Our profession has its share of knotty little business problems cropping up in the course of every-day work. As rugged individualists, we usually proceed to solve these in our own time and way, without benefit of text book or formula. We know from experience that our own pet system of figuring things out really works, and are skeptical about changing. So, far from proposing any mathematical New Deal for you professionals, this paper merely tries to explain simply the solution of a few ordinary, elementary kinds of water purification problems for the beginner's benefit. Our common types of treatment plant problems are concerned with all kinds of size measurements, dealing with proportions, equivalents and relations between weights, volumes, concentrations, densities, etc. Since the every-day language of size is mathematics, one is obliged to understand and use it for making constant comparisons of how much, how little, and how big. Problems involving figures and arithmetic are said to be the best test of intelligence; at any rate, the ability to juggle figures intelligently and correctly is quite important in every stage of the water purification process. A good memory is also rather important, since it enables one always to have ready at hand all those old-fashioned tables of weights and measure once learned back in grammar school under protest. These are essential now, because they inventory all the numerous, different units by which we are wont to express how much, how big, how little, etc.