to smile66 and derech hamelech: about what you wrote “Are we supposed to give tzeddakah because it’s a mitzvah or because we are rachmanim bnei rachmanim?” and “Then again, how can mitzvos and our inborn rachmanus contradict?”
From where did you hear that tzedakah does not go together with the mida of rachamim and beney rachamim, or even to say, they contradict each other?? You’re implying that giving “smaller” sums to different organizations it not being bene rachamim. Quite the contrary. The more often you give, even if its much smaller sums, the more that you practice your middah of giving. And the more an action is done, the greater positive change it has on your middah. Furthemore, tzedakah has two “parts.” One is the physical aspect, and one is the spiritual. So even if you give a coin, the spiritual reward for the mitzvah is enormous. And who knows what “effects” this spiritual merit will have on the physical needs of others – just to open the horizons a bit.
And true, we don’t do a mitzvah because of the rewards – but I wanted to point out from your example there’s no basis to concluded that giving tzedakah in small amounts to different places contradicts being benei rachamim. Furthemore, if a thousand people give 1 dollar to a thousand organizations, or a thousand people each give one thousand dollars to one unique organization – the monetary outcome is the same. But in the first example, each gave 1000 times, and has build up that trait much more.
But certainly, a Rav would need to be consulted.
All the best