These lines usually seem to evoke some giggles out of various students: the thought of a youngster with the opportunity to throw pebbles at his mother. One thing that I always have my students consider is this: What if it had been Davy in the circle and his mother who had to pick up the stones?
As Jamie said in an earlier post, the significance is in the ritual; everyone participates. The hidden savagery in this piece is the expectation that even family members help with the stoning, regardless of age.
The line in question reads: "The children had stones already, and someone gave little Davy Hutchinson a few pebbles."
It is significant because little Davy must take part in the stoning of his mother, Tessie. By doing so, the townsfolk make sure that even the littlest, seemingly most innocent member of the bloody ritual has some culpability. It is not that his stones will harm his mother (others will see to that), but that he shares responsibility.
We know Davy contributes to actions he does not understand in the least. Consider the lines where he is choosing his paper from the lottery box:
"Harry, you help little Dave. Mr. Graves took the hand of the little boy, who came willingly with him up to the box. "Take a paper out of the box, Davy," Mr. Summers said. Davy put his hands in the box and laughed. "Take just one paper," Mr Summers said. "Harry you hold it for him." Mr. Graves took the child's hand and removed the folded paper from the tight fist and held it while little Dave stood next to him and looked up at him wonderingly."
It is significant that Davy Hutchinson was given a few pebbles because the overall summary of The Lottery is the lethal traditions that everyone is following.
When the name is drawn, that person is chosen to be killed or "the sacrifice". The person gets killed by being stoned by all the villagers.
Davy Hutchinson was given pebbles to be prepared to throw the stones at the "chosen one" (lol)