Binomial Cube 二項式正方體

binomial cube1Earlier this week, Astroboy worked on the binomial cube.

I’d tried to present this material to him before but he wasn’t interested.  This time, it was just laying around on the mat because I had to take pictures for my class.  Now he was interested.  I feel like evidence is building that often kids are more interested in materials when it’s just laying around, enticing them, rather than when I choose a material to present to him.  Not sure what this translates to when it comes to the classroom.  Do I now need to really focus on making all materials enticing? (which is really hard when it comes to math, most of the materials are always covered!)

Binomial in Chinese

Since I’m focusing somewhat on Chinese, I think I’m going to research all Chinese names related to the materials.  Bionomial cube is called 二項式正方體 in Chinese.  Cube is 立方體.  Another word for cube is 方塊.  I think the first one is the math term and second one daily use.  Other vocabulary you may have to use is 正方體 (square cube), 長方體 (rectangular cube).  Though in our english presentation, we call it prism.  I’m guessing (with only a little googling) it’s because we consider prisms as something that reflect light in Chinese?

The binomial cube in a primary classroom?

So what’s the binomial cube?  It basically shows you the equation (1+2)^2 as a concrete material.  In the primary classroom it’s part of the Sensorial Curriculum, things that cultivate your senses; in this case your visual sense.  It’s NOT in the math curriculum.

But that is totally the brilliance of Montessori.  The kids are going to see this again in Elementary when they learn squaring and cubing in earnest in 3rd-5th grade.  And if they have attended a Montessori preschool, they would have been familiar with the material, in how to handle and construct them.  And the kids don’t really know any different.  It’s just blocks to them that you have to construct a certain way in order for it to fit back in the box.  It’s a puzzle.

The cubes are color coded as a control of error: all red, all blue, blue-black, red-black.  When your construct it, the same color should kiss each other.  In Elementary, the red is labeled ‘a’, and the blue ‘b’.  So a red cube is a^3, a red-black rectangle is a^2b.  It all works.

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