One of the most surprising things about being a parent is the amount you have to improvise. Way more than in anything else I've done, despite this being probably the most commonly done thing I've done. I think it's because kids are incomparable generators of chaos.
Kids think their parents are experts, but in many respects they're complete noobs. If you're the oldest child, you're probably the first n-year old your parents have ever had to deal with.
Good thing to do with a 6 yo: type stories they dictate. At that age, the physical act of writing is a bottleneck, so this can release a torrent of imagination. They love seeing their stories printed, like “real” stories they read in books. And it's a fun thing to do together.
Good game to play with small children: go through the alphabet naming some category of things (countries, animals, professional football players) beginning with each letter.
When your child is 5, the two of you are actors in a play. When he's 10, it's more often the case that he and his friends are the actors, and you are the stage crew. One tends to mess up this transition. My trick is to make a conscious effort to notice which times I'm stage crew.
One of the surprising things about being a parent is the degree to which the instinctive protectiveness that kicks in transfers to other kids. You don't just notice when your kid gets too near the curb; you notice when any kid does.
Taught my kids a way to trick bad people. Most bad people assume everyone else has the same motives, so they'll believe you want to do x if they'd want to. E.g. a selfish person will believe you'd want to do something selfish.
Your parents miss you and wish you'd call. Later you'll miss them and wish you could.
Something I wish I'd done while my mother was still alive: I wish I'd written an essay, just for myself, about what she was like as a person. I knew her pretty well, but I'd know her better if I'd had to observe her and ask her questions in order to describe her in writing.
One way to tell what your kids have an aptitude for is what kinds of advice they listen to eagerly. This probably works for adults too, but not as well, because adults have learned to be diligent about things that bore them.
Explained liberal and conservative to my 10 yo and 7 yo on the way to school. I ended up describing them as forms of bias that each produced distinctive patterns of error when they hit the truth.
Parenting trick: When one of our kids does something really good (usually but not always at school) we give them the “royal treatment.” For the next couple days, all the rules are slightly bent. Stay up late? Candy with breakfast? Ok, since they're getting the royal treatment.
When my kids tell me things I didn't know, I always make a big deal about it in order to encourage them to learn more such things.
One thing you learn after having kids is what's the biggest favor you can do for anyone with kids: something that helps their kids.
I was trying to explain to my 7 yo how powerful it is to be able to read, because you can now learn anything from books instead of waiting for teachers to teach you. When I described a shelf of books as an army of robot teachers, he started to get it.
Trick that delights 7 year olds (n=1): Show how you can draw a pyramid with any shape base by drawing a polygon, drawing a dot above it, and drawing a line from each corner of the polygon to the dot.
Most of making things is figuring out why they don't work.
When I was a kid, I thought mistakes were simply bad, and to be avoided. As an adult I realized many problems are best solved by working in two phases, one in which you let yourself make mistakes, followed by a second in which you aggressively fix them.
I talk to my kids as if they were naive colleagues. I think they learn a lot this way, and if not, it at least seems fairly harmless.
The idea of spending (small amounts of) “quality time” with your kids is dangerously mistaken, because the best moments happen at completely random times. You not only can't predict them, you may not even know they've happened.