I designed the first stage to reveal initially relatively little information to get students to begin thinking about the problem. In subsequent stages I gradually provided additional clues -- both visual and analytic -- to help students succeed. I told the class that I would award full marks for the correct solution of the problem regardless of the stage during which the solution was submitted.
While the entire class of 35 students accessed the stage 1 "leaflet" document, they appeared to have difficulty solving the puzzle in the "virtual" mode. Only a handful of students submitted their solutions at that stage, and none of them were correct.
Sixteen students executed the sequence of moves in stage 2, almost all of them providing the correct frame number values, as expected. Three students submitted correct solutions, linking the puzzle to the Gauss-Jordan reduction and elementary row operations. Three additional students made the correct connection after studying the document in stage 3.
Having just six students out of 35 successfully complete this activity may not strike someone as a particularly impressive outcome. However, I viewed the experiment described here as a "proof of concept", and, in this sense, it has been successful. One can modify the activity described here to make its appeal broader, by providing additional information to students, increasing the credit value, etc.
At the conclusion of the activity, I posted the solution:
Every time we turn a door plane to make it parallel to one of the axes (x,y, or z), we end up removing the corresponding term from that equation (e.g., the plane 2y+3z=5 is parallel to the x axis). Therefore, each move corresponds to an elementary row operation, and the entire game corresponds to the Gauss-Jordan reduction leading to the reduced row echelon form.
I illustrated this by the animated sequence of correct HINGES moves along with the corresponding elementary row operations.
Here are a few additional points, which you may want to discuss with students after they participate in the HINGES activity:
The HINGES activity could be used to compare geometrically the Gauss-Jordan reduction procedure (which transforms the augmented matrix to its reduced row echelon form) to Gaussian elimination (where row echelon form is used instead).
Also note that the rotation and scaling of a plane -- and of the corresponding normal vector -- can be discussed in a more concrete setting of linear transformations in R^{3} after this material has been reached -- see, e.g., (Anton, 2000, pp. 180-181).
Journal of Online Mathematics and its Applications