Lay the cheesecloth over one of the cups.
Secure with an elastic band near the rim of the cup.
Use the other cup to gently push down on the centre of the cheesecloth, while using the other hand to roll the elastic band down a little, to make a well in the cheesecloth.
Add 1 teaspoon vinegar to the other cup.
Heat the milk in the microwave until very warm (can be done in bulk and while students are preparing cups).
Add 1/4 cup warm milk to the vinegar in the cup.
Let sit for a minute for the solid "curds" to form.
The watery liquid that separates out from the curds is called "whey".
Protein molecules (specifically casein) in milk mix with the loose hydrogen atoms in the vinegar (an acid) and a chemical reaction happens, making solid "curds". Heating the milk helps the reaction.
(For older students: the casein molecules in the milk have a negative charge. The loose hydrogen atoms in the acid have a positive charge. Opposite charges attract, so the casein molecules and loose hydrogen atoms group together to make the curds.)
Pour the curds and whey mixture into the cheesecloth on the cup, so that the curds are trapped in the cheesecloth and the whey drains into the cup below.
Pour 1/4 cup of drinking water over the curds to rinse the extra acid off.
Press the curds with the spoon, to drain any last liquid, then scoop out onto a plate.
Add a sprinkle of salt and mix in, before eating on a cracker.
Notes on commercial cheesemaking:
Instead of adding acid directly to milk, most cheese-makers use a bacteria e.g. lactobacillus, which slowly releases lactic acid as it grows, to form curds. (Lactobacillus, naturally present in milk, can be used, and/or more lactic acid bacteria can be added.)
Rennet is also used to help curd formation. It cleaves a piece from casein molecules, which, like the hydrogen ions, cause them to clump together.
Cottage cheese is a made using lactic acid bacteria and milk. Ricotta cheese is made from whey.
Mature cheeses also have other bacteria and mould added to give the cheese more flavour and to change the texture. e.g. swiss cheese uses lactobacillus to form the curds, then other bacteria to remove the lactic acid to add other flavours and to make the holes.
Notes on spoiled milk:
When milk is pasteurized most bacteria is killed, including harmful pathogens E.coli and Salmonella. However some spores and some kinds of bacteria survive e.g. lactobacilli. Milk "spoiling" i.e. forming curds when it gets old, is due to the lactobacillus bacteria growing and producing acid. Spoiled milk may also contain harmful bacteria which have grown from spores, so should not be drunk.
See the attached cheese booklet, for an inedible version of this activity run as a stand alone in a science museum (the curds are separated in a centrifuge for speed).