Why do you need math?

I work as a tutor. I help students (mostly 6-9 grade) with mathematics. Naturally, parents find me, since it is usually uninteresting and unnecessary for schoolchildren themselves. Moreover, tutors are hired for those who study not very well.
I have been tutoring for five years, there were about ten students. Mostly girls. I have been working with some for years. And almost everyone is completely lacking motivation. Firstly, they are not interested, secondly, it is difficult, and thirdly, they are not very sure that this is generally necessary. Of course, from time to time one may hear outraged phrases like “Yes, why is this algebra necessary at all?

And this question puzzles me. I don't want to answer something like “Don't ask stupid questions, let's decide this and that”. To lie that without mathematics, well, just nowhere - too. Useful for admission to university? So they are not going to technical universities (some, judging by the overall performance - and generally universities). Those who come to my classes, as a rule, do not have special hobbies. TV, glossy magazines, spree - that goes without saying, of course. But there is no such thing that these mathematical trio students and triplets are interested in history, language, literature. In this case, one could at least say: “Yes, I understand that you are more interested in humanitarian subjects. But it is necessary to teach mathematics anyway, let's prepare so as not to spoil the certificate. ” However, this is also a dull answer, because it provokes the next “Why is it necessary?”

I remember myself in school. I studied well, and I almost didn’t have questions like “Why is all this necessary?” Something was interesting and done with pleasure, something did not like, but taught, "because it is necessary." Perhaps, the Soviet childhood also affects. Mathematics and other technical subjects were useful for a university (my basic education is an engineer, the second is a translator, I work as a technical translator as a result). And yet, why do I need all this in life? Just thinking better? For general education? I don’t regret my education, but I don’t recall anything that could attract a silly schoolgirl. So far, nothing better than “Mathematics is gymnastics for the mind,” is not invented. And I really want not just to drive knowledge into the head, but to interest a person.
')
Maybe you tell me, dear habraradi? How to explain to a teenage girl why she is being hammered with all sorts of equations, functions and roots?

PS Answers like “I never used mathematics once, I don’t understand why children are hovering”, perhaps interesting, but of little use.

Upd. Many thanks to everyone who participated in the discussion!

Some results.

1. Mathematics is really first of all gymnastics for the mind. Useful for the development of thinking, dedication, logic.
2. Interesting tasks may be of interest.
3. The practical application of mathematics can motivate it to study. But not necessarily. The more complex the topics being studied, the more difficult it is to give examples of practical application that are not sucked from the finger. And sucked can cause not interest, but disgust.
4. Payalnik translations about the secrets of educating smart children ( part 1 , part 2 ) really liked. arestov - thanks for the recommendation.

Note 1. Mathematics was taken as an example, as the most frequent subject in my mind. I in no way set goals to make all my students mathematicians. But I really want them to have enough intellectuals to solve school (and then life) tasks.
Note 2. Not all of my students are as bad as you can think from the main topic topic. There are quite successful "projects" :) Why did I ask this question? I just thought that there could be some reasons for studying, in particular, mathematics, which simply did not come to my head, but could convince the student. In principle, nothing was found.