Caught in the Net of a Triangular Prism (A Report From the Fourth Grade)

As regular followers of are aware, it is generally devoted to political commentary. But once in a while a change of pace may be in order, and this blog is one. As it happens, it is not entirely unrelated to previous concerns of, where we have already commented on issues involving K-12 education and plan to do so again soon. 

I recently began some tutoring at a nearby public school. Before embarking on this mission, I had warned the sponsoring organization that I would be of no use in attempting to help anyone with High School math homework. I have not solved an algebraic equation in well over half a century and the only thing I ever knew about calculus was that it gave frequent headaches to my freshman roommate at Cornell. “Not to worry,” they said, “we have a fourth grader for you.” “Sounds good,” I said. 

Following an introductory meeting, my tutee and I got down to business in our second session with some homework. After a few minutes of moving rather quickly through some language exercises, we came to math: triangles. At that point, I was dismayed to find that my memory of isosceles and scalene triangles was a bit rusty. (Or, I am tempted to say, more obtuse than acute.) Fortunately, I was able to find a dictionary and work the questions out. (For those whose memory may also be a bit rusty, an isosceles triangle has two sides of the same length and a scalene triangle has no sides of the same length.) I felt a little proud of having helped my tutee and looked forward to our next meeting.

At the next session, however, I was confronted by a thornier problem: a question involving the “net of a triangular prism.”  Hmm… That was not anything that sounded even vaguely familiar and I was not optimistic that the dictionary would help with this one. Instead of doing the sensible thing and simply admitting my ignorance, I decided to improvise. I sketched something that looked like a rather crude pyramid, and we proceeded from there.

Later on at home, my curiosity drove me to the font of modern learning, Mother Google. What is a triangular prism and what on earth is its “net”? The answers were readily available. Was a triangular prism a pyramid sort of thing? Well, not really. A prism is a solid object that has two identical ends and all flat sides (which, incidentally, are parallelograms), And a triangular prism is composed of two triangular bases and three rectangular sides. (Having five sides in all it is, of course, a pentahedron).

A net, I discovered, is a two dimensional pattern that can be folded to form a three dimensional figure—such as a triangular prism. And astonishingly enough (to me anyway) a triangular prism has no less than nine!

Embarrassed by the misinformation I had conveyed to my tutee, I sent an apologetic email to his teacher and asked if I might have access to some of the instructional material on which his homework is based. She replied in a kind way, agreed to my request, and assured me that the subject of nets “is only introduced in 4th grade & mastery is not expected.”

In the near future will discuss issues concerning K-12 education, including the growing political controversy over the Common Core State Standards Initiative. WE may, however, approach the subject with somewhat more than our usual humility.

2 thoughts on “Caught in the Net of a Triangular Prism (A Report From the Fourth Grade)

  • No matter how you you fold it, each net has 5 segments to make one prism, cool!

    By the way, your crude pyramid was not so far off, it also has 5 segments to it’s net which has a total of 6 possibilities, go figure.

    Fun exercise, look out for that 4th grader!

  • I ALWAYS ask to see the teacher’s reference books when assisting math students. They learn way different things and methods than when I was young! You’re a champ to help!

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