In teaching students how to do iterated integrals, I would like to find some analogy using a finite task nested inside another finite task. It would be especially nice if it satisfied the following criteria:
natural to visualize as a 2-dimensional grid
involves familiar objects
doesn't involve a sum (for initial simplicity), but can easily be altered so as to involve a sum
An example that isn't naturally grid-able would be: Go to the library and find all the books by your favorite author. For each book, open the book, read all the pages, and close the book.
Another possibility would be something like building a wall out of legos. This seems almost optimal except that you would normally stagger the brick pattern.