The alligator eats the bigger number is the common approach for student to use inequality symbols (< > < > ). I find that students remember the sentence but many do not retain the concept or use the symbols correctly, even in high school. The reason, I believe, is that we introduce additional extraneous information: the act of eating, the mouth which is supposed to translate into a symbol, the alligator itself. For a student with processing or working memory challenges this additional information can be counter productive.
I use the dot method. By way of example here is the dot method. I show the symbols and highlight the end points to show one side has 2 dots and the other, 1.
Then I show 2 numbers such as 3 and 5 and ask “which is bigger?” In most cases the student indicates 5. I explain that because 5 is bigger it gets the 2 dots and then the 3 gets the 1 dot.
I then draw the lines to reveal the symbol. This method explicitly highlights the features of the symbol so the symbol can be more effectively interpreted.
That is the presentation of the symbol. To address the concept of more, especially for students more severely impacted by a disability, I use the following approach. I ask the parent for a favorite food item of the student, e.g. chicken nuggets. I then show two choices (pretend the nuggets look exactly the same) and prompt the student to make a selection. This brings in their intuitive understanding of more.
I think use the term “more than” by pointing to the plate with more and explain “this plate has more than this other plate.” I go on to use the quantities.
Finally, I introduce the symbol to represent this situation.
Below is the example my 3rd grade son used to explain less than to a classmate with autism. This method worked for the classmate!