Things we could use manipulatives for, but shouldn't
We could use one color counters to add 32 and 73, but that activity is much easier to perform using base ten blocks. We could divide 130 by 4 using paper plates and counters, but doing so would feel extremely tedious. In general, I think manipulatives are best used when a small number of actions will lead to a greater understanding. As another example, I don't think manipulatives should be used for ordering a list of numbers. Manipulatives could be used to compare two numbers, but once comparing written numbers is understood, it's easy enough to order a list of them. That is, no understanding is gained by moving the manipulatives around, and thus the activity feels tedious.