Hello there,
In order to choose an appropriate topic, you should analyze your assignment and your audience:
1. what are you asked to do? Write a PERSUASIVE speech. The word persuasive is helps you to identify the goal of your speech: persuade and convince.
2. Adressed to whom? School faculty and administrators. Thit is important because it gives you a clue: these are academic people and, thus, the topic should be related to their context.
Now, let's dismiss.
1. The importance of chores at home: do you really think your school faculty and administrators care about the household chores? You are in an academic context; therefore, no, they do not care.
2. The history of global warming: You do not really persuade somebody on the history of something.
4. The difference between blogging and texting: it could work; but I do not really think the administrators of the school care about it, unless it is a matter of worry in the school.
4. The need for more time between clases: this is a topic that concerns all the school; the ones who are rule, administrators; and the rest of the community, school faculty.
For all the reasons explained, correct answer is C. The need for more time between classes
Hope this helps,