Fainting By Numbers Trivia Quiz

Answer: Natural numbers

The natural numbers are the counting numbers--either {1,2,3...}, or {0,1,2,3...} depending on the context. "Eponymous" isn't a number set; it refers to naming something after a person. The other answers, rational and transcendental, are legitimate number sets, but go well beyond simple counting.

Answer: Integers

The integers include all counting numbers, both positive and negative. Remembering the rules for adding, subtracting, multiplying, and dividing integers gave some of my students fits before they figured it out.

Answer: Rational numbers

The rational numbers are defined as any number that can be expressed as a ratio, and they include fractions and decimals, as well as all integers. In my fraction lessons, I used to start and end every class by saying "fractions are our friends" to try to engender some appreciation for the topic. Needless to say, it didn't always work.

Answer: Five-fifteenths

Five-fifteenths can be written in fraction form as 5/15 or 1/3; it is hence a ratio. The others cannot be so written, and are irrational numbers. In my experience teaching, irrationals have engendered enough ill will in math classes, that sometimes I fear that the only way to cause teenagers to be rational is to try to make them learn irrational numbers. (Sorry--that was terrible, but I couldn't resist making one teacher joke.)

Answer: Real numbers

Teaching the real numbers often results in rolled eyes, and sarcastic comments such as, "thanks for letting us know that numbers like 4 aren't fake!" On the bright side, learning that set doesn't seem to be quite as difficult for the typical student as learning, say, fractions. Quaternary refers to a geologic time period; I just like the word.

Answer: "If they're imaginary, then why do we have to learn them?"

Imaginary numbers are most simply derived by taking the square root of a negative, which is a theoretical impossibility. It is, however, a very commonly-occuring impossibility, given the number of formulae that include variables that are squared.

The complaint along the lines of "why do I have to learn something that's imaginary" is by far the most common complaint I have heard in my years as a math teacher, and has led me to wistfully wish that the imaginary numbers had been differently named.

Answer: Complex numbers

Complex numbers consist of a real part (a) and an imaginary part (bi, where i is the square root of -1). All of the real numbers and all of the imaginary numbers are complex numbers. (For example, 2 is a complex number if one decides to write it in the form 2 + 0i.)

Again, in math classes, there is often much loud bemoaning of the fact that students have to learn something "complex." I suspect that the word "complex" on the syllabus has led to more than a couple dubious illnesses in my students.

Answer: Radians

Radians are a very clever and useful measure of circular angles, found by comparing the distance an angle measures around a circle with the circle's own radius. Radians also tend to make certain mathematical functions (especially in trigonometry) work out very easily. Still, I often have students dispute both my definitions of "clever" and "useful" in various ways when I introduce radians.

Answer: Polar graphing

Cartesian graphing locates points by telling you how far left/right, and how far up/down, the points are from an initial point. Polar graphing uses a similar principle, but instead tells you how far away, and how far around (in angular form), the points are from an initial point.

Despite the similarities between the system, I do sometimes get wails of "I'll never understand this!" when teaching polar graphing (although the wails often subside when we get to do cool-looking flower graphs).

Answer: All of these are legitimate responses.

As a math teacher, I hope everyone loves and appreciates math--if not for their own enjoyment, for the benefits that its study brings to us all. Math is a fabulous subject!