Elements of Mathematics

I remember Pi in the Sky by John Barrows very fondly. It has more of a focus on geometry and logic. A Programmer's Introduction to Mathematics by Jeremy Kun is wide ranging and appropriate if there is also interest in programming. Nature and Growth of Modern Mathematics by Edna Kramer is a wonderful book if history is a passion as well. Elements of Mathematics by John Stillwell is a broad overview of subjects. It has a crisp mathematical feel to it. Vector Calculus, Linear Algebra, and Differential Forms by John & Barbara Hubbard is a beautiful introduction to the multi-dimensional aspects, but it is a book that should happen after knowing one dimensional calculus. . If your child hasn't been exposed to Guesstimation, then a book on that is highly recommended. The book with that title by Weinstein and Adams is a nice guide to investigating that realm. If the child does arithmetic from right to left, as is sadly too common, the book Speed Mathematics Simplified by Edward Stoddard is a great remedy for that. Everyday Calculus by Oscar Fernandez could also be worth a look.

Mathematics is typically approached in a different way than physics. But there are some books that offer a similar perspective to what Feynman tried to achieve, IMHO. I would recommend to look at works by John Stillwell, for example 'Elements of mathematics' or 'Mathematics and its history'. Nathan Carter's 'Visual group theory' also seems an interesting experiment, if you are interested in that part of mathematics, though I have not read it.