I was diagnosed with ADHD when I was in 1st Grade. I was having a hard time learning to read, just moved to a new school, and was supposed to go into 2nd, but was held back because of my reading level. Once I was medicated I improved so much, I went from hating school to actually wanting to go and spend time with my friends. It also helped me to stay in control, it brought me down to a normal level.
It's really interesting that you used the story of him knocking something over. I can think of many times I have knocked something over or touched something and broke it. I remember when I smack myself or just break down. I did this when I was younger and yeah it's a feeling that will be hard for him to control. I felt like an idiot and that I ruined everything when it happened. Just build him up and let him know it is okay!
It's hard to make a recommendation but going to a neurologist and also seeing a therapist have been huge. That helped with the medication and diagnostic.
What has helped with everything is exercising and eating clean. There was an article posted recently that showed children's test scored improved by 10% (not positive on the 10 but it was enough) when they did cardio before tests. I know and feel totally different when I have exercised. It's hard to tell a child that they need to run or do some form of exercise, but getting them out and running around with them will do so much. Also not eating food with food coloring or sugar will be so helpful as well. It's simple but it is super key.
TL;DR: Go see a neurologist/Therapist. You don't need to medicate, and it's not the only solution, but it has helped me. Read as much as you can on ADHD. Exercise. (Scooters are hot right now)