Origami Math Project
Origami is the art of folding a flat piece of paper to create three-dimensional figures. Origami is useful in teaching many aspects of geometry, such as shapes and rotations. The PHiZZ unit is a folded paper that creates not only its own interesting shape, but can be connected to other PHiZZ units to create larger pieces.
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PHiZZ Unit
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The PHiZZ Unit is created from one small square of paper. The letters in its name stand for pentagon, hexagon and zigzag, which describe the shape of the unit when it is laid flat -- zigzag -- and some of the larger projects it can create, such as a pentagon and hexagon. The PHiZZ unit can be made using post-it notes, which are cheaper than origami paper, and are almost always kept on-hand by teachers. If students make a large store of these units, they can use them to build larger projects.
Construction
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Make a valley fold down the middle of the paper, folding the right and left edges together. Fold the top edge back so that it lies against the first fold. Turn the paper over and repeat this step with the other edge, creating an accordion-like appearance. Pick up the paper so that the folds face up and fold the upper left-hand corner down toward you until its corner meets the bottom edge. Fold the length of the paper down so that the top edge meets the side of the triangle you created when you folded down the left-hand side. This creates a hook shape. Fold the length up, creasing against the straight bottom edge of the triangle. Fold the strip down so that it sticks out. Finish by folding the last strip into a triangle. You should have formed two connected triangles.
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Shape
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Not only do PHiZZ units help students learn the names of shapes, they also help them learn how and why these shapes are granted their names. The pentagon, for example, is named for the fact that it is a polygon, a closed shape with at least three sides and angles, and that it has specifically five sides, indicated by the prefix "penta-." Students can create multiple PHiZZ units, then combine them to create a variety of patterns and shapes. They can also give a brief explanation of why their shapes have their names.
Symmetry
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While the PHiZZ units themselves are not perfectly symmetrical, the pieces they can create often are. Once the students have created their projects of combined PHiZZ shapes, whether pentagons, hexagons or another shape of their choice, have them find lines of symmetry in their shapes. Some shapes will have a great many lines of symmetry, and students should be encouraged to find all they can. While students have a strong grasp of simple symmetry, PHiZZ projects can help them extend that knowledge to more complicated, even 3-dimensional shapes.
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