Corral

COMBINING LIKE TERMS — you can only add or subtract terms of the same kind; the x-terms gather with the x-terms and the plain numbers gather with the plain numbers.

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01 Opening

Corral worked, for twelve years, at the great stockyard on the edge of the river town. On market mornings the drovers brought their animals down from the hills — sheep, goats, geese, all mixed together in one dusty, noisy, complaining drove — and Corral's job was to sort them.

She sorted them into pens. Sheep into the sheep pen. Goats into the goat pen. Geese, honking, into their own fenced corner. She did it quickly and calmly, with a long crook and a patient whistle, and by the time the buyers arrived every kind was in its own place, ready to be counted and traded.

The reason for the sorting was simple, and Corral had understood it since she was small: you can only count and trade things by kind. A buyer who wanted sheep wanted to see all the sheep together. Nobody bought "five sheepgoats." There was no such thing. Three sheep and two sheep made five sheep. Three sheep and two goats made three sheep and two goats — two separate piles, counted separately, sold separately.

"You add the same to the same," Corral would say, whistling a goat back into line. "That's the whole trick of a tidy yard."

02 Corral

One morning a boy named Rilke, whose father sold geese, watched Corral sort a great mixed drove and asked why she did not simply count them all at once.

"Because they aren't the same," said Corral. "Watch." She pointed her crook at the pens. "Three sheep here, two more sheep there — that makes five sheep. But these four geese don't join the sheep. They stay four geese. I can add the sheep to the sheep. I cannot add a sheep to a goose."

Rilke thought about this. Then he said, slowly, "So if you had three of something, and two more of the same something, you'd have five. But the other things just... wait in their own pen."

"That's it exactly," said Corral. She looked at him with new interest. "Where did a goose-boy learn to say a thing so neatly?"

Rilke shrugged, but he was pleased. That evening Corral scratched a note on the gatepost of the sheep pen: SAME WITH SAME. Three of a kind and two of a kind make five of a kind. Everything else waits in its own pen.

03 Corral

After that, Corral began to notice that the whole world seemed to want sorting before counting.

Coins sorted by value before you tallied them. Beans sorted by colour before you weighed them. Even words, she thought — you could count the questions and count the answers, but a question plus an answer was just a question and an answer, two different things.

A year passed. Then the EquationQuest academy, which was always looking for people who understood one true thing very deeply, heard about a stockyard hand who "only ever added the same to the same." The academy master wrote her a letter. Corral, who was ready for cleaner air and quieter mornings, accepted, and brought her long crook with her.

04 Corral

The board at the academy, Corral found, was a stockyard with the animals rubbed out and letters written in their place. But it worked the same way.

She set up her first lesson. On the board she wrote: 3x + 2x + 4 + 5.

"Here is a mixed drove," she said. The children leaned in. "It looks like a muddle. But it sorts, just like the yard. What kind is 3x?"

"An x kind," said a girl in front.

"And 2x?"

"Also x."

"So they share a pen." Corral drew a loop around the two x-terms. "Three of the x-kind and two of the x-kind make five of the x-kind: 5x. Now — the 4 and the 5. Are those x's?"

"No," said Rilke's neighbour. "They're just numbers."

"Just numbers. Their own pen." She looped them. "4 + 5 is 9. So the whole muddle — " she wrote it clean underneath — "3x + 2x + 4 + 5 becomes 5x + 9. Two tidy pens. You can only add the same kind."

The children copied it down. One of them drew a little fence around the 5x. Corral thought that was exactly right.

05 Closing

She still visits the old stockyard once a season, and the drovers still let her sort a drove for the pleasure of watching it done well.

At the academy she tells the new children, when they arrive nervous and sure that algebra is a muddle, that it is really only a stockyard, and that the first thing you ever do with a muddle is sort it — the x's with the x's, the numbers with the numbers, each kind waiting patiently in its own pen until it is counted.

"It isn't hard," she says. "It's just tidy. Put the same with the same, and the count comes easy."

When the children have gone and the board is wiped, Corral loops one last empty pen in the corner out of habit, and feels the deep, settled gladness of a yard where everything is finally in its proper place. It is the same gladness she felt at twelve, at the end of a long market morning, and she is glad it has never worn off.

The EquationQuest ensemble

Corral is part of EquationQuest's distributed-narrative cast. Each character embodies a different curricular primitive; together they teach the full subject.