Learn German: Das Kind fährt Rad. - The child is riding a bike.

The verb fahren (to drive or ride) is a strong verb. In the present tense, when the subject is du (you) or er/sie/es (he/she/it), its stem vowel a changes to ä (a-Umlaut). Since das Kind is a third-person singular subject (acting like es), the verb becomes fährt.

Why is there no word for 'a' before Rad?

In German, the activity of cycling is treated as a set phrase: Rad fahren (literally 'to bike-ride'). Because Rad and fahren belong together so tightly to describe the general activity, you drop the article and just say fährt Rad instead of using ein (a).

Does Rad mean 'bike'? I thought the word for bicycle was Fahrrad.

You are right! Das Fahrrad is the full word for bicycle. However, Germans very often shorten it to just das Rad (which literally translates to 'wheel') in everyday speech. Both are completely fine to use.

The English translation says 'is riding'. Why isn't there a word for 'is' in the German sentence?

German does not have a separate 'continuous' tense like English does (using 'is doing', 'am going', etc.). The single German present tense verb fährt covers both 'rides' and 'is riding'. You just look at the context to decide which sounds better in English.