Una

Una was an inchworm, and inchworms measure the world one exact, equal step at a time.

At the Times Workshop, the little animals thought they knew fractions. “A fraction is a piece of pizza,” they’d say. “A slice.” And that was fine, until someone asked where does one-fourth live on the number line? Then they were lost. To them a fraction was a floppy piece of food, not a number. It didn’t have a home on the line between 0 and 1.

Una would arch and stretch her little green body — inch, inch — and smile. “A fraction isn’t just a piece,” she’d say. “It’s a place. It’s a spot you can stand on, right here on the line. Watch me walk to it.”

The little animals frowned. A number was something like 3 or 7. How could a fraction be a real number you stand on?

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Una remembered being a tiny inchworm who thought fractions were only slices too. Then old measuring-worm Vernier showed her a number line — a straight path from 0 to 1 — and said, “Cut this into equal steps. Not sloppy. Exactly equal.” So Una cut the path into 4 equal steps. Each step, she realized, was one-fourth — one of the four equal parts.

“Now,” said Vernier, “stand on the first step from 0.” Una inched to it. “Where are you?” She was at one-fourth. Not holding a slice — standing at a spot. “Take another step.” She was at two-fourths. Another — three-fourths. Another — and she was at 1, the whole.

Una’s whole body tingled. A fraction wasn’t a floppy piece of food. It was a place on the line, reached by equal steps. It was a real number, with a real home.

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Now a puzzled turtle named Shelly was staring at a number line. “The teacher says put three-fourths on it,” she said. “But three-fourths is a piece of pie. It doesn’t go on a line.”

“It does,” Una said gently. “Because three-fourths is a number. Let’s find its spot. First — how many equal steps from 0 to 1?”

Shelly counted the tick marks. “Four.”

“So each step is one-fourth. Now — three-fourths. How many steps is that?”

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“Three steps?” Shelly said. She inched her finger along — one-fourth, two-fourths, three-fourths — and landed on the tick just before 1. “It’s there! Three-fourths is a real spot!”

“Exactly three equal steps from 0,” Una said, arching happily. “A fraction tells you two things: the bottom number is how many equal steps make the whole, and the top number is how many steps you take. Three-fourths — four equal steps make a whole, take three of them.” Then she showed Shelly a predicting game: “Before you move — where do you think three-fourths is? Closer to 0 or closer to 1?” Shelly guessed closer to 1, then walked it and checked. She was right, and predicting-then-checking made it stick.

Shelly tried to place two-thirds but made her steps uneven — a big one, then two little ones. “That doesn’t look right.”

“The steps have to be exactly equal — that’s the one rule,” Una said, no scolding in it. “Uneven steps isn’t a mistake, it just means measure again. Make each step the same.” Shelly evened them out, landed two-thirds true, and Una treated the re-measure as simply what careful measurers do.

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By the end, Shelly could walk to any fraction on the line and knew, for certain, that a fraction was a number — a place you stand.

“How’s it feel?” Una asked, resting mid-arch.

Shelly let the idea settle. There was a quiet, clicked-into-place feeling, like a puzzle piece finally turning the right way. “Clear,” she said. “Fractions used to feel like floppy pieces that didn’t really mean anything. Now they’re real spots on the line. I know exactly where each one lives.”

Una gave a slow, satisfied stretch. That was the feeling she loved — not speed, but the calm certainty of knowing exactly where a number stands. “That’s the whole gift,” she said. “A fraction was never just a slice. Cut the whole into equal steps, and every fraction is a place — a real number — waiting for you to walk to it.”

Shelly crawled home turning everything into equal steps — the sidewalk cracks, the fence posts — and standing, just for fun, exactly one-half of the way along.