First, students will learn how to evaluate square roots of small perfect squares by drawing dots, as seen here. In my opinion, this method becomes tiresome for the square root of any number larger than 25. After that, students will learn the abstract method. That is, to find the square root by thinking in terms of square numbers. Students can practice the abstract method here. Students will also learn how to evaluate nested square roots. For example

$$\sqrt{\sqrt{16}} = \sqrt{4} = 2$$As an interesting aside, show your students how to find the square roots of larger numbers using dots, as shown here. Before attempting this section, you should be excellent at multiplying whole numbers. Next, give your students this challenge. Tell students they're only allowed to use +, -, *, /, and sqrt. This greatly reduces the difficulty of the puzzle. Here's my solution:

$$\begin{align} & 6 = 2 + 2 + 2 \\ & 6 = 3 * 3 - 3 \\ & 6 = \sqrt{4} + \sqrt{4} + \sqrt{4} \\ & 6 = (5 / 5) + 5 \\ & 6 = 6 + 6 - 6 \\ & 6 = 7 - (7 / 7) \\ & 6 = 8 - \sqrt{\sqrt{8 + 8}} \\ & 6 = \sqrt{9} * \sqrt{9} - \sqrt{9} \end{align}$$Keep in mind, there are likely other solutions, some of which may be better than my own. Conclude by giving your students this challenge. Let your students know they can use a calculator to help them solve this challenge.

Next, give your students these challenges:

- 2018 Math Kangaroo Levels 5-6 Problem #17 by STEM4all

2021 Math Kangaroo Levels 1-2 Problem #23: Julia only eats fruits. She eats apples on Mondays, Wednesdays, and Fridays; she eats mangoes on Tuesdays and Thursdays. She eats either 2 apples or 3 mangoes a day. On Saturdays and Sundays she eats nothing. How many pieces of fruit does Julia eat in two weeks? Here's the solution.

Conclude by leading this investigation:

Tetracide (percentages, algorithm)

by MathPickle