Yes! And this idea of a test testing potential rather than what kids have been taught and have practised in is quite rubbish. Quite often, you can't distinguish this! In some way, you won't know the real potential of the person until they grow up, and maybe not even then.
Yes, you can include puzzles and problems that are interestingly formulated, but most of them, as models, have been developed in terms of 'entertaining maths' for the last 2 centuries and if the kids have been exposed to them, are way easier to solve than if you see them for the first time.
How can potential and giftedness make kids discover what a square root is, or make them calculate 17*8 quickly if they only done 5 of such calculations and not 105? You can't expect that kids who are not taught maths concepts properly excell in maths. If a child hasn't been taught maths properly in years 1-6, there is no way his hidden mathematical potential will be discovered by a test. Such a test doesn't exist. This is a myth. His knowlegde achieved through teaching, learning and practice must be adequate in order for the ability to become manifest. Things in maths build on each other, you can't suddenly become brilliant with fractions and percentages if you never learned basic arithmetic operations properly, systematically and consistently.
In my experience, this is often not done in the primary. In my DS school, they do data, geometry, whatnot, projects instead of maths, maths gets cancelled at the first opportunity, jumping like fleas between topics, and I had to consolidate all the basic knowledge. This is the new function of the mother.
This is not tutoring to the test - this is just straight teaching. Parents end up having to teach their kids. And this has nothing to do with 'natural smartness' or 'dumbness' of children - this is another myth that only exists in Britain. If you said in Finland that you can differntiate 6-7 year olds by ability, this will be a national outrage and a scandal!