Abstract
How do your students react to such numbers as 2 ± root3 or 1 + root3/2? If your students are like mine, they regard such numbers as unfortunate “answers” rather than numbers with a precise location on the number line. Some of my students do not easily distinguish between 2 + root3 and 2root3. I devised the following low-tech, hands-on activity to improve my students' understanding of these irrational numbers. Each student creates a number line from adding-machine tape and uses a square and a precisely folded triangle as the only measuring devices. The activity can be introduced in any algebra or geometry class after the Pythagorean theorem has been presented.
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