The teacher draws a right triangle on the board, labels the legs 3 and 4 and the hypotenuse x, and asks the student, “Can you find x?” The student rushes up to the board and pointing, says “Here it is!”

The teacher writes (a + b)

^{2}on the board, and asks if anyone can expand it. A student comes up and writes

( a____+____b )

^{2}.

The teacher writes an equation on the board, and says “Suppose x is the solution to this equation” and starts to do some algebraic manipulation. A student waves his hand wildly. When the teacher calls on him, he says “But sir, suppose it isn’t?”

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