I'm not a teacher.
In most cases the differentiation between the gerund and the participle does not present any difficult.
Unlike the participle the gerund may be preceded by a preposition, it may be modified by a noun in the possessive case o by a possessive pronoun; it can be used in the function of a subject, object, and predicative.
In the function of an attribute and of an adverbial modifier both the gerund and the participle may be used , but the gerund in these functions is always preceded by a preposition.
There are cases, however, when the differentiation between the gerund and the participle presents some difficulty; for instance, it is not always easy to distinguish between a gerund as part of a compound noun and a participle used as an attribute to a noun. One should bear in mind that if we have a gerund as part of a common noun, the person or thing denoted by the noun does not perform the action expressed by the ing-form: e.g. a dancing-hall (a hall for dancing), a cooking-stove (a stove for cooking), writing-table (a table for writing).
If we have a participle used as an attribute the person denoted by the noun performs the action expressed by the ing-form: e.g. a dancing girl ( a girl who dances), a singing child (a child who sings).
However, there are cases which admit of two interpretations: for example a sewing machine may be understood in two ways: a machine for sewing and a machine which sews.
Entering the room, he said “Please, excuse my intrusiveness!”
And going over to the window, he stood looking out.
He sat in the armchair reading a newspaper. (Present Participle)
On reading the letter I put it into the drawer. (Gerund)
That night walking up the great street with his sisters and brother, he wished that they need not do this any more, or at least that he need not be a part of it. (Present Participle)
He received more and more letters, so many that he had given up reading them. (Gerund)
Then she had gone to her room, saying she was deeply disappointed with them.
The man crossing the street is my brother.
They stopped to admire the stream winding away among the trees.
Drinking, even temperately, was a sin. (Gerund)