have to agree with the others. The child must remain quiet..I wouldn't even offer books until he's done whatever amount of time you choose for lying without sound/moving. At 3, I'd say it should be an hour. If after an hour, he is truly unable to sleep, then choose x amount of books to give to him and he must silently look at the books while staying on his mat. If a 3 year old stays quiet for an hour after a busy daycare morning, I'm thinking he'll fall asleep!
Good luck!