Perhaps a jumping spider. If so,not a problem.

thank you. I took a couple more photos to see if I could get more detail. He is living on my house so from what I read that is the right habitat. I touched him to see if he would jump and form the "lifeline" but he didn't. He just jumped all the way to the ground and then i couldn't find him anymore.

Looks like a jumping spider. Not a problem. She's helping limit the insects at your place.

Goin' with Platycryptus undatus.

Yup, definite jumping spider in any case. They are active hunters by day, and are noted for their visual acuity. Also, many observers (including scientists) that have studied them have noted how intelligent they seem. One study that I read perhaps 8 or 10 years ago of a particular variety concluded that they use trial-and-error learning. (Meaning, they try something, and decide whether to continue doing it or try something else based on the results.)

I have never known them to be aggressive, even some quite large ones that I handled, not that I would recommend this to someone else. In any case, not known to be dangerous. Very special creature, there. Maybe your daughter could learn to watch it to see if she can catch it doing something that looks smart? If so, she'd probably forget her fear.
Jill

Thank you all for your information about this spider. I am glad to him around my house. My daughter would never study a spider butI am fascinated. This might be one more excuse for not having time to do housework! My daughter doesn't mind spiders outside but doesn't want them in the house, so I just gently remove tham to the outdoors when I find them inside.