Introducing philosophy or doing things with numbers?

    One of the ways I introduce philosophy to those newbies is by talking about mathematics. Yes, you read that right mathematics.

 

[Picture above is from http://www.stmarysballina.ie/mathematics.html.]

    I do this because frequently many students find references to ancient history (whether Eastern or Western) as too unfamiliar. But many are more familiar with doing things with numbers at the very least. Another good reason is that many times you have to do some analysis when doing word problems in mathematics. 

     So how to go from doing things with numbers to philosophy? Well if you were to count things in the world, would you also count the numbers that you used to count them with? Like if the world was made out of seven objects would you also count  1, 2, 3, 4, 5, 6, and 7, thereby coming up with 14 objects? "But numbers aren't objects! They don't count!"  They don't count? What about the operations like division and addition? "Hey, I thought we were just counting and adding here?" So do we count the numbers and the addition sign (operation of addition)? " No, because they aren't real!" So, what is real?
    If numbers are not real, and equations deal with numbers, are we also to say that these equations are not true? Or are they true because we decide they are true? Think of an engineer who has to rely on equations. So it is true because it works?
   Hopefully, not to long-winded. From doing things with numbers to questions about reality and truth.