Simply make the < and > into Pac-man by drawing a circle around them.

Now, say that Pac-man, being the ever-hungry eating machine that he is, always wants to eat the bigger number, so 5 > 3 and so on.

It doesn't get any simpler, and it's easier to remember than which symbol is greater or less than.

Disclaimer: This probably works better if you live in 1986 when they taught me this and Pac-man was still recognized by all and sundry.

If Pac-Man is not available to you as a teaching device (i.e., your students are more likely to be playing Smash Brothers than having ever touched Pac-Man), the same principle can be applied in a more general sense. I was taught this mnemonic when I was seven years old, and it has stuck with me since.

Our teacher simply drew the greater than and less than signs. Then she drew a bumpy nose over the top of each of the signs, and drew teeth inside of them. The signs were instantly transformed into Hungry Hungry crocodiles! (Rar!) They were ready to devour anything within range and they always wanted the biggest snacky-treat.

Mentally, I never think "greater than" or "less than," I always mentally interpret the signs as one sign that points out which quantity is larger. When doing algebra and quantitative comparisons on standardized tests, I think this is helpful. This method is also a good one because it gives third-graders an excuse to draw little crocodiles on their math homework.