Most French adjectives have to agree with their nouns in gender and number, but there are many exceptions, known as invariable adjectives. These have just one unchanging form no matter the gender and number of the noun they modify.
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Adjectives comprise one of the eight French parts of speech, but certain members of other grammatical categories can sometimes be used as adjectives. These "non-adjectives" are invariable: there's no gender/number agreement with the nouns they modify.
Most French nouns and adjectives become feminine with the addition of -e, but there are some exceptions. Some nouns require an additional spelling change, depending on the final letter(s) of the word.
Most French nouns and adjectives become plural with the addition of -s, but of course there are exceptions.
The indefinite French subject pronoun on literally means "one," but is usually translated by an indefinite subject. Agreement with the subject implied by on is optional - at least in theory.
French possessive adjectives (mon, ma, mes, ton, ta ...) are used in front of nouns to indicate to whom or to what those nouns belong. They are considerably more complicated than English possessive adjectives because French has several different forms depending on the gender and number of the possessed noun.
French possessive pronouns (le mien, la tienne, les siens ...) are used in place of nouns to indicate to whom or to what those nouns belong.
When used as a noun or adjective, the present participle follows the same agreement rules as other nouns and adjectives, and some verbs have a different present participle conjugation for these usages.
Reflexive pronouns reiterate the subject, which may seem redundant, but in fact serves an important purpose: it indicates that the subject of the verb is performing that action on itself.
In French, the past participles in compound tenses and moods sometimes have to agree with another part of the sentence, either the subject or the direct object.