About ___% of children score within one standard deviation above or below the national average in intelligence.

The question is not influenced by the fact that it's about intelligence - standard deviation is a way of describing data and it's the same for all kinds of data.

So in general, one standard deviation away from the mean in both directions encompases around 66% of the cases - so here it would be 66% of children.

Additionally, 95% of all children should lie withing two standard deviations - so two standard deviations below or above the average.