Seattle proper in 2010 had a total population of 608,660. Of that, Black or African American was 7.9% of the total, or 48,084. 15.6% of the total population was under 18. So, if the percentages were roughly accurate, there'd be 7,501 black students (15.6% of 48,084) in Seattle's schools.
Source: https://en.wikipedia.org/wiki/Demographics_of_Seattle
The numbers get fuzzier when two or more races are involved (5.6% of total population - but no breakdown on those mixes).
Well, actually that's a bit high, considering kids under 5 or 6 wouldn't technically be in school, and then there's Juvie (another topic altogether)...
So, just taking under 18 and dividing by 18, then multiplying by 13 (K-12), we get 5,417.