1. We decided to sail across the lake – Infinitive phrase.
An Infinitive phrase is a sentence that uses an infinitive (to + verb ). Word that expresses action. “TO SAIL” would be the infinitive.
2. Tachels favorite pastimes are dancing and reading – Gerund phrase.
Gerunds are “ing” words. They always function as a noun. In this case the gerund would be “dancing and reading” accompanied by its modifiers.
3. We watched the children playing soccer – Participle phrase.
A participle is a verb ending in “ing” that modifies a noun. In this case “playing” would be the present participle which modifies the noun that in this case is “children”.