These families are on the FamilySearch database of the 1880 Census, Cross Plains, Dane Co., WI:GURTEN, Fritz, 43; wf. Mary, 33; they and parents b. Prussia.Children b. Wisconsin:Elisabeth, 16; Mathias, 14; Kate, 11; Maria, 8; & Ann, 1."Other" John RAUELS, 17, WI.
You could suggest checking with the churches of Cross Plains.
Cross Plains was the original place of settlement for many German families who later moved on through Iowa and then to Hutchinson Co., South Dakota, under the Homestead Act, when the railroad reached the area in the early 1880's.
We have a good friend named "Tom" LICHTER, of Mitchell, SD.