Cute Cubes

At some stage, most students will have made a cube from a net. In this activity, they make a cube using 6 squares of paper that are folded origami-style and slid into each other. The result is an attractive mathematical model in which all the pieces interlock, so there is no need for glue or sticky tape. Memo cube squares are ideal for this activity: they are a good size and weight, they donÕt need cutting, they are cheap, and the colours are a bonus. To complete their cube, the students will need to carefully follow each of the steps as described and illustrated. They will also need to fold their squares with precision. Give your students maximum opportunity to work the instructions out for themselves and to assist others who have trouble. The critical step is instruction 5, where the students must flip the paper over and fold it back onto itself. If they don't flip it over, they will get a result that looks similar to diagram 5 but that won't interlock correctly with other pieces. Tucking each of the corners under the centre fold (instruction 9) locks all the folds in place. The students then flip it over again so that all the folds are face down and then make two last folds. When this is done, there should be 2 triangles sticking up. The hardest part of the task is assembling the cube from the 6 folded squares. Regard this as a problemsolving task for your students and resist the temptation to rescue them if their first attempts fail. Once some students have worked it out, their expertise will be in demand. You should try the task beforehand so that you know what you are asking your students to do. To assemble the cube, start with 2 of the folded squares (folded side up) at right angles to each other. Slide the point of the second piece into one of the pockets of the first piece. (See the diagram on page 9 for an explanation of terms.) Take a third piece and slide one of its points into the remaining pocket of the first piece. Following the pattern you have now established, introduce the fourth, fifth, and sixth pieces. Some students may take an hour or more to complete their cube, but they will be proud to take the finished product home. Fantastic Folding (on the adjacent page) is an extension of this activity. For origami techniques and ideas, see: http://www.origami-instructions.com/ activity.

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