Can I freeze potatoes?

Silly question but I have a bag of potatoes that needs using soon and I was wondering can they be cut up and froze without going soft or nasty? It's only my daughter who eats them and with everything going on, I dont want to waste food and want to avoid going to the store again. Do I cut them and then cook them first? Is there a way to store baked potatoes in the freezer also? Since it's just my daughter that eats them(shes 3 so only has maybe 1 or 2 at a time) they always end up going bad before we get round to finishing them. Sounds silly but I genuinely dont know lol thanks!