How do you entertain a 4 month old?  

I have just been through this stage as my daughter is 6 months. I used to give her a small toy, like a teething ring and put it in her hand, she would just drop it at first, but then she'd just start staring at it, and she got interested in it. I just talked to her, and laughed with her, I would take her chair into the kitchen while I cooked, or the laundry room when I did laundry, just change her environment and she'll probably be content watching you do normal things, and involve her, by talking to her and smiling telling her what you are doing. I found that helped a lot.

Do you have an exersaucer? My daughter loves it, she eats her wet rag and watches cartoons. She does get fussy if she's doing one thing for too long. (haha like now)DO you have a ceiling fan, they love those as well, she will lay on some pillows and kick and screech for quite a while. Also she lives trying to do new things, like get her toes, make funny sounds, sit and stand up. They are entertaining for the both of us.

my baby is also 4 months now. what keeps him occupied is sucking on his hand, on anyone's arm or clothing whenver you try to pick him up, he liks his hands more than his pacifier. he also love to stare at crib toys especially those hanging and rotating ones. once he gets fussy, he would crawl away and then start staring at crib toys on a different angle.

Four month olds don't really appreciate toys as much as a six month old. Instead they have people. They love to watch your facial expressions and listen to your voice and touch your skin and hair. So basically anytime you pay attention to her, she's entertained and thrilled. It's flattering really, but they're very into the bonding thing at that age.