Ernie and Sasha

"First we estimate," Ernie said. "We get a guess in the right neighborhood. Then we make it nicer."

Maya held up the phone so both of them could see the jar.

"Okay. Tell me what you see," Ernie said.

Maya squinted at the jar. "It's tall."

"How tall?"

"As tall as my arm. From my elbow to my fingertips."

"What's that, in inches?"

Maya thought about it. "Eighteen?"

"Sounds right," Ernie said. "Now. A jellybean is about an inch long. How many jellybeans tall is the jar?"

"Eighteen," Maya whispered.

"Good. Now look at the bottom of the jar. How wide is it?"

"As wide as my hand."

"Four jellybeans?"

"Yeah, about four."

"So a flat layer at the bottom is roughly four by four," Ernie said. "That's sixteen jellybeans per layer. Eighteen layers tall. Multiply, and you get…"

Maya's brain froze. Sixteen times eighteen. In her head. Without a pencil.

Sasha leaned forward through the screen. "Hold on, hold on. Don't multiply yet, Maya. Let me make those numbers friendlier first."

She tapped a finger in the air, like she was poking the numbers themselves. "Sixteen is just ten plus six. And eighteen is twenty minus two. So sixteen times eighteen is the same as sixteen times twenty, minus sixteen times two. Sixteen times twenty is three hundred and twenty. Sixteen times two is thirty-two. Three hundred and twenty minus thirty-two is…"

"Two hundred eighty-eight," Maya said.

Sasha's pompoms wobbled. "Yes! Two hundred eighty-eight. That's the square-jar guess."

"But the jar is round," Ernie said. "So we have to fix that."

Maya turned the jar slowly with her free hand so both of them could see all sides. The jellybeans on the curved edge were not packed in neat layers. They were jostled together.

"How do we fix for round?" Maya asked.

Ernie tapped his chin. "Round jars hold a little more than square jars of the same height. Maybe a quarter more. Maybe a fifth. Let's say a fourth."

"Two hundred eighty-eight plus a fourth," Sasha said. "Sasha-friendly math. A fourth of two hundred and eighty-eight is…"

"Seventy-two!" Maya said. She had practiced that one. Halve, halve again.

"Look at you!" Sasha cheered. Her pompoms went wild. "So two hundred eighty-eight plus seventy-two is…"

"Three hundred and sixty," Maya said.

Ernie grinned. "Three sixty. That's our first guess. We're in the right neighborhood."

But Maya was staring at the jar with a slightly worried face.

"What?" Ernie asked.

"The jellybeans look really small. Smaller than an inch. They look more like half an inch."

Ernie's grin got bigger. "Now THAT is a good observation. That changes everything. Sasha?"

Sasha was already nodding. "Half-size jellybeans means we can fit way more in. Twice as many per layer, and twice as many layers. Two times two is four. So we have to double-double our guess."

"Double-double?" Maya said.

"Multiply by four," Sasha said. "Friendly. Three hundred sixty times four. That's three hundred sixty, plus three hundred sixty, plus three hundred sixty, plus three hundred sixty. Or — friendlier — three hundred sixty times two is seven hundred twenty. Times two again is…"

"One thousand four hundred and forty," Maya whispered.

She stared at the jar. The number sounded enormous. But the jar was very, very full.

"Tiebreaker," Sasha reminded them. "Closest without going over. So we should guess a little under our best guess. Just to be safe."

"How much under?" Maya asked.

Ernie thought about it. "Round to a friendly number that's a little below. One thousand four hundred is friendlier than one thousand four hundred forty. And it's safely under."

"But what if the real answer is, like, one thousand five hundred?" Maya asked. "Then I'd lose by being too low."

"You might," Ernie agreed. "That's the risk. Estimation isn't certainty. It's your best guess based on what you can see. And if the rule is closest without going over, you have to leave yourself a tiny cushion."

Sasha was nodding. "And one thousand four hundred is friendlier than, say, one thousand three hundred ninety-nine. Easier to remember. Easier to feel proud of."

Maya thought about it. The jar looked very full. The jellybeans were definitely small. She made a decision.

"I'm going with one thousand four hundred," she said.

She wrote it on the slip of paper from the table. She folded it carefully. She dropped it into the entry box.