How Stable Is Childhood IQ?

[T]he correlation between [an IQ] score obtained at 5 and the eventual adult score is probably no more than .5 or so. However, the main limitation seems to be unreliability of any single administration of the test to a child that young. Scores averaged over several administrations are a very good predictor already at a fairly young age. The average of three scores obtained at age 5, 6 and 7 correlates about .85 with adult score. This suggests that while it is difficult to measure a child's IQ in any single sitting, the IQ itself is relatively fixed already by age 7 or so . . .

This is using data in which the IQ was tested *three times* over the interval listed and the results averaged. A single measurement at age 5 would probably do worse than what is listed below. [N=61] . . .

age range correlation with adult score

42,48,54 months .55
5,6,7 .85
8,9,10 .87
11,12,13 .95
14,15,16 .95

. . . . another study of 80 kids [based on a single test at age 7] that appears in Bias In Mental Testing. . . found a .7 correlation between scores at 7 and 17.

From here.

Another study looked at pre-formal instruction number sense in two hundred children who were four years old and found that "the precision of children's estimations correlated with their math skill. That is, the children who could make the finest-grained estimations in the dot comparison task (for example, judging that eight yellow dots were more than seven blue dots) also knew the most about Arabic numerals and arithmetic.  According to the researchers, this means that inborn numerical estimation abilities are linked to achievement (or lack thereof) in school mathematics."
This is also supported by earlier research, with a sample size of sixty four, which use the same test involving estimating a number of dots in a time period too small to count them and comparing it to past academic performance.

Good "number sense" at age 14 correlates with higher scores on standardized math tests throughout a child's life up to that point and weaker "number sense" at 14 predicts lower scores on those standardized tests. . . . They then examined the teenagers' record of performance in school math all the way back through kindergarten, and found that students who exhibited more acute number sense had performed at a higher level in mathematics than those who showed weaker number sense, even controlling for general intelligence and other factors.

Thus, it both showed mathematical ability to be somewhat distinct from general IQ and showed that this measurement is strongly tied to academic performance in mathematics despite not having any formally overlapping content base.

It also suggests that tracking in educational instruction based on multiple middle school performances is as accurate as tracking at later points in an educational career in sorting students by IQ which is closely related to academic ability (although it lacks a component akin to conscientiousness).

The study does not test if it is possible to train children to develop number sense, something that is not generally done in modern math curricula, and if such training would bear fruit in generalized mathematical ability.  It also offers little guidance regarding the most sensible educational strategy to take knowing the some students have a greater aptitude for learning math than others.