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Fake Origami & Fractions

Folding paper to explore fractions

When preparing Origami, Symmetry & Peace (, I made a major, but fortunate, blunder. I posted this diagram which has little to do with origami. Nonetheless, the folding of this square allows for a nice exploration of fractions. When working with paper-folding to introduce fractions, a nice exploration is to find (with supporting arguments) the area of each region of the folded paper! A lesson (in middle to upper primary school) can start with just four folds (the diagonals and the 'cross'). This gives eight congruent isosceles right-angled triangles, allowing for an elementary discussion of eighths. Next, make just one of the folds joining a vertex of the square to the mid-point of an opposite side. What new triangles arise? What fraction of the whole is the area of each triangle? Make more folds of this kind and address these two questions as each fold is added ... As an additional activity, the learner might compare and contrast the 'real' origami paper-folding with the 'fake' one ...