Suggestion: get yourself a bunch of say penlight batteries of nominal 1.5V but it would be good if some were old and some brand new so you have a range of voltages from say 0.5 to 1.6 or whatever.
Measure their individual voltages and mark them on some masking tape on each battery. Maybe even mark an arrow on each cell pointing to the pip. Now line them up, flat end to pip, and measure the voltage from the bottom flat to the top pip. Note the voltage: it should be the sum of the individual cells' voltages. Reverse the leads: same number but -ve? The meter takes the black lead as its reference point, its zero. That's a local zero for that test: not an absolute zero in some greater cosmic sense.
So with black on the bottom flat you get the top pip being say 4V "higher"; with the black on the top pip, the bottom flat is 4V "lower".
Now, poke the black lead into a join in your battery string: measure from there to the very bottom and very top, and any other joins. Taking into account the signs (ie the pip of each cell being "higher") and your arrows, and the difference numbers noted on each cell, verify that the readings make sense.
Then fool around:
Do that with the meter black on a different join in the string.
Mix the order of the batteries in your string
Reverse one of the cells so its pip is on another's pip (it might be difficult to get the flats to mate nicely but you could stick a bit of folded tin foil in to connect them)
In all cases make sure that the arithmetic sum (ie, accounting for the direction of the arrows) of the known individual voltages agrees with the value and sign on your meter.
NOW find another bunch of batteries and make another string. Connect the lowest flats, the very bottoms, of the two strings to each other with a wire and do some measurements: measure within each string and across strings. (Take the inter-connecting wire away and measure across strings: what happens?)
Move the wire into the middle of one of the battery strings. Measure some more. Mix the orders of the batteries in the strings, and battery arrow directions.
You'll find that in all cases, taking into account the individual numbers , the direction of the battery arrows, and the position of your black lead as your local zero, everything stacks up arithmetically.
(I'm thinking that would make a handy video. Mix in a switch or two and a some pullup/pulldown resistors, and that's a very handy tutorial.)