Lesson 4

In this lesson, students begin to transition from understanding square roots simply as side lengths to recognizing that all square roots are specific points on the number line. This understanding takes time to develop because students have previously only worked with rational numbers, which can be found by dividing the segment between two numbers into equal intervals. In the first activity, they still find \(\sqrt{10}\) by relating it to the side length of a square of area 10 square units, but then are asked to approximate the value of \(\sqrt{10}\) to the nearest tenth. In the second activity, students find a decimal approximation for \(\sqrt{3}\) by looking at areas and also computing squares of numbers. This lesson shows students that irrational numbers are numbers—specific points on the number line—and we can find them by rotating a tilted square until it is sitting "flat." This is the conceptual foundation for the approximation work in the next lesson.