Honestly, giving reward for honor is like making honor void... I must say taht it's true that there are some honor-null-space depending on your level of play and your queue'ing, but one thing for sure, whenever you are truly honorable, you end up getting teamwork.
I'm currently on a Poppy craze, and I'm giving honor to anyone that simply doesn't flame me, because I know that most people do. In the same way I also receive honor in most cases where I choose to fill for the team and actually work with the team to get our objectives.
I once got teamwork because while losing lane, I diverted our jungler's attention toward more important ganks and chose to even give my top lane to create plays elsewhere.
Basically, if you're questing for honor, choose one of the 3 kinds, and try your hardest to represent that honor kind. If you want teamwork honors, play with the team even if it means less gain for yourself. If you want friendly, choose to fill, ask your teammates what they want, offer custom bans/trades, in-game, ask people for their consent about X item/play, and most of all, just congratualte them for their plays and comfort them in their slip-ups. If you want Helpful, it's imo the hardest, but the key is to work for both others. Basically, "teaching" the game, without sounding like a total jackass.