Alex’s idea — instead of dividing by 35, we divided by 350 to approximate the number of people who celebrated a birthday on May 2, since 350 is close to 365 but gives a much nicer answer.
Wow. There are roughly 20 million people who will celebrate their birthday on the same date as you. Crazy, huh?
All of this reminds me of a few jokes.
Recent research shows that those who celebrate more birthdays live longer.
And all the time, I tell my wife:
Honey, you’re one in a million. Which means that there are 7,000 people on Earth exactly like you, so just remember that it wouldn’t be that hard to replace you.