How to turn all sounds off Iphone 8+

I just got my new phone, iphone 8plus. When I'm at work I like to turn the sound off so my phone will just vibrate. I hit the side volume button but text messages etc still make sounds when coming in, on my Ipad if I hit the side button it MUTES ALL, how do I do that on this phone? It's very distracting to my coworkers, to me too actually. Please help.,