You probably already know this but there are really advanced Lego Technics sets you can buy. The older used stuff probably is more interesting as the newer sets have probably been dumbed down since I started building Technics 35 years ago.
teach them to make an extremely strong castle by interleaving cardboard with sand
There are finite element analysis programs that might offer insight as well.
There is nothing wrong with the LEGO stuff, the EV3 for Education kit is a great place to start and teaches you programming too in a Scratch-like interface. There are also some great books like "The LEGO Power Functions Idea Book, Volume 1: Machines and Mechanisms" by Yoshihito Isogawa, which taught me so much. The advantage of LEGO is that it is really easily reusable (although expensive to begin with) so reduces repeating costs.
Beyond that, if you have access to any machines, try starting to learn CAD software and buy a 3D printer, you'll be able to make so much from that. It's not so budget-friendly, but it's a great option. Then try building some cool mechanisms to develop your understanding of the principles, such as the ones below:
- https://www.youtube.com/watch?v=lXO69eRWkkY - https://youtube.com/playlist?list=PLq_UHnXWA4jI_gSAW9rvOr-I5... - And the ones in the aforementioned book "The LEGO Power Functions Idea Book, Volume 1: Machines and Mechanisms" - you don't have to do this all in LEGO, it shows some neat mechanisms.
I wasn't homeschooled, so I got to create some projects at school which were great fun. You can try the following out of plywood, modelling card and a few motors (there's tonnes of electronics tutorials online, all you need is some basic materials, a soldering iron and a ventilated space to solder in). Our challenges were:
- Using only 3 motors, create a crane that can pick up small objects. Use gears to increase mechanical advantage. - Using cables/string, create a robot hand like at (https://www.youtube.com/watch?app=desktop&v=FCkWexqO2LU). How can you motorise it? How can you improve its accuracy?
For electronics and programming, I'd recommend the Raspberry Pi. It's easy to use with components. Someone I know is also starting a startup called Electrotilez that teaches you electronical engineering (https://www.linkedin.com/company/electrotilez/?originalSubdo...) so I'd recommend checking their product out once it launches.
So now you have the fundamentals nailed, try entering a competition! These are so exciting and have taught me so much. You also meet people that enable your future career. Some great ones include:
- PA Raspberry Pi Awards (ages 8-18, split into age categories) - Samsung Solve for Tomorrow (ages 16-25, in 2 age categories) - Samsung Solve for Tomorrow Next Gen (ages 11-15) - The Big Bang Competition