When I first started out playing with electronics, making printed circuits was difficult. It required tedious printing of the "mask" onto the copper-clad board, caustic chemicals, and usually multiple attempts to get it right.
It has gotten easier over the years and there are fabrication houses that can print them from drawings, but that takes time and it's not particularly cost effective for experimenters testing simple designs.
Here's an interesting option called Circuit Scribe for the budding STEM student in your house. Using a conductive ink, you can now draw circuits onto any insulating surface (even paper) and stick electronic components to them magnetically. It will certainly be useful in teaching electronics and even has connectors for Arduino.
I think I'd still prefer to do this kind of testing with a breadboard, but if your kids want to learn more about basic electronics, this might be just the thing.
https://123d.circuits.io/shop/circuitscribe sells Circuit Scribe kits.
Here's a video that shows off the technology: https://youtu.be/e0NM1jJbjrM