Class Openers

Class Opener – Day 21 – 3D Graphs

Today’s opener turned into much, much more than I originally expected – and a truly powerful share at the end.

binomialsFor the last few days, my students have been working through the binomial theorem, expanding and finding specific terms. There has been much movement around class, with students at the board, working together, sharing ideas. I provide problems off the top of my head, giving more difficult ones if the students seem ready, and peeling back if we need more practice.  To provide solutions, I use WolframAlpha to expand the binomial and project solutions from my iPad. This has worked well, but students have also taken note of the deeper info Wolfram provides in these calculations.  In today’s opener, one of these interesting graphs appeared on screen as students enetered:


The Wolfram player allowed students to move around this strange object and explore it from all angles. One of my classes impressed me by relating what they related the picture to the Continental Shelf, which they were exploring in science. I provided a 2-minute intro to the (x,y,z) plane – always a fun time.

It was then that one of my students who participates in robotics shared his experience with a 3D printer this summer. I was surprised that few students had heard of these devices, and they seemed intrigued by the idea.  I was reminded of a powerful video involving a student their age, whose father “printed” a prosthetic hand for his son. The end of class then featured two videos I dug up and shared in the last few minutes of class to make students aware of the engineering possibilities.

3D Yoda:

Inspiring story of 3D printing in action:

When the kids leave with a “wow” moment, something has gone right!


By Bob Lochel

HS Math Teacher. Hatboro-Horsham School District, Horsham, PA.

2 replies on “Class Opener – Day 21 – 3D Graphs”

The above work is really deserves appreciation,their theorams and tricks are really interesting.The 3d graphs really set a not so easily reachable standards for the modern time data visualization experts,many of them are much eager to know it.

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