The way I see it is to abandon classical mechanics as a model of the truth, and start with quantum mechanics. Assume that the world is quantised and fuzzy, then see what happens when you get lots of small particles in one place.

Dice are a good starting point for understanding the phenomenon of indeterminacy. As we know from the double-slit experiment, a single particle can be anywhere, and the smaller the particle, the broader its wave function (i.e. the probability of its being at any particular point). Now a single throw of one die can give you any result from 1 to 6 - an absolutely flat wave function. If you throw two dice, you are more likely to get a score of 7 than any other number - the wave function of the ensemble has a peak. If you throw n dice, the score will approach 3.5 n as n increases: the peak gets sharper, until I can confidently bank on 3,500,000,000,000 plus or minus about 10 if you throw a billion (that is, an imperial billion) dice.

So: you can't predict the position of a single atom at a given moment, to any better accuracy than the diameter of the atom itself, but the indeterminacy of the position of a cannonball is negligible compared with its diameter because it consists of a hell of a lot of atoms stuck together, like one throw of 10,000,000,000,000,000,000,000,000 dice.

Thus classical (deterministic) mechanics is consistent with and can in principle be derived from quantum mechanics, but you can't do it backwards.

I gather you are a teacher. Try a bit of spread betting with your class. Give then 50 dice each and ask them to record a single throw (what noisy fun!). Get them to bet 10 cents on a spread of the class average - any number in the range 1.000 to 6.000 plus or minus 0.02 - but reserve 3.480 - 3.520 for the house (yourself). See how quickly the parents complain!