What are some activities a child 4 years old with a broke arm do to be entertained
I would suggest you wrap some packing bubble wrap on the outside of the cast so kiddo doesn't hurt himself or others and let him go play. It worked pretty well for my nephew.
Watch tv, maybe color, or draw, or fingerpaint
make a play with them then act it out.
build train tracks or play with cars
Nap, stickers, crafts,
Color, draw, painting, I wouldnt reccomend tv since its harmful in more than two ways, same as the videogames, except those can be even more harmful. Gby