We’ll cast the binary arithmetic of numbers into a three-dimensional manipulative dialect.
Here, the illustrations are two-dimensional cross-sections. Units are represented by round disks, blocks by rectangles.
Iconic math can be expressed in three-dimensional manipulatives and interactive experiences.
Animation: iconicmath.com/arithmetic/blocks/ 
The Image shows the number 100 if each block were interpreted as multiplying what sits upon it by 2. The linear parens version of the iconic number is ((((((•)•)))•)). If each block were read to multiply what sits upon it by 10, then the image is a representation of the common number 1100100. If each ball were to represent a group of 5, then the number in the image would be 5500500.
The iconic rules of transformation for block numbers is the same as the rules on the Parens Notation page and the Container Numbers page . Parens represents iconic numbers in the one-dimensional space of a textual line. Containers represent iconic numbers in the two-dimensional space of a planar page. Blocks represent the same iconic principles in the three-dimensional space of physical objects. By extruding two dimensional containment into a third direction, container numbers are converted into block numbers. The image of nested containment becomes one of stacked height.