This phase III trial studies how well blinatumomab works in combination with chemotherapy in treating patients with newly diagnosed, standard risk B-lymphoblastic leukemia or B-lymphoblastic lymphoma with or without Down syndrome. Monoclonal antibodies, such as blinatumomab, may induce changes in the body's immune system and may interfere with the ability of cancer cells to grow and spread. Chemotherapy drugs, such as vincristine, dexamethasone, prednisone, prednisolone, pegaspargase, methotrexate, cytarabine, mercaptopurine, doxorubicin, cyclophosphamide, and thioguanine, 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. Leucovorin decreases the toxic effects of methotrexate. Giving monoclonal antibody therapy with chemotherapy may kill more cancer cells. Giving blinatumomab and combination chemotherapy may work better than combination chemotherapy alone in treating patients with B-ALL. This trial also assigns patients into different chemotherapy treatment regimens based on risk (the chance of cancer returning after treatment). Treating patients with chemotherapy based on risk may help doctors decide which patients can best benefit from which chemotherapy treatment regimens.