Estimating Square Roots

Introduction

When teaching students to estimate square roots, I emphasize the importance of understanding how to approximate these values on a number line. I start by having them identify the two closest perfect squares that surround the given number. For example, if they're estimating √20​, they would recognize that it's between √16​ and √25​. Next, they calculate the square roots of these perfect squares, which in this case are 4 and 5. I then guide them to determine whether √20​ is closer to 4 or 5 on the number line based on how close 20 is to 16 or 25.

Once they have practiced placing these values on a number line, I reinforce the concept with a matching activity. Finally, I have students estimate square roots to the nearest tenth and use calculators to check their work, ensuring they understand both the process and the accuracy of their estimates.

Notes

I have both digital and PDF versions of this notes set, but I prefer using the PDF version with my students. In this set of notes, they practice estimating values on a number line. It also includes a detailed page that guides students on how to estimate numbers to the nearest tenth without using a calculator.

Activities

The two activities I use to reinforce this school is a number line activity and a matching activity.

• Number Line Activity: For this activity, I have students put a sheet of number lines in a clear protector. They determine the location of various square roots and place a mark and a label on the number line. I have students get each number line checked before they move on to the next one. 

• Matching Activity: For this activity, students match various square roots with pictures of points labeled on a number line. I l