Creating Unique
3-D Figures: A Lesson in Discovering “Sameness” Through Flips, Turns, and Rotations
By: Welcome to the Math for Young Children, The Blantyre Lesson Study Team, Public Lesson, 2012
The students were very engaged and worked tirelessly trying to figure out how many different 3-D figures they could create if using 3, 4 or 5 interlocking cubes. It was wonderful to see the level of camaraderie that developed during this activity.
"If they are flipped it looks different." A.T.
"I put this one like this and I put this one a different way, they looked different. I flipped them around and I could tell they were the same shape!". O.S.
"You can't make so many shapes, there are only certain ways to make the shapes with three cubes!" D.S.
This
activity, which lasted for a couple weeks, supported students in understanding that
certain 3-D figures, although different in orientations, could be flipped or rotated
and be made to look the same. In discovering how and why some 3-D figures were the
same, students also learned how and why some 3-D figures were different.
As some students progressed from building with 3 interlocking cubes to eventually building with 4 or 5 interlocking cubes, they were increasingly challenged to think of the multiple combinations in which the interlocking cubes could be combined to create new and unique 3-D figures.
As some students progressed from building with 3 interlocking cubes to eventually building with 4 or 5 interlocking cubes, they were increasingly challenged to think of the multiple combinations in which the interlocking cubes could be combined to create new and unique 3-D figures.
Blantyre Lesson Study Team, 2012, pg. 4
The students were very engaged and worked tirelessly trying to figure out how many different 3-D figures they could create if using 3, 4 or 5 interlocking cubes. It was wonderful to see the level of camaraderie that developed during this activity.
"If they are flipped it looks different." A.T.
"I put this one like this and I put this one a different way, they looked different. I flipped them around and I could tell they were the same shape!". O.S.
"You can't make so many shapes, there are only certain ways to make the shapes with three cubes!" D.S.
"There are four ways because if you make a chair with two on the bottom and one on the top, you can flip it and make it into something else." G.B.
"No, it doesn't change the shape because you are just flipping it and you don't take it apart. They're all the same, you don't pull it apart, you are just flipping it over and over. You can only make two shapes with three cubes." A.M.
"It was a little harder to build with the four cubes because it took long to make all the different shapes. I thinked it and then I found that this shape was missing." M.P.
"Once you get past six shapes it gets hard!" E.H.
"I got it! This one is missing!" A.P.
"Oh yea! It was pretty hard because on the last one I could't have anymore ideas and I tried and tried and I didn't know how to do it. I saw that two were the same and then I was trying to fix it but I had no more ideas and M.P. and C.D. helped me." H.S.
With minimal teacher guidance, students explored, investigated and started helping others when they were stuck. They naturally started working in pairs and groups, reasoning with each other, comparing, and debating, in order to accomplish the task of figuring out as many different 3-D figures as possible.
This is a great challenging activity that can be continued at home. All you need is some interlocking cubes!
*Hint: 2 possible 3-D figures if using 3 cubes, 8 possible 3-D figures if using 4 cubes, and 29 possible 3-D figures if using 5 cubes! Good luck!
Thank you for sharing! It's wonderful to see into your classroom.
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