Your recollection of the mnemonic (memory aid) is right. The way I've heard it (with appropriate illustrations) was that an alligator - which is notoriously hungry - always wants to eat the larger number.
3 < 8 Alligator wants to eat the 8, so 3 is less than 8
5 > 2 Alligator wants to eat the 5, so 5 is greater than 2
Dadd, The symbols fall into the rule of the largest word. On the left is less-than, fork, port, red, etc., i.e. the smaller words. On the right is greater-than, knife, spoon, starboard, green, etc. i.e the larger words.