Ida and Grant were both 9 years old in the 1880 census, so I'm assuming they were twins.

1.  Iowa Marriage Index, 1851-1900 (online at GenealogyLibrary.com):

Alfred Jackson married Sarah M. Beghtol on Oct 18, 1870 in Hamilton, IA. FHL Film #1404699.

2.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org).

Husband: Alfred JACKSON Wife: Sarah BEGHTOL Child: Ida May JACKSON; Birth: 29 May 1871, Boone, Iowa; Death: 08 Oct 1945 Source: patron submission

3.  1850 Census Every-Name-Index/Images (online at Ancestry.com):  There is a Sarah BEGHTOL (æ 4, b. IL) in the 1850 census of Ashland Twp., Schuyler Co., IL; she's the only Sarah BEGHTOL in the entire census who was born in IL.

4.  1860 Census Every-Name-Index/Images (online at Ancestry.com):  There is a Sarah BEGHTOL (æ 14, b. IL) in the 1860 census of Oakland Twp., Schuyler Co., IA; she's the only Sarah BEGHTOL in the entire census.

5.  1870 Census Every-Name-Index/Images (online at Ancestry.com):  There is an unmarried, apparently orphaned Sarah M. BEGHTOL (æ 17, b. IL), living in Boone Co., IA.  There are also several BEGHTOL families living in Oakland Twp., Schuyler Co., IL.  I can't find a Canadian-born Alfred.

6.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #16 of 27):  Oakland Twp., Schuyler Co., IL, Roll T9-0250, p. 434D, PN 16, SD 3, ED 271, enumerated 7 Jun 1880, official enumeration date 1 Jun 1880 (extracted by Diana Gale Matthiesen):

1880:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).

1

2

3

4

5

6

8

9

11

13

21

24

25

26

143

143

Jackson Sarah

W

F

28

/

Keeping house

Illinois

Ken

O

_______ Ida

W

F

9

Dau

/

/

Iowa

Kanady

Ill

_______ Grant

W

M

9

Son

/

/

Iowa

Kanady

Ill

_______ Elizabeth

W

F

7

Dau

/

Iowa

Kanady

Ill

7.  1890 Census:  the 1890 Census Population Schedules were destroyed.

8.  1900 Census Every-Name-Index/Images (online at Ancestry.com, Image #15 of 20):  Vermont Twp., Fulton Co., IL, Roll T623_302, p. 306B, SD 8, ED 34, enumerated 12 Jun 1900, official enumeration date 1 Jun 1900 (extracted by Diana Gale Matthiesen):

1900:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	19	20	22	23	24	25	26	27	28
153	153	Stroop Jeremiah	Head	W	M	May 1840	60	M	18			IN	IN	IN	Farmer	0	Y	Y	Y	O	M	F	109
		______ Sarah	Wife	W	F	May 1852	48	M	18	3	3	IL	KY	IN			Y	Y	Y
		______ Hattie	Dau	W	F	Feb 1873	27	S				IL	IN	IN	Seamstress	3	Y	Y	Y