Tuesday, November 14, 2006

Swallowing horses and other maths phenomena

For our Grade Two maths block we're back in the swing of things with the continuing saga, "The Adventures of Clara."

This time out, our heroine Clara (your average Wiseman's daughter who lives in an age of castles, horse-drawn carts, gnomes, talking dragons, and good sturdy walking shoes) is making her return journey home from helping nurse a sick family in a neighboring village. On the way she encounters an odd man on the side of the road. He is deep in contemplation but then abruptly looks up and yells out fantastic numbers, "1, 342, 105!" And then "2, 684, 210!" Clara interrupts him and they begin a great discourse on all the possible things you can count. Birds, ants, clouds, cows, trees... He even does some quick calculations to count the leaves on a nearby tree, assessing the number of branches, first, and then the number of leaves on each branch, and WOW! What a huge number of leaves! And WOW again, what counting!

I decided for the introduction to this lesson, that I would just put it all out there-- the BIG PICTURE. I wanted Sunburst to get a taste for the possibilities. My goal was to inspire her with the grandieur of large numbers, the quickness of counting, and how it can be used like a trick or entertainment. Numbers are fun and fantastic, and there are no limits.

Lucky for me, it worked. Sunburst was awestruck, and she loved how fast the man counted the leaves on the trees. She repeated the same trick on Einstein while we were sitting at the dinner table with some creative math of her own. She just made up some wildly large numbers and threw them out there, filling up the air with some kind of mathematical magic. Abracadra, I'm counting into the millions! And with that exciting introduction, we were off!

I gleaned this introduction and story idea from a book called The Man Who Counted which was written by a Brazilian mathematician in 1949. It's a marvelous story, and I'm finding a lot of useful story material that needs little adaptation to make it meaningful and useful for what I'm trying to present. It would be useful for any grade, with a bit of tweaking here and there, and that's precisely what I aim to do.

I'm also throwing in a bit of Aesops and other stories (fairytales, Sikh stories, legends, etc.) to mix it up a bit, deepen the work, and balance it out so that we keep it centered in the heart. We'll still practice our rhymical counting with games as we go along, too, but for Sunburst, a good story is everything. It has to move her and inspire her to carry us through.

The first thing we did was draw a picture of Clara encountering her new counting friend, Beremiz (yup, straight from the book.) At the top of the picture we put one of those astronomically large numbers he was calling out. Sunburst loved that. She got to write a number that was in the millions! Then we counted the leaves on the trees, but not into the millions. We counted much smaller trees --and ended with totals like, 16, 24, and with Sunburst's suggestions, 90, and 120. We counted from whole to parts and parts to whole, just for fun.

Next, Clara and Beremiz decided to walk together and the two were met by Clara's trusty horse, Penny (Sunburst is feeling deep horse-love right now.) The three were going along when they encountered three brothers arguing over the division of a pasture of horses (again, from the book.) They were trying to divide 35 horses between them, as per their father's will, by 1/2, 1/3, and 1/9. We worked it out and it necessitated cutting up a few horses-- a head here, a flank there (the gross factor works every time.) But Beremiz had a better idea - a trick!

This is what I love about this book. It's all about tricks and surprises, which is just where Sunburst is developmentally at. It just fits so well. Anyway, Beremiz offers to add Clara's horse to their hoarde (it's okay Clara, trust me) and everything turns out peachy. Each brother gets more horses than they would have gleaned from the original 35, and look! There are two left-over. Penny, which belongs to Clara, and another for Beremiz. Tricks and happy endings.

Sunburst wanted to draw the two horses and then we worked out a horse division problem on a smaller scale: 12 horses, divided between 3 brothers: 1/2, 1/3, and 1/6. She really, really understood what was going on. It was fantastic! Until she swallowed one of the marble counters we had been using to count horses... unfortunately, it was the one she had carefully selected to represent Clara's horse, Penny.... Poor Penny, down the hatch!

That night Clara and Beremiz stayed at an Inn. It was awfully cold and stormy, so to pass the time that night Beremiz and Clara sat in the parlor with their thick mugs of tea and played a dice game called "Twelves." Each person takes their turn at the same time, rolling two dice each. They add them up and keep a tally sheet. The goal is to get to (or surpass) twelve. If both players reach twelve on the same turn, they both win (which happened quite often.) If only one player does, then he or she wins. No one loses, really, because you just pick up your dice and play again and again and again. It was good counting and adding and estimating practice. And Clara enjoyed the game very much.

Next Clara taught Beremiz a dice game... this was Sunburst's idea. It was called something like, "Get to the Boat." We have a striped area rug in our living room. This was the sea full of logs. At the end of the sea is a loveseat pretending to be a boat. We used a large die we fashioned out of cardboard awhile back and took turns rolling it. Each roll of the die told us how many stripes we could move forward. The game was made more interesting by the fact that some of the stripes are skinny and hard to stand on without falling over, SPLASH! Finally we both reached the boat and then we had to ask the die questions, like Should we swim back? Should we cook dinner now? Rolling a 1 or 2 was a YES answer. 5 or 6 were NO. It was some kind of magic 8-ball dice thing, and all of this was made a bit more difficult with Kitty Bill's repeated attempts to abscond with our die.

Eventually we managed to swim home again and make dinner, but you knew that already. As for Clara and Beremiz, we left them stuck at the Inn... and who knows what counting fun they will encounter next! I've got a few ideas mapped out, but we'll have to wait and see...


  1. Wow, this sounds like so much fun! Now I'll have to see if I can find the book. Thanks for sharing, I know I'll be getting some inspiration from this when we return to "schoolwork" at some point in the future.

  2. We just got our book-we LOVE the Man Who Counted! Great stories!


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