I teach kids in a village and I was wondering if there is a list of Facts, Procedures, things, a kid 6-15 years of age should know to be able to easily understand things at his/her level of Math. Basics like What are Numbers? Operations etc.
I have written before about what should be taught at the high-school level, and anyone who knows basic logic as described there will "be able to easily understand things at his/her level of Math" and beyond to every area of mathematics in the future as well. Besides that, you should also let students (especially but not just children) explore concrete interesting mathematics.
I think it cannot be denied that attempting to teach or do mathematics without a solid foundation of basic logic is just like writing software by copy-pasting from StackOverflow. So basic logic has to be taught well. On the other hand, you need to motivate learning the basics, and that is what the games, puzzles and other recreational mathematics are for.