It appears that this may be the family you are seeking. Nancy (the mother) must have died somewhere arouned 1878-1879 leaving all the young children with Haden (her hsuband). Note that Nancy was 17 years younger than her husband. Does this match your records?
1870 CENSUS
Name Age
Haden Burk 42
Nancy Burk 25
Lowerna Burk 7
John Burk 6
Lewis Burk 4
Isaac Burk 1
1880 CENSUS
Household Members: Name Age
Haden Burk 51
John Burk 15
Lewis Burk 13
Isaac Burk 12
Wm. A. Burk 10
Leweller Burk 7
Simon P. Burk 4
Harrison Burk 1