## From 3D to 2D and Back

Last class we explored how 3-dimensional objects can be represented in 2 dimensions.  We started with a brief study of the cube; we counted the number of faces, vertices and edges (for some of the younger kids, this was not very easy).

Next, we explored how many faces of a cube one could see at any given time, without moving one’s head.  Unfortunately, all of our cubes were one solid color, whereas this task would have been quite a bit easier if the faces were different colors.  Nonetheless, the kids discovered that one can hold the cube so as to see just one face, two faces, or three faces and that it is impossible to see more than 3 faces of the cube at once (the last assertion was made without formal proof 🙂 ).

Here is a picture of me showing them a way to look so as to see exactly two faces:

The kids were then tasked with drawing the cube on paper.  I did not have any expectations but just wanted to see what they would come up with.  Many kids just drew a square, some by tracing a face of the cube.  However, a number of kids had more intricate and quite impressive drawings.   Here is a sample:

After trying their hand at drawing 3D objects, the kids had to do the reverse.  The next activity involved them building 3D structures based on 2D drawings.  They each received a set of geoblocks and puzzles from the great game Architecto.  This is what the puzzles (and solutions) look like:

And a few more pictures of the kids building:

Even though this was by no means an easy activity (I had to think about a few of them and we only gave the kids the easiest 10!), I can safely say that all the kids were thoroughly engaged.  Additionally, the joy and sense of accomplishment on the kids faces when they succeeded in building a structure were priceless.

One final thought.  This was another one of those activities where how well the kids did only slightly correlated with age.  With activities that involve arithmetic, the kids that are a grade or two ahead in school are generally faster and more accurate.  This activity leveled the playing field a bit, which was encouraging for the younger kids and humbling for some of the older ones – in my opinion, a win for all.