In this lesson students use different strategies to approximate the value of square roots when a drawn square is not given (MP2). While this lesson offers students some practice with using square root notation and approximating values of square roots, there will be additional opportunities throughout the unit.

Students begin by finding the areas of tilted squares, writing their exact side lengths, and approximating those side lengths using tracing paper. Next, they create a table and graph of side lengths and areas and use them to verify the accuracy of their tracing paper estimates. Lastly, students work in pairs to find the areas of two squares. While the squares have different orientations, both have an area of 50 square units, and so they must also have the same side length of .