Task# Placing a square root on the number line

Illustrative MathematicsVaries

The purpose of the task is to make connections between the definition and properties of squares and square roots and ordering on the number line, as prescribed by standard 8.NS.2. The key algebraic underpinning to this task is that squaring and square-rooting preserve order, i.e., if and are positive, then The solution to this task requires repeatedly applying this idea. At the teacher's discretion a calculator with basic functions may be appropriate, though we note that all that is really required by the solution is three 2-digit multiplication problems. In fact, students might be shocked that they can complete the task without a calculator!