Kindergarten · Ages 5–6

The Ordering Year

The tell at five is not counting high. It is counting in order when nobody asked them to — and noticing when they skipped one.

  • 1 Hard Thing
  • 5 days · 85 minutes
  • 3 unmarkable questions

The Hard Thing · about a grade above

Every Way to Make Ten

Find every pair of numbers that adds up to ten. Not some of them — all of them. Then prove to somebody that you did not miss one.

Stuck for ten minutes? Good. Open one hint, not three.

1Hint 1

Start with 0 + 10. What comes next?

2Hint 2

Write them one under the other. Does the first number in each line do something you recognise?

3Hint 3

You can stop when the first number reaches 10. Work out why that is allowed.

The answer — only after you have written something down

Eleven pairs, if 0+10 and 10+0 count as different: 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0. You know none are missing because the left-hand number climbs by exactly one every line and never skips.

The genius move

Go in order, and the proof comes free.
What it is training: Systematic search — the habit of knowing when you are finished.

Five days, five muscles

The week

Never the same muscle two days running. The weekend is not on this list on purpose — being bored is the sixth muscle and it needs two clear days.

  1. MondayThe Hard Thing

    Every Way to Make Ten. Stop at twenty minutes even if it is not finished.

    20 min
  2. TuesdayBuild

    Make each pair out of real objects and photograph it. The photos become a strip they can point at.

    20 min
  3. WednesdayRead up

    A book a year above them, read by you, with one word a page they guess from the picture.

    15 min
  4. ThursdayTeach

    They teach the ten-pairs to a toy, out loud, badly. Do not correct it.

    10 min
  5. FridayBreak

    Give them a pattern with one mistake in it. Their job is to find the mistake — not to fix it.

    20 min

Start Monday now

Read the problem once more, out loud, and press start. Solving it is not the measurement.

25:00Sit

Nothing rung today yet

The twenty-five minutes

Four phases. The middle one is most of it, and it is meant to feel slow.

  1. 1SitRead the problem again, out loud. Write nothing yet.
  2. 2AttackTry the wrong thing. It is faster than thinking about the right one.
  3. 3StuckWrite down the exact place you are stuck. “I don’t get it” is not a place.
  4. 4LogOne sentence: what you will try tomorrow. Then close the book.

No answer key

Three questions you cannot mark

Ask one at dinner. Do not resolve it. A question that survives the washing-up is doing its job.

  • ?1

    Is zero a number, or is it nothing?

  • ?2

    What is the biggest number that has a name?

  • ?3

    If you count forever, do you ever finish?

Where this goes

The ladder

The same idea, three times, roughly a year apart. This is what depth looks like from the outside.

  1. This year

    Pairs that make ten, listed in order.

  2. Next year

    Pairs that make twenty — and the moment they notice it is the same eleven with a ten stuck on the front.

  3. The year after

    Three numbers that make ten. A much longer list, and the first time going in order really earns its keep.

What lives on the desk this year

  • Ten of something identical — pegs, cubes, coins
  • A strip of paper long enough for eleven lines
  • A pencil that will not need sharpening mid-thought
  • A number line on the wall at their eye height
  • A drawer they are allowed to raid without asking

All twelve years

A tower that has to stay up while you count to ten, at three. A proof that no list can contain the real numbers, at fifteen. Same practice, twelve sizes.

Last updated: September 2026

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