In regards to a paper analogy, a square with 4.54 inch sides of standard 20 lb paper is about 1 g.
For a visual aid, I would want something reasonably sturdy, and uniform. So, say, metal.
Copper: 1 cubic cm masses about 9 gm
Iron is slightly less dense.
Lead comes in around 11 gm / cm^3 (solder usually somewhere between lead and copper)
(all values from wp)
Water: 1 cubic cm is 1 gm.
So, if you can make 1 cm^3 cups, fill one cup with water, one cup with solder.
For something easily broken down or grouped up, the most obvious choices would be shotgun pellets, wires, nails, or fishing weights. Those are all measured in “qty in one oz”. One 28 gauge pellet looks to be in the 20-ish gram range. Ah, found a sporting good store that gave actual weights of fish “split shot”. Their smallest sizes were 8, 10, and 18 grain which is 0.5, 0.6, and 1.2 grams.
For paper, the gsm number & the moisture absorption were mentioned upthread. One other caveat is that the number in biggest font is poundage, which is unhelpful. Standard printer paper is “20lb”, which is the weight of some number of sheets, of a specific nonstandard size, with a bit of slop for edge trimming and maybe other weird fudge factors I can’t remember right now…
Now that the serious answers are out of the way, here’s the physics way: Pick the closest object that catches your eye. Define it to be 1 gram (times a fudge factor constant to be determined by the undergrads). If doing this in a car, the fudge factor might become rather large. 