The Open Hand · Grower · ages 9-14
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Read by an AI-generated voice. The words on this page are the transcript.
1. The Fourth Lock
The hammer rang once. A spark jumped off the anvil and did not go out. It waited. They followed.
It rolled across the Green to the painted wagon. Three of the trunk's seven locks were open. The fourth glinted in the afternoon sun.
On the trunk, one old lock had a new pin. Next to it was a tiny scratched hammer.
A performer was bouncing on the wagon step, on her toes, as if the step were too hot. Her name was Squarl.
"I never fight an awkward number," said Squarl. "Give me one. Something near fifty."
2. Two Seconds
"Forty-seven," said Beto. "Times forty-seven."
Squarl closed her eyes for a moment. "Two thousand, two hundred and nine."
Beto grabbed some paper and did it the long way. Forty-seven fours. Forty-seven forties. Add them up. It took him nearly two minutes.
"Two thousand two hundred and nine," he said. "She's right."
"Again," said someone in the crowd. "Fifty-three."
"Two thousand, eight hundred and nine," said Squarl.
Right again.
3. Round It and Stop
Danya was not impressed. "I can do that," he said. "Forty-seven is nearly fifty. Fifty times fifty is two thousand five hundred. Done."
"Done," said Squarl, "and wrong. By two hundred and ninety-one."
"That's not very much," said Danya.
"It's a whole crowd," said Squarl. "Round it and stop is never the answer. You have to come back."
She wrinkled her nose. "Forty-seven is awkward. Fifty is delightful. But I only visit fifty. I don't move in."
4. What She Whispers
After the show, Danya sat on the step with Marlow, who was coiling a rope.
"How does she do it so fast?" asked Danya.
"I won't tell you," said Marlow. "But Squarl talks to herself when she works. Next show, sit at the front and write down what she whispers."
Danya sat at the front. He wrote down every word.
Forty-seven. Up three, down three. Forty-four times fifty. Add nine.
Forty-eight. Up two, down two. Forty-six times fifty. Add four.
Fifty-three. Down three, up three. Fifty-six times fifty. Add nine.
Danya did the sums. Forty-four times fifty is two thousand two hundred. Add nine: two thousand two hundred and nine. It worked every time.
"But why add nine?" he asked. "Where does the nine come from?"
"Three times three," said Marlow. "But don't take my word for it. Draw it."
5. The Reveal
The next evening, Danya stood at the front with a big sheet of squared paper and a pencil. Beto held the scissors, closed and pointing down, until Danya needed them.
"Forty-seven times forty-seven is a square," Danya said. "Forty-seven squares along, forty-seven down."
He drew it. Then, with Beto's scissors, he cut a strip three squares wide off one side.
"Forty-seven take away three is forty-four," he said. "So now this part is forty-four wide."
He turned the strip and laid it along the bottom of what was left. The strip was forty-seven long, but the bottom was only forty-four wide. Three squares of it stuck out past the end.
"Now look," said Danya. He covered the bit that stuck out with his hand. "Without this, it's a rectangle. Forty-four wide and fifty tall. Fifty times forty-four is two thousand two hundred."
He took his hand away. The piece sticking out was three by three. Nine squares.
"That's the nine," said Danya. "The strip is a little too long, so a little square is left over. Forty-four times fifty, and nine more."
Beto counted the nine squares with his finger, twice.
Squarl bounced on her toes and clapped.
That night, the fourth lock on the trunk clicked open.
Back on the Green
The spark dimmed to a warm dot and settled back on the anvil. The Green was just the Green again.
On the bus home, Beto asked Danya what thirty-one times twenty-nine was.
Danya smiled. "Thirty times thirty, take away one."
Saved. The next chapter will be here whenever you come back.
Who you met
-
Squarl To square an awkward number, bounce to a round one and back, then add the square of the bounce from ShowMath -
Marlow Rehearse, perform, then reveal the reason instead of protecting the mystery from ShowMath -
Danya a child of the Green Asks "how do we know?" -
Beto a child of the Green Takes things apart
Every recurring character has a short tune, so you can tell who is on stage before a word is said. The tunes play only when you tap, and the Reading Access sound switch turns them off.
The Honest Page
Which parts of this story are true, stretched or made up?
True
- 47 × 47 = 2209, and 44 × 50 + 9 = 2209. Going up and down by the same amount and multiplying always gives one little square less than the true square.
- This is the rule (a + b)(a − b) = a² − b², which can be shown by cutting and moving a strip of a square, as Danya does. Source
Stretched
- Squarl does it in two seconds. What we simplified: Fast mental calculators practise for a long time; most people need a little longer, and that is fine.
Made up
- The Open Hand troupe and its wagon are made up. Squarl and Marlow come from ShowMath.