It seems like organic chemistry consists of learning a bunch of reactions, but is there any qualitative set of rules for predicting the way a set of organic reagents will react? I know that quantum calculations can help with this, but is there theory that can be taught and used without a calculator?
Organic chemistry is better explained as acid-base reactions (Lewis acid concept). You have the nucleophile (base) and the electrophile (acid) - even for cycloadditions you will have the electron rich partner and the electron deficient in order to get efficient reaction; also the radicals you have electrophilic like radicals and nucleophilic like.
In order to predict which partner is the acid or the base - the nucleophile or electrophile - we have to access which partner possess the most acidic bond (electronegativity, size, resonance, induction and hybridization) between atoms of the molecule.
The reaction which takes place first will be between the most powerful nucleophile (base) and the most electrophilic (weak bond) respecting some basic rules such as the octet.
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