Climb a tower one floor at a time, paying each toll to the exact ones, tens and hundreds, regroup ten-for-one whenever a place comes up short.
Each floor demands an exact toll in ones, tens and hundreds. You can only spend a place if you hold enough of it, so when a place is short you must regroup, break one ten into ten ones, or one hundred into ten tens, to make change. Limited holding slots cap how many blocks you can keep, which forces you to bundle small pieces up too. Pay every floor's toll to reach the top.
Tens Tower makes place value and regrouping physical, turning carrying and borrowing into the tolls you pay climbing a tower.
Paying an exact toll in ones, tens and hundreds, and breaking a ten into ten ones when a place runs short, is regrouping — the mechanic underneath written subtraction, and a direct demonstration of positional notation.
The original constraint is the limited holding slots, which cap how many blocks you can keep at once.
That cap is what forces the lesson. With unlimited storage you can break everything into ones and never think about place value again; a ceiling means you have to regroup only when you must, and in the right direction, which is precisely the judgement the written algorithm encodes.
Tens Tower is an original, free browser game that makes place value and regrouping tangible by turning carrying and borrowing into the tolls of a climb. Play instantly in your browser.