Dasatinib and Combination Chemotherapy in Treating Young Patients With Newly Diagnosed Acute Lymphoblastic Leukemia

Inclusion Criteria: * Newly diagnosed acute lymphoblastic leukemia (ALL) * Definitive evidence of BCR-ABL fusion (Philadelphia chromosome positive \[PH+\]) from an approved Children's Oncology Group (COG) cytogenetics laboratory * Meets one of the following criteria: * Concurrent enrollment on Clusters of Orthologous Groups (COG)-AALL03B1 (or a successor trial) AND COG-AALL0232, COG-AALL0331, COG-AALL0434 or other front-line COG ALL clinical trial * Concurrent enrollment on COG-AALL03B1 (or a successor trial) AND scheduled to receive a 3 or 4-drug standard induction regimen * Concurrent enrollment on a Dana-Farber Cancer Institute (DFCI) Childhood ALL Consortium trial (or scheduled to be treated as per a DFCI Childhood ALL Consortium induction regimen) * All patients must have definitive evidence of BCR-ABL fusion from an approved COG cytogenetics laboratory; patients may NOT have received Day 15 of Induction chemotherapy (or day 18 vincristine if enrolled on a DFCI Childhood ALL Consortium trial) prior to enrollment on AALL0622 * Patients must have a performance status of 0, 1 or 2 at completion of two weeks of Induction; use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70mL/min/1.73 m\^2 or maximum serum creatinine based on age and gender as follows: * 0.4 mg/dL (for patients 1 to 5 months of age) * 0.5 mg/dL (for patients 6 to 11 months of ag…