Testing for manganese in water Is there a decent way to test for solvable manganese in water without purchasing a 150USD test kit? I have a fair chemistry set available (I use it to teach my kids chemistry), and would rather pay 50USD for something to add to it that can also be used for other things later than pay for some test that may not be that accurate anyway.

Our city water supply to our house produces a black slime that is likely from bacteria that feeds on iron or manganese. I’d like to start getting to the bottom of it. This is a first step.
Best way is sending a sample for Atomic Adsorption Spectroscopy (AAS). You can get the concentration for $\ce{Mn, Pb, Fe, Cr, Ni}$, and other water goodies. Contact a local university or lab and get a price quote for a test. 
Or get a flame spectroscope and DIY https://web.pdx.edu/~atkinsdb/teach/427/Expt-AtomicSpec.pdf