This phase II/III trial is studying the side effects and how well giving dasatinib together with combination chemotherapy works in treating young patients with newly diagnosed acute lymphoblastic leukemia (ALL). Dasatinib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Giving dasatinib together with combination chemotherapy may kill more cancer cells.