The main goal of this study is to find a safe dose of dasatinib and to find out the side effects of dasatinib when it is given in combination with standard chemotherapy to children and adolescents. Similar studies are currently being done in adult patients. Dasatinib has been proven safe and effective in the treatment of other types of leukemia, both by itself and in combination with standard chemotherapy. It is not, however, FDA-approved for use in children.