We adopted our EM, Oscar, at 3-ish years old and discovered he wasn't always sure what to
do with toys. It's improved over time, but I got in the habit of playing Hide & Seek. We've got a lot of large trees in the yard, so I'd discretely step behind one when Oscar wasn't looking, then make an obvious noice like "Hey!" or "Over Here!". We don't run from him, but when he "finds" us, he gets pettings and such. Since you've got older kids they should be able to play the game without running or squealing or otherwise "overdoing" it.
Also, with the weather getting warmer there's the possibility of kiddie pools and sprinklers. I haven't tried it out on Oscar yet, but I've known a lot of dogs to go all wiggly at being able to run through/bite/lick moving sprinklers.
Do you take walks with him at all or just play in the yard? Oscar has a lot of bonding time/fun just going to state parks and getting to smell and experience new things. We discovered he'd never been in a river recently and it was a blast watching him get used to running water up to his chest.
Congrats on the new family member
~Marrow