##### Example \(\PageIndex{1}\):

*Here’s a classic Fermi problem: How many elementary school teachers are there in the state of Hawaii?*

You might think: How could I possibly answer that? Why not just google it? (But some Fermi problems we meet will have — gasp! — non-googleable answers.)

First let’s define our terms. We’ll say that we care about classroom teachers (not administrators, supervisors, or other school personnel) who have a permanent position (not a sub, an aide, a resource room teacher, or a student teacher) in a grade K–5 classroom.

But let’s stop and think. Do you know the population of Hawaii? It’s about 1,000,000 people. (That’s not exact, of course. But this is an exercise is estimation. We’re trying to get at the *order of **magnitude *of the answer.)

How many of those people are elementary school students? Well, what do you know about the population of Hawaii? Or what do you *suspect* is true? A reasonable guess would be that the population is evenly distributed across all age groups. That would give a population that looks something like this:

age range |
# of people |

0 – 9 |
125,000 |

10 – 19 |
125,000 |

20 – 29 |
125,000 |

30 – 39 |
125,000 |

40 – 49 |
125,000 |

50 – 59 |
125,000 |

60 – 69 |
125,000 |

70 – 79 |
125,000 |

We’ll assume people don’t live past 80. Of course some people do! But we’re all about making simplifying assumptions right now. That gives us eight age categories, with about 125,000 people in each category.

An even better guess (since we have a large university that draws lots of students) is that there’s a “bump” around college age. And some people live past 80, but there are probably fewer people in the older age brackets. Maybe the breakdown is something like this? (If you have better guesses, use them!)

age range |
# of people |

0 – 9 |
125,000 |

10 – 19 |
130,000 |

20 – 29 |
140,000 |

30 – 39 |
125,000 |

40 – 49 |
125,000 |

50 – 59 |
125,000 |

60 – 69 |
120,000 |

> 70 |
105,000 |

So, how many K–5 students are in Hawaii? That covers about six years of the 0–9 range. If we are still going with about the same number of people at each age, there should be about 12,500 in each grade for a total of 12,500 × 6 = 75,000 K–5 students.

OK, but we really wanted to know about K–5 *teachers.* One nice thing about elementary school: there tends to be just one teacher per class. So we need an estimate of how many classes, and that will tell us how many teachers.

So, how many students in each class? It probably varies a bit, with smaller kindergarten classes (since they are more rambunctious and need more attention), and larger fifth grade classes. There are also smaller classes in private schools and charter schools, but larger classes in public schools. A reasonable average might be 25 students per class across all grades K–5 and all schools.

So that makes 75,000 ÷ 25 = 3,000 K–5 classrooms in Hawaii. And that should be the same as the number of K–5 teachers.

How good is this estimate? Can you think of a way to check and find out for sure?