Question

The teacher said to the student, "We are going on an excursion to kerala next week".

Answer 1

the teacher told the students they were going on an excursion to Kerala the following week

Answer 2

It is not implicitly mentioned in the question what needs to be done yet looking at it, it seems as if the sentence has to be converted into an indirect speech.

We can convert the sentence into indirect speech as follows - 'The teacher informed the students that they were going on an excursion to Kerala in the following week'.

An indirect speech is used when the said words have to be quoted in an indirect form.