By which is meant: knowledge of multiplication tables, of squares, cubes and other powers, lots of other multiplication skills so that many primes can be recognised from familiarity. Particularly the use of some algebraic techniques to render some arithmetic easier. Also, the use of several skills to check an answer.
One of the fundamental skills to pick up in year 8 is the automatic checking of an answer for sense. Is your answer the right size? Is it in sensible units? Is the precision appropriate? Is it the right sort of answer? (maybe you can tell whether it should be even, or prime, or end in a particular digit, ...)
The more advanced version of these skills occurs when each number you use has a recognised error bound, a sort of fuzziness. ~As in “Yes, I know 2.5 lies between 2.45 and 2.55, but I have no idea where in that range the value lies.” Given such an appreciation, the other numbers related to this one reflect a similar vagueness. Some people find this very uncomfortable; some find it quite the opposite. Yet we do preserve much of the same sort of vagueness, often to a far greater extent, with non-numeric values. Example: on the Leave/Remain issue, scaling from 0 to 100, where would you place yourself? I might even reply that this is not a one-dimensional; answer.
