My Elementary School book is aimed at this kind of need -- covering some of the finer points of 3rd-5th grade math and asking much harder problems. Parts might be too elementary, but there are very few 7-year-olds who'd have this problem with the whole book.
Among books of elementary school challenge problems, George Lechner's books are probably my favorite. The only drawback is that they're fairly expensive. I'd also recommend any of Martin Gardner's books. Their emphasis is more on puzzles than curricular math, but they're stimulating and there are Dover editions of some. you can get for around $5. Some people also like Edward Zaccaro's "Challenge Math" books. They're more curricular and a bit less challenging.
There are several good books oriented toward Mathcounts preparation. The AMC 8 is less demanding than Mathcounts, but the material is similar so any of these books would be good preparation. "Art of Problem Solving: Volume 1" is a classic. Jason Batterson's "Competition Math for Middle School" is also very good. I, of course, also like my middle school book.
There are also lots of good free online resources at this level. The AOPS website has a resources section where people have posted most old AMC problems. Their "Alcumus" is a nice online tool that asks questions and adapts to what kids know. They also have a set of "Mathcounts Mini" video lessons. My book is organized around old problems from "IMLEM". The IMLEM website (
www.imlem.org) has a link to (free!) past contests which provide hundreds of problems with detailed solutions.
MIT is more STEM focused than most American colleges, but you still spend time on non-STEM subjects as well. It's more complex, but roughly the requirements for an MIT degree are: (1) Take 8 core STEM classes (2 math, 2 physics, 1 chemistry, 1 bio, 2 others); (2) Take 8 courses in humanities, arts, and social sciences; and (3) Take a number of courses (12-16) in your major area. The typical student ends up taking 35-40 courses in total. But for a math major, for example, this would probably be at most 50% math by the time you do the other requirements (and most students also do other things just because they're interested).
