The oak tree they find the gifts in is the one in the Radley's yard, and that happens during the summer, not when school starts.
Here's what happens:
* Summer: Jem and Scout find gifts in the knothole of the oak tree in the Radley's yard. These gifts include gum, a small, carved figure of a man, and a small box containing two shiny pennies.
* School Starts: When school begins, the knothole is filled with cement, stopping the gifts. This is done by Mr. Radley, who is afraid of what the children are doing.
The gifts in the tree are a key part of the novel's plot, symbolizing the mysterious and hidden nature of Boo Radley and the children's fascination with him.