Side Lengths and Areas

In this lesson, students learn about square roots. The warm-up helps them see a single line segment as it relates to two different figures: as a side length of a triangle and as a radius of a circle. In the next activity, they use this insight to estimate the side length of a square via a geometric construction that relates the side length of the square to a point on the number line, and verify their estimate using techniques from the previous lesson. Once students locate the side length of the square as a point on the number line, they are formally introduced to square roots and square root notation.