Unschool Christmas Card Maths

“It’s just as well Dad’s a school teacher,” observes my daughter, Imogen, “because if he wasn’t, our Christmas card display would be very small.”

Yes, Andy has a nice stack of Christmas cards that he brought home from school. But the rest of us have only three cards between us.

“I suppose we got crossed off everyone’s Christmas card list,” I say. I didn’t send cards to anyone last year. I haven’t sent any this year either. I don’t suppose we can complain about our lack of mail.

“I know how we can get lots of cards.” Everyone raises their eyebrows and waits for me to elaborate. “How many of us live here? Seven? Well, if we each buy a card for everyone else… 7 x 6… we’d have 42 cards. They’d make a great display.”

Then I remember my eldest daughter and my second son and my daughter-in-law. “If we include Felicity, Callum, and Casey, there are ten of us. We’d have 10 x 9 or 90 cards.”

But what about Thomas, our son who died some years ago? “We always include Thomas in our Christmas,” I say. “I’m sure he’d like to give cards to everyone else. That’s eleven people and so we’d have 11 x 10 or 110 Christmas cards.”

Can cats and dogs give cards? “What if Poppy, Jenny, Sammy and Nora gave everyone cards too? They’d be fifteen of us. What’s 15 x 14?” A quick calculation reveals the answer: 210

Wow! Imagine if we had 210 Christmas cards! Where would we put them all?

Of course, we’re only having a bit of fun. It’s very unlikely that each person in our family is going to sit down and write greetings in 14 cards before we all do a huge card exchange.  Quite apart from the fact the pets can’t write, and someone will have to stand in for Thomas, cards aren’t necessary. We’d much rather say the words out loud: “Happy Christmas!” and accompany them with a hug.

But what if eleven people gave a gift to every other family member? That would be 11 x 10 or 110 gifts sitting under the tree waiting to be opened on Christmas Day. Imagine!

“Some families do a Secret Santa thing,” I say. “They choose a name from a hat and only give a present to that person.” If eleven of us only bought one gift each, they’d only be 11 x 1 or 11 gifts under the tree.

“Oh no, we couldn’t do that,” says the girls. “We like giving presents.” Everyone wants to arrange a special gift for every person in the family.

Eleven gifts under our tree? No, there’s going to be a sea of them! Of course, they won’t be expensive gifts. Some of them will be handmade. And some might even be secondhand treasures.

So I’m wondering..

Does everyone in your family buy or make or find a gift for everyone else? Or do you organise a Secret Santa? And have a lot of cards arrived in your mail?

PS Even though Thomas is no longer here with us, he does give everyone a Christmas gift. I do his shopping for him!


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  1. Reply

    We’re woefully late on Christmas cards this year, but hope to make a lot of progress this week! As for our gifts, the kids are getting into helping making and delivering presents to our neighbors this year. We’re baking cinnamon rolls, and distributing them to all our friends in our neighborhoods. (thanks to public transit, we’re fairly wide-roaming).

    I got a big kick out of the math you described! It’s technically called combinatorics, a field which contains problems that ask “How many different ways can you do a thing, or make a combination of things.” I found an old book a few years back called “The Mathematics of Choice” by Ivan Niven. I instantly fell in love with it both for its subject matter, and its history, (it was borne of the U.S.’s Sputnik wake-up call). Since it was part of a program to revitalize math studies here, (what we still called the “New Math” when I was a kid), I’m not sure if it would have made it into your libraries. If you can find it, you might enjoy it. It’s intended to be a self study math book on the sorts of Christmas card problems you described. I’ve written a few times about it on my blog.

    Merry Christmas!!!

    1. Reply


      I love how you and your children are making cinnamon rolls for your neighbours. They will be appreciated very much. Unfortunately, we haven’t baked anything for our friends and neighbours. We haven’t even thought about Christmas food for our own family. I’m starting to worry. We need to do some shopping very soon!

      Combinatorics? And I just thought I was writing a simple unschool maths story! Thanks for mentioning the book. I found a PDF copy. I shall enjoy reading it. It’s great sharing ideas and resources!

      I hope you have a wonderful Christmas with your family!

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