4 days isn't very long for him to be in your house. He'll probably need to settle in quite a bit more.
I'm curious, did the rescue give you specifics on his interactions with children or any other part of his history, or were they just kind of guessing?
I would give him another week or two to settle in without pressuring him - keep him off the furniture for now, and try to encourage your kids to be calm around him. Separate if you must during times when your kids want to run around. It's not forever, just so he can acclimate.
Then, I'd look into either a private trainer or a group class where you can go and just do some training with him. It's a great way to build a bond and it may be fun for your kids to take part as well. It's also a great way for a pro to assess if his behavior is worrying or not and give you tons of solutions.
Just be sure to steer clear of any trainers that use dominance training methods or talk to you about needing to be the "alpha" and stick with those that use positive methods. If in doubt, you can always ask here if the methods they use will be good or not!
Honestly, I wasn't much into private training until I got a reactive dog who NEEDED it...now I love training classes. It's nice to have a pro help me out because I can get frustrated a bit on my own.
As always, reward your dog for good behavior whenever you can. He's playing nicely with a child? Treat, toy, or whatever he finds rewarding! He's laying down and being calm? Treat!