My kids are 8, 6, 4, and 2. They don't have to do this stuff all the time, but the 2 oldest wash/rinse dishes and load and unload the dishwasher. The two youngest put the silverware away and some things in the lower cabinets away. They sort the socks and put away their clothes. They all sort the wash and the oldest 2 have started doing their own. Soon they will be *mostly* completely responsible for their wash.
They all help bring groceries in.
We are by no means perfect, but I found routine cards helped immensely for this stuff. That way all they have to do is look at their cards and they know what needs done.
Keeping track of book bag: I told them they are starting school and that meant their book bag and homework is their responsibility. We have a basket they go in so they can always see if they are there. I will ask sometimes if they have their bag, but it isn't a big deal since they know where to find it.
Brushing teeth: I told them their teeth are their responsibility. If they are not taken care of they will get cavities. Sometimes they complain and don't want to. Me: "are you choosing not to brush your teeth?" Most of the time that is all it takes. Brushing teeth is on their routine cards so it is not too big of a deal.