Fence chapter opener illustration

Fence

THE FENCE OR THE FIELD - *the fence goes AROUND the edge, the grass fills the INSIDE; how-far-around and how-much-inside are two different counts and they are not the same number.*

Fence the Goat

Fence is a sturdy, friendly goat with a soft coat and two little horns. Fence lives at the edge of a square field in Mayor Tila’s town, and Fence knows something that trips a lot of animals up. So Fence has one patient, kindly idea: “The fence goes AROUND the edge. The grass fills the INSIDE. They are not the same thing.”

One morning two rabbits are having a friendly muddle. “The field is four lots on each side,” says the first, “so the answer is… um… a big number!” But he can’t say WHICH big number he wants - the fence, or the grass.

Fence trots over calmly. “Let’s not mix them up,” Fence says. “There are two different counts here, and they answer two different questions.” Fence puts one hoof up on the low fence-rail. “This first count is the fence - it goes all the way around the edge. If you want to know how far you’d walk right around the field, you count the fence: along the top, down the side, along the bottom, up the other side. That’s the around.

Then Fence steps softly onto the grass inside. “This second count is the grass - it fills the whole inside. If you want to know how many little lots of grass fit in the field, you tile the inside and count them. That’s the inside. The around and the inside are two different jobs, and they give two different numbers.”

The rabbits’ ears perk up. “So we weren’t wrong - we just hadn’t SAID which one we wanted!”

“Exactly,” Fence says, gentle. “Around, or inside. Ask yourself which one first, and you’ll never muddle them again.”

That is Fence’s whole patient idea.

The fence goes AROUND, the grass fills the INSIDE.

A grown-up can play too! Mark out a square with string or blocks. First trace all the way around the edge with your finger - “top, side, bottom, side” - and count the steps: that’s the fence, the around. Then lay little tiles or coins to fill the inside and count those: that’s the grass, the inside. Say each one out loud: “this many AROUND the edge… this many INSIDE.” Notice they are different numbers! Around and inside are two different counts.

That is the fence or the field. One question asks how far it is around the edge; the other asks how much fills the inside. They sound alike, but they are two different counts - so always ask which one you want first.

When the rabbits finally sort the two counts apart and each one makes sense, Fence feels a warm, settled calm - the quiet relief of a muddle gently untangled. Fence gives a soft, steady nod. “Around the edge,” Fence says, “or inside the field. Two different things. Now you’ll always know.”

The arraypals ensemble

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