Richard Rusczyk, in his article The Calculus Trap, notes that our mathematical education system is based on doing a little of a lot, rather than on a lot of less. In other words, we tend to push the upward race to Calculus rather then giving our students the time to study discrete math: logic, algorithms, number theory, and probability. This is the math that will help them with college math. I like to call this “padding” – we pad the basics so that when a child hits the brick wall of advanced math, (s)he will have the “protection” of a broad base of mathematical knowledge.
For the child who has an insatiable thirst for math, I would highly recommend the series of math books titled, the Art of Problem Solving. It starts with Pre-Algebra and goes through Calculus, with many additional books devoted to “padding”. Their second sets of books is called The Beast Academy which is for elementary children.
For those who enjoy an occasional challenge, the books by Edward Zaccaro are excellent. The Cricital Thinking Company’s books on “Critical Thinking” (see below) are a great way to encourage analytical thought.
Here are a few websites and alternate curricula you may find useful:
The Art of Problem Solving: https://www.artofproblemsolving.com/
The Art of Problem Solving (see above)
Edward Zaccaro: Challenge Math
Edward Zaccaro: Primary Grade Challenge Math
Edward Zaccaro: Real World Algebra
The Critical Thinking Co.: http://www.criticalthinking.com/bestseller
The Calculus Trap: Richard Rusczyk
Multiple articles on the Art of Problem Solving Page: https://www.artofproblemsolving.com/articles