If you genuinely think that 'proper Maths' is something that has a single 'right', closed answer, then have a look at the nrich site. Yes, some have 'right' answers, some do not.
Even very basic primary Maths doesn't always have a 'right' answer - or has several right answers.
Say the four 4s problem. Can you make all the numbers between 1 and 20 using four 4s, and the 4 operations? (You can make this harder or easier by allowing square root, factorials or powers). Extensions are easy - can you do it with four of another number? Five 4s?
It's accessible to any child who can add, subtract, multiply and divide using 1 and 2 digit numbers, and has many 'equally right' answers.
There's more stuff here, though some of the chat around it isn't entirely to my taste:
www.youcubed.org/week-of-inspirational-math/
I think Maths for the gifted is hugely harmed by the attitude that 'Maths is only Maths if it is a calculation that leads to a single right answer'.
In the Science example given, the simple extra question 'Explain why' would involve a student in a lot of harder thinking around electron diagrams, stable states etc.