That's what I've found myself having to do. I've never had to have a sorting strategy before living in the US. The lack of distinction between notes is frustrating. I love it when Americans tell me they have colored notes too.

I still can't understand the preference for one dollar notes. Whenever I use a washing or vending machine I need to flatten out and align a dollar bill or insert dozens of quarters. Every few weeks I have to buy a couple of rolls of quarters from the bank. I paid a cashier with dollar coins yesterday and she did a double take and inspected each coin.