So, I've been replacing outlets in a bedroom in the house I just bought.  It's actually the house my parents owned and remodeled when I was a kid, so this is probably a question for my old man, but I figured I'd try here first.  The outlet near the floor, near the light switch in this bedroom has 3 hots, 3 neutrals, and 1 ground run to it.  It's an older outlet with 12-gauge wiring and 2 hots and 2 neutrals are pushed into the back quick-connect spots and 1 of each is on the corresponding terminal screw on either side of the outlet.  Ground is, of course, attached to the ground terminal screw.

That being said, my new outlet back push-in terminals only accept 14-gauge wire, so I can't hook it up the same way.  That being said, is this the correct approach?

3 neutrals and neutral pigtail to wire nut; pigtail to neutral terminal screw
3 hots and hot pigtail to wire nut; pigtail to hot terminal screw
1 ground to ground terminal screw

?

There are no switched outlets in the room, by the way.

Thanks!!