Communicating Units of Measurement

The basic problem is this. You have a magical telephone connection to the intelligent beings in another solar system. They have learned most, but not all, of English.

Now the aliens want to learn how long a yard is. Or an inch. Or how tall the children are.

If and when the students say a yard is 3 feet, or 36 inches, they will learn that the aliens don't understand feet, inches, or any of our units of measurement.

You might want to start with a question concerning time. That is an easier question, yet more than difficult enough for a sixth grade class. The slight problem is that time is a "red herring" -- how you communicate time does not work for communicating length.

The underlying problem is this. Measuring length involves first selecting an arbitrary length. How do we communicate this arbitrary length (or time) on the telephone?

Answers that Do Not Count

They might tell the aliens that a finger is about 2-3 inches long. But the aliens might not have fingers, and if they do, their fingers might be much bigger or smaller than our fingers are. Their world could be just like ours except that everything is twice as big, or twice as small. How would we know, using just a telephone?

A somewhat standard answer to the question of communicating time is to have the aliens say "One Mississippi, two Mississippi, etc." I think this does not count as a good answer, because the aliens might say it very quickly or very slowly. However, we could say that and it would be a fine answer. Or, because we are talking on the telephone, I can listen to hear if they are saying it at the right speed.

So, depending on how you handle this, you could in a sense give them the answer. That might be appropriate, because they are on the right track.


For example, the aliens want to know how long our day is, or how old the people in the class are. Again, they don't understand hour, minute, second, or year either.


Time can be communicated over the telephone -- you play two sounds, a given length of time apart. (Or better, you do a rhythmic pattern.) The problem with communicating "day" this way is that it will take too long. So you can point out this problem, if you want, to force them to communicate a shorter period of time. The problem with shorter times is accuracy, if you want to get into that. (I chose not to.)

The answer to length varies. In most scenarios, they cannot see the width of our sun, but they would know the distance between our planet and theirs. So that is one possible answer. If that isn't possible, then you have to get into finding things that are constant. For example, the distance between the two hydrogen atoms in water would not differ from planet to planet. The distance that light travels (in a vacuum) would not vary.

This type of answer also could have been used for second.

Background Information

In the 1700's, it was argued that the meter should be defined as the length of a pendulum having a half-period of one second. Unfortunately, this varies with gravity. In 1960 the meter was defined in terms of the wavelength of krypton-86 radiation, and in 1983 it was defined as the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.

There are also some interesting physics questions. One is to describe what water is. Logically, the would have the concept of a liquid and so I gave the class that such things as liquid and clear were already known. I didn't give them hydrogen and oxygen. Perhaps that was wrong -- the terms hydrogen and oxygen would probably be learned very early on.

Teaching Goals

This obvious gets into the nature of units of measurement, and some questions get into physics. There is a deeper question of what we have in common with aliens on another solar system.

And ultimately, I think it teaches some very deep concepts in communication. Perhaps one idea is that communication is not a matter of words, but instead relies on shared understandings, which we build on to communicate something new. The problem itself is very real -- people are sending out radio broadcasts, hoping that the messages sooner or later reach aliens. But it relates to real-life problems too.


It makes sense to do the basic exercise of constructing a unit of length. Whatever that teaches, it is useful to this exercise. I did this as a class exercise, and the two students who had not done the unit-of-length exercise were obviously (to me) behind in that concept.

The Wrapper

Aliens works very well for sixth-graders. Obviously, when I am teaching one-on-one with someone who likes faeries, I call the faeries.

I brought in a phone. I have found that the less students have to imagine, the better.

Bob Newhart became famous first for doing a comedy routine where he talked on the phone. It was obviously an imaginary conversation, yet people laugh at what the imaginary people are saying. That worked very well for this. For me -- I had just seen a Bob Newhart history and that type of humor fits my personality. So I would say "Do you know seconds? didn't think so.....just checking." Then I would turn to the class and say that the aliens don't know what seconds are either.

For me, telephoning aliens is a great wrapper for other exercises, such as defining words. It is fun, it let's the aliens be the bad guys instead of me, and it restructures the mileau in line with surfin math.