Her name is given variously in census records as Augusta, Acta and Agatha.  She was recorded as Agatha in the 1900 and 1910 census and that is the name I am using here.
In 1900 and 1910 she lived with her son Folkert in Chatsworth, Livingston Co IL.
1900 Census of Chatsworth, Livingston Co IL
Name                   	AgeFolkert R Beckman	46    Dec 1843   Germany Germany Germany, blacksmith, immigrated 1857, naturalized, m 17
Theresa Beckman	37    Nov 1862   IL Germany Germany, m 17, mother of 2, 2 living
Robert Beckman	12    Oct 1887    IL Germany IL
William Beckman	  6    Oct 1893    IL Germany IL
Agatha Beckman	83    Feb 1817    Germany Germany Germany (mother of 7, 6 living) immigrated 1857
1910 Census of Chatsworth, Livingston Co IL
Name                 	Age
F R Beckman       	56   Germany Germany Germany (no occupation, ”own income”)
Tressa Beckman	47   IL Germany Germany
William Beckman	16   IL Germany Germany
Agatha Beckman	93   Germany Germany Germany 
The following newspaper articles are reproduced from research of Mary Runyon-Hanshew2930
From the Chatsworth Plaindealer
MRS. AGTE BECKMAN
JANUARY 20, 1911
The death of Mrs. Agte Beckman, which occurred on Saturday (Jan. 14) morning at the home of her son, F.R. Beckman, and family, on the south side of town, removed one of the oldest and most highly respected ladies of Chatsworth and one of the oldest women in this section of the state. Had Mrs. Beckman survived until the 4th of next month she would have been 94 years of age.
Mrs. Beckman was a native of Germany, having been born on February 4, 1817, at Victorbue, Ost Friesland. On April 10, 1846, she was married to Rolf K. Beckman. In 1857 they came to America, landing in New Orleans, coming up the Mississippi and Illinois rivers to Peoria. They were nine weeks on the ocean voyage and two weeks on the river trip. In crossing the Atlantic Mrs. Beckman's mother and infant child died of ChoLera, as did others on the vessel in which they took passage. In 1857 they moved east of Minonk and in 1869 to a farm near Fairbury. Ten years later they moved to Charlotte township, where they resided until Mr. Beckman's death in 1899, since which time Mrs. Beckman had made her home with the family of her son, F.R., in this city.
Mrs. Beckman was the mother of the following children, all of whom are living; Mrs. Lena Johnson, of Fairbury; Mrs. John Ommen, of Charlotte; C.R. Beckman, F.R. Beckman, of this city; John C. Beckman, of Rensselaer, Ind.; George W. Beckman of Cullom. She is also survived by 24 grandchildren, 33 great-grandchildren and 2 great-great-grandchildren.
The funeral services were held on Monday afternoon at one-thirty o'clock at the German Evangelical church. Rev. Koepp, of Charlotte, officiating In German and Rev. Gronewald making a few remarks in English, and the remains were interred in the Chatsworth Cemetery.  The attendance at the last obsequies was large, showing the high esteem in which Mrs. Beckman was held in this community.
Among those from out of town who attended the funeral were: Mr. and Mrs. Alex Tronc, of Pontiac; Mr. and Mrs. Henry Yonkers, of Saunemin; Mr. and Mrs. John McKinney, Mr. and Mrs. H.G. Flessner, F.O. Walrich, Mrs. and Mrs. James Keefe, Mrs. John Parsons, Mrs. H.J. Parsons, Mrs. F.J. Nightingale, of Piper city; Mr. and Mrs. G..W. Maddin, of Thawville; Mr. and Mrs. M. C. Madden, of Del Rey; Mr. and Mrs. Robert Beckman, of Kankakee; Mr. and Mrs. J.C. Beckman, of Rensselaer, Ind.; Mrs. Lena Johnson and two sons, of Fairbury; Mrs. John Ommen and two sons and one daughter, Ralph and Albert Ommen, of Charlotte; Mrs. and Mrs. Geo. Beckman and son, Mr. and Mrs. Walter Mackinson and daughter, Lawrence Haag and two daughters, of Cullom.
Agte had celebrated her 93rd birthday one year before:
NINETY-THREE YEARS OLD TODAY
FEBRUARY 4, 1910
Mrs. Agte Beckman is celebrating her 93rd birthday at the home of her son, F.R. Beckman, today, and she is probably the oldest, or at least one of the oldest women in Livingston county, if not in this section of the state. 
Mrs. Beckman is a native of Germany, having been born on February 4, 1817, at Victorbue, Ost Friesland. On April 10, 1846, she was married to Rolf. K. Beckman. In 1857 they came to America, landing in New Orleans, coming up the Mississippi and Illinois rivers to Peoria. They were nine weeks on the ocean voyage and two weeks on the river trip. In crossing the Atlantic Mrs. Beckman's mother and infant child died of choLera, as did others on the vessel in which they took passage. In 1850 they moved east of Minonk and in 1860 to a farm near Fairbury. Ten years later they moved to Charlotte township, where they resided until Mr. Beckman's death in 1899, since which time Mrs. Beckman has made her home with the family of her son, F.R., in this city. 
Mrs. Beckman is the mother of the following children, all of whom are living, and whose visits make her advanced years pleasurable; Mrs. Lena Johnson, of Fairbury; Mrs. John Ommen, of Charlotte; C.R. Beckman, F.R. Beckman, of this city; John C. Beckman, of Renesselaer, Ind.; George W. Beckman, of Cullom.
For a person of her age Mrs. Beckman enjoys very good health and retains possession of her faculties to a remarkable degree. She is loved by all who know her, and her many friends only hope that she may be spared to enjoy many more years with those by whom she is held in such high reverence.
 
A schematic of the family and descendants of Rolf Beckman and Atge Uphoff was prepared in 1995 by their great grandson Kenneth Wayne Beckman.  This schematic does not contain many dates, but it does outline the members of the family as known by Kenneth.  This shematic may be downloaded from: 
http://heathcock.org/genealogy/Beckmans.pdf
1860 Census of Pleasant Plains, Sangamon Co IL
Name                  	Age
C Beckman         	39       Hanover
A Beckman          	33       Baden
L Beckman          	  4       IL                 (Lena)
B Beckman          	  2       IL
H Beckman           	2/12   IL
C Boyd                	36       Russia 
The adjacent listing is for L. Beckman, 37, b Hanover, and wife R. Beckman, 29, b Switzerland.  This may be a brother of Rolf Classen Beckman.
1870 Census of Avoca, Livingston Co IL
Name                  	AgeRolf Beckman        	49      Hanover, Germany
Augusta Beckman	53      Hanover, Germany
Closs Beckman     	17      Hanover, Germany
Folcot Beckman 	15      Hanover, Germany
John Beckman      	11      IL
George Beckman	  8      IL
This census suggests that the family immigirated from Germany between 1855 and 1859;  however, this is not in agreement with the birthplaces given in the 1860 census.
1880 Census of Charlotte, Livingston Co IL
Name                  	Age
Rolf Beckman      	59     Friegland Friegland Friegland 
Acta Beckman    	63     Friegland Friegland Friegland 
George Beckman	18     IL Friegland Friegland