Problem of the day

In my school, many of teachers give their students a mathematical problem of the day. I think this is also the case in some other schools too. This past week, I accidentally posed a very challenging math problem to my colleagues and principal.

Here is the situation. Last year the early childhood and special education classes took a trip to see a play in December. Last year the principal gave me the money for our tickets in advance and then as the students' families paid, he collected the money. This year, he said that was not doable because of some accounting problems he had last year with the school account. He asked me to pay for everyone out of my pocket and I think that is an absolutely unreasonable request. It is 5 dollars per student and we are planning the trip for fifty students. News Flash: that is 250 dollars!

Once I got over my initial shock at his request, I thought some more about it. I am comfortable putting up the money for the students in my classroom because I have good relationships with their parents and would be better able to follow up with them in case someone did not pay. I do not even know all of the other early childhood or special education parents, so how can I ask my them for money? My colleagues are little lazy and or unorganized so I don't feel that I can trust them to do it. I wanted to just take my class but my principal said that was wasteful because the bus would not be full at all.

So I asked each teacher to pay for his or her class upfront. I explained that it is five dollars for each student. Everyone with me so far? Then, I explained that the ratio of chaperones allowed by theater is 1:10. One chaperone for every ten students.Since some of our classes have fewer than 10 students and 2 adults, they are over the ratio and the second adult also has to pay 5 dollars.

Did I lose anyone yet? Because 2 of my colleagues and my principal could not follow this reasoning. I gave an example: If I have 2 adults in my classroom and only 9 students, I need to pay five dollars for each student (45 dollars) and five dollars for that second adult. 45+5 = $50.

Still blank stares and confusion. So I explicitly talked about the numbers of students in each of their classes. One has 6 students and one has 7. Each of their classrooms has fewer than ten students and they have an extra adult. Therefore, they need to pay for that extra adult.

Chaos erupts. My principal whips out his scientific calculator. The teachers explain that they want to combine their classes. They will then have 13 students and four adults, and will still need to pay for two of those four adults. The math was beyond all of them. My early childhood colleagues may have the excuse that they don't teach such complicated math to their students, however, my principal, the person who is somewhat in charge of school finances, should be able to comprehend this.

Frustrated with their lack of understanding, I resorted to drawing pictures. I started drawing stick figure representations. After 25 minutes, I still don't think they truly comprehended the math. They did agree to pay up front for their students. I was annoyed. I find I have a lot of patience for helping students understand something, but very little patience for explaining something that I take to be basic math to adults. People who have been teaching longer than I have been alive. People who are supposed to be mentoring me.

I explained this math problem to other people and they could follow the reasoning. Could you follow the math in this post?