You may ask yourself, "Is it 'Down's' or 'Down syndrome'?"
Down Syndrome Fact of the Day #6:
Down syndrome is named after Dr. John Langdon Down, an English physician who first described the characteristic features of Trisomy 21 in 1866. People now use the term “Down” syndrome, as opposed to “Down’s” syndrome. (Dr. Down did not have Down syndrome nor did he own it.)
Additionally, it is no longer appropriate to describe someone as a "Down's kid". A child may have been born with Down syndrome, but the condition does not in any way "own" him or her. Therefore, people first language is most acceptable, i.e. "a child with Down syndrome".
Jack is not a "Down's kid" ... he is just a kid who happens to have Down syndrome.
Down syndrome does not own me. I own it.