Students will learn how to approximate square roots by drawing dots, as seen here. Then students will learn how to bound a square root by making tables, as seen here. Students should also be asked to make rough approximations of square roots by guessing, as seen here.

Watch these Khan Academy videos:

Do these Khan Academy exercises:

Next, give your students these challenges:

- 2018 Math Kangaroo Levels 3-4 Problem #20 by STEM4all
- 2019 Math Kangaroo Levels 7-8 Problem #29 by STEM4all
- Triangle Island by NRICH

Conclude by leading this investigation:

Pinocchio’s Playmates (pattern puzzle)

by MathPickle

8.NS.A.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). *For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.*