I did a fuzzy search for Jakub Kirsztajn, which led me to Jakob Kirsztajn. In addition to being the closest name match, Jakob was born in 1931, which made him the right age to attend School #20A.
I matched Jakob to his family by matching addresses of people with the same last name. I found his mother (Chana, b. 1898), and presumably siblings (Fajga, b. 1925) (Henoch, b. 1921) (Hersz, b. 1926) (Mina, b. 1930) (Sara, b. 1923).
There is no information listed regarding the fate of Chana, Fajga, or Mina.
According to hospital records, Jakob died on March 3, 1943 of tuberculose meningitis. Sara died of unknown causes on April 4, 1943.
According to a separate profile for Hersz (I'm assuming it is the same person because of the same birth year), he was transfered from Auschwitz to Sachsenhausen on November 27. 1944, although there is no record of his original deportation to Auschwitz.
According to Henoch's laber card, he worked with paper products and was perhaps a box maker (according to the translation of the occupations.) Henoch either moved or was deported on July 12, 1944, although I feel he was perhaps deported since, according to Secondary Sources, there was a deportation to Chelmno on that date.