If the 1099-DIV is listed with your SSN, then you would report this income on your return.
If the 1099-DIV is listed with the SSN(s) of your grandchildren, then they would need to file taxes if the total of their investment income is more than $1050. See link below for when a child may have to file their own taxes.
https://www.irs.gov/pub/irs-pdf/p929.pdf
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