Plain-Form A + のに + B as “Even though A, B”
The grammar construct is nearly identical to the English construction of “Even though A, B,” however it cannot be used when B is a request, suggestion, or any kind of volitional expression (such as desire and intention). The first clause, or A, must always be in Plain-Form, while the second clause, B, can be conjugated into either Plain or Polite-Form (doing the latter would result in an overall Polite-Form sentence).
For い-ADJECTIVEs, the Plain-Form is simply the entire adjective itself. For な-ADJECTIVEs and NOUNs, the character な has to succeed the な-ADJECTIVE or NOUN before のに occurs if the clause is presented in the present tense. In the case of non-present tense, the respective conjugation of です is used (i.e. じゃない、だった).
Kare wa kuruma ga aru no ni mainichi no you ni jitensha o norimasu.
(Even though he has a car, he rides a bicycle almost every day.)
Tetsuya shita no ni zenzen tsukarete imasen.
(Even though I pulled an all-nighter, I’m not tired at all.)
Takai no ni basketball ga heta da.
(Even though I’m tall, I am bad at basketball.)
Kinou no shiken wa kantan datta no ni yoku shuuchuu dekinakatta.
(Even though yesterday’s test was simple, I wasn’t able to concentrate.)
Kare wa team no ace na no ni renshuu ni kimasen.
(Even though he’s the team ace, he does not come to practice.)