People have it too easy today, what with the prevalence of computing devices everywhere. As a result our basic math skills are dwindling. To combat this we should eliminate the nickel, dime and quarter and replace them with the trio, hepto and elevener. A trio is one third of a dollar (33 and 1/3 cents)
. A hepto is one seventh of a dollar (14 and 2 sevenths of a cent). An elevener is one eleventh of a dollar.
"How much for a cherry jawbreaker Mr Smith".
"That will be 65 cents Jimmy"
"Aw shucks, all I have are a trio and a couple of heptos, can I pay you the remaining 3.09 cents tomorrow?"
"No problem Jimmy. Ill see you then"

Why can't you do the math with simple calculating machines?
Oh...
You mean by hand.. You should be able to do most math in head.
Learning in the abstract forms without assigning to the objects should not be a problem. It's just has to be practiced.
Should do with 1x1 = 1 to 20 x 10 = 200 and you should be fine.

we don't you leach of that "electrified keyboard" idea, and wire microcircuitry into the coins so that it gives them an electric shock if they get it wrong???

how would multiplier coins work? to give everyone the same amount of money in such a system wouldn't you need to know how much money they had at the time - exactly - and hope to god that the amount of money they have, plus the amount your giving them... is evenly divisible by a number that could be given to them in prime coins...

All you would need to do to get more money than everyone else is to hide a few of your coins...

What is needed is a sort of collect-a-card game, a bit
like Top Trumps (an unfortunate choice of name in
the present climate). Children could challenge
eachother to calculate or estimate the answers to
algebraic or arithmetic questions formed by
combining values and operators on the two cards
being played, with a correct answer winning both
cards, and a wrong answer losing both cards.