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We Need More Unifix® Cubes!

One day in October, Ms Spence plopped down a bin of Unifix® Cubes for her 1st graders to play with.  I sat down to play with them too.  We made various patterns, and then we started to make stacks of 10, which we placed next to each other and which allowed us to count by tens: 10, 20, 30, etc.  When we got to 100, we saw that we had a square.  What would happen if we made another square?  How many would we have?  We began to madly build stacks 10 and lay them on top of the 100 square: 110, 120, 130… 200!  Excitement mounted as we continued to build, anticipating that we would get to 300, then 400.  We ran out of time and materials.  “We need more Unifix® Cubes!”

Over the next week, Ms Spence’s class and I were excitedly exploring parallel tracks.  While Ms Spence scoured the building for more Unifix® Cubes, and her students were constructing cubes of 1,000 Unifix® Cubes, I consulted with Mr. Werderich about ways to represent large numbers of Unifix® Cubes.  Mr. Werderich 3D printed some joints for the corners and ripped some pine boards into 7.5 inch strips and 75 inch strips.  We also cut some ¾ inch plywood into 7.5 inch squares to represent blocks of 100.  Now properly outfitted, we returned to Ms Spence’s class.  Since not all students were present the first go-around, we started at the beginning.  We dumped piles of Unifix® Cubes on the floor and everyone constructed stacks of 10, and like before, we grouped them in squares of 100 and then cubes of 1,000.  Now we had enough Unifix® Cubes to make several cubes of 1,000, but not enough to get to 10,000.  “We need more Unifix® Cubes!”

Mr. Werderich and I broke out our new tools.  Next to a cube of 1,000 Unifix® Cubes, we placed a stack of 10 plywood squares and our 7.5 inch wood and plastic cube and asked the class how many Unifix® Cubes each represented - 1,000!  Then we lined up the 1,000 cubes, placed our representations at the end, and began to count: 1,000, 2,000, 3,000.  When we ran out of existing cubes, we rolled the wood and plastic cube: 7,000, 8,000, 9,000, 10,000!  Mr. Werderich and I swapped out four of the 7.5 inch pine strips for 75 inch pine strips to create a representation for 10,000 Unifix® Cubes, and then we rolled it across the carpet: 10,000, 20,000, 30,000… 100,000 Unifix® Cubes.  “Should we keep going?”  YES!

We swapped out four more short pine strips for the longer ones to create a representation of 100,000 Unifix® Cubes and imagined stacking more on top: 100,000, 200,000, 300,000… 1,000,000 Unifix Cubes!  We swapped out the remaining four short pine strips to make a 75 inch cube that represented one million Unifix® Cubes.

We estimated how many Unifix® Cubes could fit in the classroom (20,000,000), how many Unifix® Cubes could fit in an average 6-year-old (5,000), and what kind of space we might need to create a square prism of ten million Unifix® Cubes (the blacktop).  And so a couple of weeks later, we headed out to the blacktop with our one million Unifix® Cube. 

Starting on one side of the blacktop, four students stood to mark the four corners of the one million Unifix® Cube.  Then we rolled the giant cube and counted: 1 million, 2 million, 3, million… and at each new million, another pair of students stood to mark the spot.  When we got to 10 million, we saw that it stretched almost all the way from the Governor’s Drive to Falk Woods.  “Should we keep going?”  YES!  We rolled the cube the other direction.  One line of students remained static, while the other line traveled with the cube: 10 million, 20 million… 100 million Unifix® Cubes!  Then we gathered together and imagined what would happen if we stacked another million on top, and then another, and another until we got to one billion Unifix® Cubes.  We saw that another one-billion cube could fit on the other side of the black top, and we all took a lap around 2 billion Unifix® Cubes.  One child did some quick math and figured out that if we ran around five times, that would be 10 billion.  We looked across at the Cathedral of Learning and estimated that it would hold more than 50 billion Unifix® Cubes!  “We need more Unifix® Cubes!”