3D Multiplication Table

The 3D multiplication table is a three-dimensional embodiment of the one hundred products in the familiar 10-by-10 multiplication chart. The result is an intriguing object-to-think-with that supports mathematical inquiry by making salient logical and quantitative properties that are embedded in the regular multiplication table yet are difficult to see therein. The object thus affords new and engaging cognitive entries into mathematical concepts. Try this: What is the volume of this object?

The Evolution of the 3D Multiplication Table
2001. Dor Abrahamson's design 3rd grader building it from plastic cubes and play-doh.
See also Maria Droujkova's try-out
   

              

2005. Paulo Blikstein's build 
using a 3D printer at Uri Wilensky's lab.
Dor Abrahamson holding the 3D Multiplication Table
   
 
2009. Mike Bryant's build — a 6 ft tall structure made of wood.

 

 

Credits: Designed and researched by Dor Abrahamson. Thanks to Paulo Blikstein then at the Center for Connected Learning and Computer-Based Modeling (CCL) (Uri Wilensky, Director) for engineering, creating the computer images, and 3D-print production of the 2005 build. See also Maria Droujkova's natural math page.