This randomized phase III trial studies how well imatinib mesylate works in combination with two different chemotherapy regimens in treating patients with newly diagnosed Philadelphia chromosome positive acute lymphoblastic leukemia (ALL). Imatinib mesylate has been shown to improve outcomes in children and adolescents with Philadelphia chromosome positive (Ph+) ALL when given with strong chemotherapy, but the combination has many side effects. This trial is testing whether a different chemotherapy regimen may work as well as the stronger one but have fewer side effects when given with imatinib. The trial is also testing how well the combination of chemotherapy and imatinib works in another group of patients with a type of ALL that is similar to Ph+ ALL. This type of ALL is called "ABL-class fusion positive ALL", and because it is similar to Ph+ ALL, is thought it will respond well to the combination of agents used to treat Ph+ ALL.