Squares, Cubes + Roots

Introduction

After covering the real number system, I like to transition to a topic where students can feel more confident: squares, cubes, and roots. My 8th-grade students typically start the year with some background knowledge of squares and square roots, but they are often less familiar with cubes and cube roots. The biggest emphasis I make on this topic is teaching students how to find square roots and cube roots on a calculator. Since our state allows students to use a calculator on the Math 8 state assessment, it's important to guide them properly. Without instruction, many students mistakenly enter a three in front of the radical (as in multiplication) instead of using the correct function for a cube root.

To reinforce these concepts, I incorporate a few quick activities, along with some fun games like Gimkit and Blooket. These platforms work well because squaring, cubing, and finding roots can be done quickly, allowing students to complete problems with ease and gain confidence.

Notes

I have a digital/PDF set of notes on this topic, but I prefer to use the PDF version with my students. The page includes four pages over squares, cubes, square roots, and cube roots. There is a numeric example, a visual example, and a real-life example for each type. There is also a practice page for students to assess their understanding of the concept.

Activities

As mentioned previously, I use online platforms like Gimkit and Blooket to reinforce the concepts of squares, cubes, and roots. These activities are quick, engaging, and students have a lot of fun playing them. Beyond these online platforms, I also like to incorporate two hands-on activities to deepen their understanding of these concepts:

• Maze Activity: This activity can be completed on paper or digitally. Students start in one corner of the page and solve various problems as they navigate through the maze to reach the end. They indicate their path by coloring the arrows (or clicking and dragging them in the digital version) to show their progress from start to finish.

• Circle Game: This is one of my all-time favorite classroom activities! Students will compete to answer various square root and cube root questions. While the circle game can be adapted in various ways, here’s how I use it in my classroom:

1. Game Setup: Print copies of the game board and place them in clear protective sleeves so students can write and erase with dry-erase markers. Pair students in groups of two, ensuring each group has a game board and that each student has a dry-erase marker in a different color.

2. Game Play: Project the questions for all to see. Students race to circle the correct answer on the game board. They can only make one circle per question and cannot erase if they realize they made a mistake. Additionally, they are not allowed to block their opponent from circling the correct answer.

3. Scoring: If a student circles the correct answer, they place a tally mark in their color on the edge of the game board. At the end of the game, the student with the most tally marks wins!