Talking Math with My Kids

I’ve gotten so many great ideas from Twitter that I wouldn’t know where to begin describing them all. One of my newest favorite ideas comes from Christopher Danielson and his “Talking Math with Your Kids” project. As he points out,

Parents know that we need to read 20 minutes a day with our kids.

In the same vein, it seems clear that we should make exposing our kids to mathematics a daily goal. At our house, our kids have always been around a lot of conversations about mathematics, but until recently I hadn’t been making a conscious effort to engage with them mathematically. (I have a 3-year-old son and a 1-year-old daughter.) It’s been fun to see where the 3-year-old is in his mathematical development. Here are some things we’ve talked about recently:

  • While buying school supplies: My son’s class required three boxes of tissues and my daughter’s class required two boxes of tissues. I explained this to him. On one hand we held up three fingers and on the other hand we held up two fingers. I asked him, “How many boxes of tissues do we need to buy?” His initial response was, “Three-two!” Then I asked him to count my fingers: “One, two, three, four, FIVE! We need FIVE boxes!” We went on to talk about that three plus two equals five (3+2=5), and then he let me count his fingers and I counted that two plus three equals five (2+3=5) as well.
  • Before watching TV: After picking both kids up from school, we have snack time and the 3-year-old can watch a few minutes of a Mom-approved TV show. (Usually it’s some PBS cartoon; for a long time, his favorite has been Dinosaur Train.) When I asked him how many minutes of Dinosaur Train do you want to watch today? he thought for a long while. I could see he was really trying to think of a very large number. He then excitedly yelled, “TEN!” We clapped and agreed he could watch ten minutes of TV during snack time.
  • On the way to school today: He asked if I was going to go to work today and I told him yes. Then I asked him if he knew I was a teacher, too, just like his teacher at school? After some conversations about whether or not I took a school-bus to my school (I don’t), he asked where my school was and if it was very far away. I told him it was twenty minutes away. Although he can count to twenty, I don’t think he has a sense of what twenty looks like, or how big it really is. He then asked lots of questions about my 20 minute distance:”Is it more than six minutes?” Yes.
    “Is it more than seven minutes?” Yes.
    … “Is it more than eleven minutes???” Yes.

    Then we were at his school and I told him, “It’s even more than nineteen minutes.” He said, “Oooh. So it IS more than six minutes.”

  • Practicing Counting: He’s been learning whole numbers larger than twenty at school recently. We were practicing counting together, and he said: “…twenty-seven, twenty-eight, twenty-nine, twenty-TEN!” We laughed and told him that after twenty-nine comes thirty, and his face let us know this did not make sense and he was not happy. If it goes eight, nine, ten, why does it not go twenty-eight, twenty-nine, twenty-ten? This seems like a really valid concern.

    I used to know a lot more French than I know now. Our conversation made me wonder what he will think in a few years when I can explain to him about soixante-dix (they use sixty-ten for “70”) and even quatre-vingt-dix-sept (four-twenty-ten-seven for “97”).

Combinatorics and Pampers

I’m a mom of a toddler and a newborn, so my house goes through a lot of diapers. We’ve been using Pampers almost exclusively since my son was born in 2010. Pampers offers a program called “Pampers Rewards” where you can enter codes found on Pampers products to their website, and redeem for cool stuff. (Let’s agree to ignore all issues about the effects of disposable diapers on the world ecology, or on family size and the exponentially growing population of humans on our planet, or the obvious questions about why Pampers is trading me stuff for lots of data about how often my kids pee.)

The coding scheme that Pampers uses has bothered me for a while. Each Pampers item comes with an alphanumeric 15-digit code, something like “T9PDXPKKGA3M4GK”. Given that for each character we have 36 possibilities, and the codes are 15 characters long, there are a whopping 3615 such codes. This is about 2.2×1023. That’s a lot of possible codes! How many? If every single one of the seven billion people (7×109)  on the planet used Pampers, there would be enough possible codes for each person to have one billion codes just for themselves — and then there would still be some left over. While my kids use a lot of diapers, I surely hope we don’t end up needing a billion boxes of Pampers for each of them.

Why does Pampers do this? I am not sure. Instead of an alphanumeric code, why not just use an alphabetical sequence of length 15? This would mean “only” 2615, or a little shy of 1.7×1021. In this case, there would still be more than a billion codes available for each one of the seven billion of us.

It’s in Pampers’s interest to make sure only a small percentage of all possible codes are actually connected with a particular product; this prevents fraud on their Rewards program. If I were going to design codes, I’d want to make sure that of all possible codes, maybe only one in a million actually worked. I’ll even be very cautious and allow only one in ten billion (1 in 1010) to actually appear on a product. What is one ten-billionth of 3615? It’s about 2.2×1013. This would still leave Pampers with over ten trillion (1013) usable codes. Surely they could find a more efficient coding scheme.

Apart from efficiency, I’d really love it if Pampers would just print the associated QR code along with the actual 15-digits. Having to type in multiple 15-digit codes on my Pampers iPhone app, while chasing a toddler, nursing a newborn, and typing a blog post, is really quite taxing!