Shafer, K. G., Severt, G., & Olson, Z. A. (November, 2011). Sketching up the digital duck.
Mathematics Teacher. National Council of Teachers of Mathematics: Reston, VA.
external image Extra_Figure.jpg?height=121&width=200external image Grass3.JPG?height=150&width=200
external image quackwood.jpg?height=110&width=200

Background
Why would a classroom teacher want to use Google SketchUp with students? SketchUp is a technology that quickly and accurately creates models in 3D. Enter the world of an architect and use his or her tools to create shapes and models. On the Shoulders of Giants : New Approaches to Numeracy (Steen, 1990), contains a chapter titled SHAPE, written by Majorie Senechal. Note that she reminds us that geometry means “earth measurement” (p. 139). Our students live in three dimensions. We move in 3D. Let’s use SketchUp as a tool to do mathematics in three dimensions, from the ground up.

Digital Ducky
The project that I showcase here focuses on two measurement topics that have caused me fits over the years. What is area? What is volume? For some reason, there is a disconnect between the numeric answer and the unit of measurement. Also, students think they need to memorize a bunch of formulas, which they promptly mix up. My approach has been to have students create a solid using cardboard (cereal boxes work well). Recently, I added the use of creating a 3D rendering to the project. What you see on this page, are images created by Zach, of the duck model created by Gina and her classmate. Zach and Gina authored a paper on this project and Nicole took the picture of the duck in the grass. For more detailed information, please consult the article (NCTM copyright).

Why use SketchUp?
Modeling is crucial to understanding the composition and decomposition of shapes. Each figure begins with a base. Faces are formed with edges and vertices. Coordinates are shown as a three-tuple. As edges are deleted, surfaces disappear (or merge together). “Circles” look like circles but are really a 24 sided polygon (why?). You can not create a regular polygon (sides > 4) without using the radius of the circumscribed circle (why?).

coke_can.png

Extension

A plethora of models can be found in the 3D Warehouse. These are created by hobbyists and professionals (like the Cap’n Crunch box created by Sydney). While it is cool to create your own models, my students have discovered some extensive mathematics by looking at models. Here is your challenge: find the surface area of a coke can.



June 2014 - Okay