In Everyday Math, one of the diagrams used to explain addition and subtraction is the parts-and-whole diagram
I believe this is a very abstract diagram for students and using a 3 compartment plastic plate and labeling :
really helps students understand the thinking behind the abstract diagram.
Imagine this… you give the students some “Farm Counter “pigs. Then you orally begin the story. A farmer had 2 pigs (they place the 2 pigs in one of the part compartments). He bought 3 more pigs (they place 3 pigs into the other part compartments). How many pigs does he have in all? (They slide the pigs from each of the two PARTS into the WHOLE compartment). For some reason touching and sliding those pigs around helps student to understand what the story problem is asking them to find.
You can show the relationship between addition and subtraction also. For example: A farmer had 5 pigs (place 5 pigs in the WHOLE compartment) and he sold 3 of them (slide 3 of the pigs into a PART compartment). How many pigs does he have now? (Look in the WHOLE compartment and there are 2 pigs left… so slide them into the other PART as you say…”This is what the farmer had left after selling 3 of his pigs. He has 2 pigs left at his farm.”