Hadhrat Qasim was the youngest son of Imaam Hassan (A.). Qasim was born in 47 AH, three years before his father was martyred. When Imam Hussain prepared to leave Madina in the month of Rajab 60 AH. Qasim's mother Umme-e-Farwa asked Imaam Hussain to take her and Qasim with him. Imam Hussain agreed. Hazrat Qasim, although only around 13 or 14years old, had, like his cousins Aun and Muhammad, learnt fencing from Hadhrat Abbas and Hadhrat Ali Akber. Hazrat Abbas was very fond of Hadhrat Qasim.    

On the night before Ashura when Imam Hussain was passing by Umm-e-Farwa's tent he heard Qasim say to his mother, "Mother, tomorrow Uncle Abbas, Ali Akber and I will defend Imaam Hussain. Mother, if I get killed please do not weep for me." Umm-e-Farwa replied, "My son although I dearly love you, I shall not weep for you. Nothing will make me prouder than to see my son give his life for Islam". When Imaam Hussain heard this conversation he prayed to Allah to bless Hazrat Qasim and Umm-e-Farwa.

Reference:

Journey of Tears, by Marhum Mulla Bashir Rahim