This phase II trial studies the side effects and how well blinatumomab and combination chemotherapy or dasatinib, prednisone, and blinatumomab work in treating older patients with acute lymphoblastic leukemia. Monoclonal antibodies, such as blinatumomab, find cancer cells and help kill them. Drugs used in chemotherapy, such as prednisone, vincristine sulfate, methotrexate, and mercaptopurine, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Dasatinib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Giving blinatumomab with combination chemotherapy or dasatinib and prednisone may kill more cancer cells.