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PBS Kids has a lot of games and activities on their website:
https://pbskids.org/games
If your kids watch any PBS shows them they'll recognize the characters.
The activities were fun enough for our twins to learn how to use computer mice at age 3.
Tux Paint is also really fun for young kids and a good way to learn mouse usage:
https://tuxpaint.org/
5. They each have come up with their own personal projects, so I tailor exercises to help them with problems that they need to solve
I wanted this to be a happy experience, so I have never pushed them, but always challenge them to push themselves. I spend a few hours with them every weekend, then a couple of hours with them mid week to help them with challenges. But that is not how I started. I started with 1 hour first thing every morning Monday to Friday to teach them the basics and get them inspired. If they seemed drained, or I sensed that they needed a break, I just let them have a day off.
We also play erion mud [3] and sometimes hexonyx [4] because I wanted them to understand what a mud is all about and to build up interest. I am really into text-based games, so not surprisingly we play nethack (rogue like) [5]. I am also into interactive fiction and started them off on Adventure [6]. If you are interested in interactive fiction, then you might enjoy reading "Twisty Little Passages - an approach to interactive fiction" by Nick Montfort [7].
Full disclosure, I believe that the main reason I am able to pull this all off is that my wife and I home-school our children. It is a challenge though. Very few families where we are from are similar to us in our philosophy of technology and education.
[1] https://www.amazon.com/GeeekPi-Raspberry-Cooling-Cooler-Heat...
[2] https://github.com/emacs-exwm/exwm
[3] https://www.erionmud.com/
[4] https://mud.hexonyx.com/
[5] https://www.nethack.org/
[6] https://quuxplusone.github.io/Advent/play.html
[7] https://www.amazon.com/Twisty-Little-Passages-Approach-Inter...