At the next math practice, Saeon walked under the arch. This was the place with the divided boards they had passed before. Dure walked alongside, carrying the honey-colored notebook.
“I'll look first this time.”
Dure put the notebook on the side shelf and turned past the last science explanation. Saeon waited while Dure opened a blank page.
That hand had followed the same water right to the end. Now it moved first, even without a finished explanation. Saeon opened the triangular folding board on the shelf, too.
Floor 1 · Class F
Puzzle Gallery · Divided Boards
The navy stone table had eight corners. All three silver trays were empty. The blue cores had been put away.
The three little lamps along the edge were dark. One flat plastic board lay in the middle. It was a long rectangle with rounded corners.
Teacher Gwak stood beside it. The wide hallway stayed open behind the friends. Saeon stopped in front of the table.
“Start by looking at this board.”
Three low dividers stood across the board. Their blunt ends could slide sideways. Between them and the two ends of the board were four spaces.
The first space on the left was teal. The color painted onto the board could wash off with water. The others were the board's pale background color.
Washable coloring tools lay on the shelf.
The first two parts were narrow and equally wide. The third was wider. The far-right part was wide enough to hold four of the narrow parts.
Saeon pointed from the left. One, two, three, four. Beneath the dividers, the board continued without a break.
“Four parts. That does it, right?”
Saeon wrote four parts on the folding board. Under that went only one part colored. That seemed to include everything Saeon had counted.
Sodam adjusted the glasses. Their eyes moved from the left side of the board to the right.
“Hang on. That's still a guess.”
Dure rested a finger on the notebook. There wasn't an answer written yet, but Dure opened a hand toward the board.
“Here. Let's look at the board first.”
Saeon stopped in the middle of underlining four. Dure's fingertip wasn't pointing at the written number. It went between the narrow first part and the wide last one.
Each was one part. But choosing one from either end meant very different amounts of space. Saeon started to touch the teal part, then pulled back.
Ichan stopped at the side of the gallery, on the wide floor inside the railing. Ichan closed the storage box they were carrying.
“I'll listen to your explanation, too.”
Last time, Ichan had fixed a missing unit. Saeon looked at today's board again. The reason for Saeon's own correction had to come from this board.
A round knot of light wrapped beside the teal space. Cream-colored eye-like gaps showed between dull amber strands. The strands circled only the board's edge below the dividers.
A Tangle. A device made from a mistaken idea. It didn't stretch toward the other trays or anyone's hands. When Saeon waited, the knot stayed in place.
Quest
Little Uneven Pieces Tangle
One board · Only one part colored
Change it to four equal-sized parts.
After the change, what fraction of the whole is one part?
Reward: New Skill
Saeon read after the change on the display. They weren't supposed to name the teal amount as it was now. First, they had to divide the board into equal-sized parts.
Was counting four parts enough?
Saeon's hand stopped before writing the next words. Two narrow spaces. Two wide ones. The next line stayed blank.
Sodam pointed along the board's top edge.
“They have to be the same size, too.”
A fingertip followed the three dividers in turn.
“Split this one board equally.”
Saeon looked from the far left to the far right. The narrow parts and the wide parts belonged to the same board. While counting four, Saeon hadn't checked their widths.
“I only counted them.”
Saeon erased the underline on the folding board. They could try matching the sizes without changing the number of parts. Saeon rested a hand on one divider's end.
“Let's explain it our way.”
Dure moved the open notebook farther onto the shelf, then stood where Saeon's hand and the board were both visible. Sodam took a hand away from the right end.
Saeon slid the first divider to the right. The first space on the left grew wider. Beside the original teal paint, some plain background now showed.
Saeon's fingertip stopped there. Widening one space made the next space smaller. They were sharing out space inside the same board.
“I need to move the next one, too.”
Saeon slid the second divider right. The third followed. The wide space at the far right grew smaller.
They hadn't taken away any board or added more. There were no empty gaps between the parts. All four still filled one whole board.
Saeon nudged the dividers again, little by little. The two left-hand spaces became equally wide. Using that width, Saeon matched the two on the right.
Sodam moved a fingertip along the top edge. First, from the left end to the first divider. Then the same distance to the next divider.
“The top gaps match.”
This time the finger followed the bottom edge.
“The bottom ones match, too. And the heights are equal.”
Saeon looked at the dividers standing side by side. Each part was equally wide at top and bottom. The neighboring parts ended at the same height, too.
A thin cream-colored pin touched the strand at the board's edge. The knot stopped in place. Saeon pulled back and looked at all four spaces again.
“Now whichever one we pick, it's the same size.”
With the washable coloring tools, Saeon erased the original color. Then Saeon painted the entire left space teal, right to its edges.
The original teal space had been very narrow. The freshly colored part was the same size as the plain part beside it. Saeon opened a palm in front of the moved divider.
Sodam pointed to the whole board.
“The whole is still the same, too. This one board.”
Dure pointed to the teal part on the left. The fingertip didn't cross into any other part.
“One of those parts.”
After pulling back, Dure checked the four spaces in order.
“Four equal parts. Only one colored.”
Dure swept a fingertip along the notebook page's edge.
“That's enough to finish.”
Saeon looked from the teal part to the whole board. There were four equal-sized parts. One was colored.
The amber knot's last strand loosened. The unraveled light scattered into cream-colored specks. The board and dividers remained on the table.
All three little lamps at the edge came on. Saeon fetched the folding board from the shelf. Beneath the first words, four parts, Saeon added equal-sized.
Saeon drew a short line and wrote 4 below it. That was the number of equal parts making up the whole. Above the line went 1, the number of colored parts.
1/4
This was a way to show parts of a whole divided equally. A number like this was called a fraction. Saeon placed the written number beside the board.
Sodam pointed to the four parts. Dure's fingertip stopped in front of the teal one. Saeon looked at both places their hands showed, then looked up.
“Teacher Gwak, we made the parts the same size.”
Saeon held up the written number. They were just about to say how to read it. The teacher's hand rose toward the board.
“So, the four parts...”
Saeon stopped with their mouth a little open. Saeon's last words seemed about to slip behind the teacher's. The hand holding the folding board stayed firm.
The teacher stopped speaking and lowered the hand. An empty palm opened toward Saeon.
“Finish in your own words.”
Saeon held the folding board upright again. Sodam and Dure were watching beside them. Saeon remembered the hand movements that had changed the narrow first space.
“One fourth.”
Saeon pointed to the teal part.
“One of four equal-sized parts.”
When the words were finished, Saeon took a hand away from the board. The teacher looked between the written fraction and the corrected board. Their explanation was all there.
“Nice and clear.”
Quest Clear
Equal sizes · One part checked
Little Uneven Pieces Tangle · Unraveled
New Skill: “Equal Parts” — Fractions
A small recess opened at the front of the table. Saeon put the folding board on the shelf and bent down. A real little stone staircase with three steps lay inside.
The tiny hollow above the top step was still empty. A little stone remained separate below. There were no letters or patterns.
Blue light flowed down from the upper edge. It reached the little stone below, then climbed again. The same direction as last time in the math area.
This time, a thin gap appeared beneath the three-step piece. It lifted a little from the floor of the recess. Saeon pressed both hands against the outside of the table.
The little stone below didn't move. No stone entered the top hollow. Only the stair piece floated briefly, then settled back down.
“The bottom of the piece lifted.”
Saeon's hands stayed out of the recess. Sodam and Dure only bent closer to look, too. The gap closed, and the little recess's cover returned.
Saeon straightened and looked at the divided board. Four equal parts remained, with one painted teal. Saeon had helped fix the board and said the final words, too.
Dure closed the notebook. Sodam gathered the piece box. Saeon folded the board and picked it up.
“It fits when all three of us explain.”
Saeon walked into the open hallway. Dure came alongside and lifted the notebook a little.
“I talked before I finished writing everything.”
“Yeah. I saw your hand first.”
The three stood side by side before the next practice arch. Saeon tucked the folding board under one arm. Today's final explanation stayed short and clear in their mind.
They were still on the bottom floor. Saeon pictured the space under the stone when it had lifted. The stairs above continued beyond view.
What was at the top?