Usage patterns
〈人〉に孫ができるto have a grandchild (be born to one's family)
Mr. Tanaka became a grandfather last year.
孫の世話をするto look after one's grandchild
My grandmother takes care of her grandchild every day.
孫を可愛がるto dote on one's grandchild
Grandpa is very fond of his grandchild.
孫と遊ぶto play with one's grandchild
I look forward to playing with my grandchild on the weekend.