~ a post for a dear friend who asked :) ~
I feel a little reluctant answering this question right now just because there is the definite risk of making it sound like we've figured out how to run things really smoothly with a four year old in the midst of homeschooling. That wouldn't be an accurate summary. Each day is new and requires creativity and a lot of patience and I feel like I've got a long way to go.
Nevertheless, I do have some ideas that have been helpful for us over time and I can share those here. This is somewhat ironic, because an idea-refresher will probably be helpful to me right now!
1. Some four year olds need more time than others. My current four year old (who will be five on Saturday!) is definitely one of those. The more time I take with him, especially reading picture books or general "floor time" (link courtesy of Willa, from whom I first heard the term) the better. This is probably exactly what I need more time on at the moment, but I've been working on the picture book reading time lately and it's been helping some. Anyway, when he's had this sort of time with me, he tends to be more contented at other points of the day.
2. Think Montessori. Not so much as in all the Montessori materials, but some general concepts. First is not doing everything for them, but allowing them to do as much as they can (within reason) themselves. This "Love2learn Moment" of mine includes a wonderful quote by Maria Montessori on the concept. The second is giving them work to make them happy. Here are some examples from our own Frank when he was a newer four year old. Unfortunately he doesn't always distract himself from temper tantrums so easily.
3. Stay Home a Lot. This Autumn was difficult for Frank, I think largely because we were running around too much. Winter is looking a little calmer and I'm working on not getting so over-booked in the future.
4. Parades any time at all. Here's one old, old post about it. Our favorite "parade" CDs are the Lyrical Life Science and Lyrical Earth Science CDs. I should probably also pull out some of the Wee Sing CDs that have been rather neglected of late.
5. Limiting screen time. Nothing seems to wig out our four year old (in particular) than too much time spent in front of the computer. Movies aren't as bad, but the idea does apply to a certain extent. If we've been over-doing it in these areas for awhile, there are sometimes a few slightly ugly days of withdrawal (reduction, not cold turkey) and then things are happier.
6. Frank, in particular, loves puzzles (including some computer puzzles that I don't mind him doing - like the "drag a state" game here which he's quite good at). He loves any sort of memory game (which the other kids love too as long as it's not the Spiderman one - we have a lovely world landmarks memory game called Heritage that everyone can play together) and he loves workbooks if I can keep up with him in that regard (he cruises through anything right at his level and gets frustrated with anything above).
I think there are more things somewhere in the back of my head, but this was all I could pull out at the moment. :)
Geography addendum for Margaret (because links are much easier here than in the comments):
A good U.S. map puzzle has always been the fun beginning of geography for our littles. Frank has already mastered this one. I sit down with one or more of them and hand out states, naming them as I hand them out. They each try to put them back in the right place. That's usually the beginning point, but it has all sorts of crazy manifestations. This is definitely a picture of some of our floor time.
Online geography games have been favorites around here for years. I have a pretty good collection of links at this very old (2005!) post about preparing for the Geography Bee (it's probably my most googled post ever):
National Geography Bee Prep
We also have loads of geography board games - most picked up from rummage sales and many which innocently teach some completely out-dated facts. :)