The Rounding Hill

About this tool

The ground has a dip at each of two round numbers — 40 and 50 — and a ridge exactly halfway between them, at 45. A numbered stone is set down anywhere on it. Let go, and it runs downhill into whichever dip it is nearer: 47 goes to 50, because that is what nearest MEANS, and there is nothing at all to decide about it.

And then there is the ridge. On 45 the ground under the stone is level. It does not roll one way after a moment. It does not pick. It teeters, and it goes on teetering, because a machine that quietly chose would be pretending there was a right answer where there is not one. Rounding a half really is a rule somebody made up, and this is the apparatus that admits it.

So the class settles it. Once they choose which way a ridge tips, the ridge is drawn leaning that way from then on, and every later tie follows it — the rule the room made, visible on the ground itself, with no words written anywhere. Take the lean away and the stone goes back to teetering, because the rule leaving must take its consequence with it. Nothing is scored, nothing is timed, and nothing is marked right or wrong.

How to use it in class

• Read the ground before the first stone: two dips with a round number in each, a ridge between them, and nothing else on it.
• Put the stone somewhere on a slope and ask the class which dip it will run to BEFORE you let go. The slope, not the digit, is the reason.
• Then put one exactly on the ridge and let go. Say nothing and let it teeter. The silence is the lesson.
• Settle the ridge together, and point out that from now on the ground itself remembers what this class decided.

Classroom ideas

• A two-minute routine: three stones, and for each one the class says which dip BEFORE it is let go. Only the last one is a tie.
• Ask why 44 and 46 are easy and 45 is not, and refuse to answer. The ground has already answered.
• Switch to hundreds and set a stone on 450. The ground looks identical, which is the point: the ridge is always the five in the middle.