Lesson objective: Practice estimating irrational square roots and order irrational numbers on a number line.

This lesson helps to build fluency with identifying the whole numbers between which an irrational square root falls, and comparing the values of rational and irrational numbers in different forms. A number line is used here because it highlights the irrational number's connection to known quantities, especially when finding the square root of a non-perfect square. This work develops students' understanding that irrational numbers are numbers which live on the number line and represent real distances.

Students engage in Mathematical Practice 2 (reason abstractly and quantitatively) as they use a combination of estimation strategies and precise number comparisons to reason about irrational numbers.

**Key vocabulary:**

- irrational number
- square root
- whole number