Paper Folding to Make Cubes

Koshy Kanicherilnalil           Chicago Public Schools 
6217 South McVicker             1819 West Pershing Road
Chicago IL 60638                Chicago IL 60609
(312) 586-4356                  (312) 535-7615

Objectives:

     Students will examine patterns of figures composed of six-squares and 
predict which of the twenty presented could be folded to make a cube.  Then 
students will fold large-scale patterns of these figures to confirm their 
hunches.  This exercise will develop the student's ability to visualize three-
dimensional objects from two-dimensional patterns. 

Materials:

     Overhead projector transparencies of the pattern sheet and the record 
sheets; printed copies of the same sheets, one for each student; scissors,  
marking pens, etc.  Construction or other extra-heavy weight paper to make 
multiple-quantities of the patterns, made with ruler, protractor, X-Acto knife 
and ball point pen. 

Strategy:

     Group students into cooperative learning teams of three or four.  Ask each  
team to close their eyes and visualize a "cube."  Is it a box?  Are the sides 
(faces) identical or different?  Is the box ("cube") open or closed?  Can they 
name any everyday objects which have cubical shape? 

     Then distribute the pattern and record sheets to each team.  Have them 
decide if a pattern will fold into a cube.  Mark answers on the record sheets.   
Teams will report their conclusions to the teacher who will enter results on the  
transparency. 

     Finally, distribute sets of the large-scale cut out patterns to each team  
and ask them to fold each to make a cube.  As the pattern numbers will match 
the printed pattern sheet, the team will be able to compare, discuss and 
perhaps revise their original judgements regarding foldability.     

     With better or older classes, this unit may be extended by asking the 
class if they are familiar with games played with cubes.  Many will respond, 
"Dice" or "Craps."  Enter a discussion of how the faces are numbered on such a 
game piece:  Opposite faces are numbered to add to seven.  Then distribute a 
third page to each team containing just the successful folding patterns with 
only a few of the faces numbered.  The team is to consult and decide upon the 
numbers to be entered on the blank faces to make legal dice.

Acknowledgement:

     Mr. Larry Freeman, of Kenwood Academy, my group's mentor and also a member 
of the SMILE staff in the Summer of 1993 has been of great help in making 
available his personal library materials and in offering many helpful 
suggestions for this project's development.