My introduction to surds this year was by setting a problem to my class:

Calculate the exact value of the length of each missing side:

Initially the class knew exactly where to start. Pythagoras. Great. The problem arose when calculating the length of the hypotenuse of the red triangle. The class wanted a calculator. This led to a discussion about exact values and accuracy.

Then I set the class the challenge of drawing the Spiral of Theodorus and to calculate the hypotenuse of each triangle and also to calculate the area of each triangle. Continue reading →

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