3rd Grade · Ages 8–9
The Backwards Year
Eight is when a child can hold a plan in their head — and the lesson of the year is that the best plan sometimes moves away from the goal.
- 1 Hard Thing
- 5 days · 105 minutes
- 3 unmarkable questions
The Hard Thing · about a grade above
The Two Jugs
You have a 5-cup jug, a 3-cup jug, a tap and a sink. There are no markings on either jug. Get exactly 4 cups of water.
Stuck for ten minutes? Good. Open one hint, not three.
1Hint 1
The only amounts you can make straight from the tap are 3 and 5. Everything else has to come from pouring one jug into the other.
2Hint 2
Fill the 5 and pour it into the 3 until the 3 is full. How much is left behind in the 5?
3Hint 3
You are allowed to tip water down the sink. Almost nobody tries it.
The answer — only after you have written something down
Fill the 5. Pour it into the 3 — that leaves 2 in the big jug. Empty the 3 down the sink. Pour the 2 into the 3. Fill the 5 again and top the 3 up: it only takes 1 more. Exactly 4 are left in the 5-cup jug.
The genius move
“Going backwards is a move. Emptying the jug is progress.”
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.
- MondayThe Hard Thing
The Two Jugs, on paper first.
25 min - TuesdayBuild
Do it again with real jugs at the sink. Being right on paper and being right at the sink are different feelings.
25 min - WednesdayRead up
A chapter book a year above you — something with a plot you have to hold in your head between days.
20 min - ThursdayTeach
Teach it to somebody and refuse to give them the third hint.
15 min - FridayBreak
Try to get 4 cups from a 6-cup jug and a 3-cup jug. Find out why it cannot be done.
20 min
Start Monday now
Read the problem once more, out loud, and press start. Solving it is not the measurement.
Nothing rung today yet
The twenty-five minutes
Four phases. The middle one is most of it, and it is meant to feel slow.
- 1SitRead the problem again, out loud. Write nothing yet.
- 2AttackTry the wrong thing. It is faster than thinking about the right one.
- 3StuckWrite down the exact place you are stuck. “I don’t get it” is not a place.
- 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 there a pair of jugs that could make any amount at all?
- ?2
When is it smarter to go backwards?
- ?3
How would you ever know a puzzle had no answer?
Where this goes
The ladder
The same idea, three times, roughly a year apart. This is what depth looks like from the outside.
This year
5 and 3, by hand.
Next year
Any pair of jugs, and the rule that decides what is reachable — every amount is a multiple of the biggest number that divides both.
The year after
That rule under its real name: the greatest common divisor.
What lives on the desk this year
- Two jugs — actual ones
- A sink you are allowed to waste water in
- Paper for writing the move list down
- A timer you set yourself
- A shelf for the puzzles you have not cracked yet
The rest of 3rd Grade
One hard thing a day is the sharp end. It sits on top of an ordinary year.
Last updated: September 2026