# Engaging students: Square roots

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Tiffany Jones. Her topic, from Algebra: square roots.

B.1 How can this topic be used in your students’ future courses in mathematics or science?

One area of mathematics I wish I had more practice with in grade school is numerical reasoning. I feel that, as a student, I was allowed to use my calculator too much and am struggling to remove my calculator crutch. I hope to encourage my students to sharpen their numerical reasoning skills and to not rely on their calculator. Does this number make sense? Is it too high, too low? Is a negative result valid given the scenario of the problem? The following video introduces a method to estimate the square root of non-perfect squares to the nearest tenth by hand:

“Estimating Square Roots To the Nearest Tenth by Hand” by Fort Bend Tutoring

It gives the students another tool for their toolbox of numerical reasoning, practice using formulas, reviews long division by hand, and strongly encourages students to remember the perfect squares.

I think that introducing this idea as an engage could intrigue student to wonder why the formula works and to wonder what else they are able to do quickly by hand.

Fort Bend Tutoring’s YouTube channel offers videos on a wide verity of high school mathematics topics and courses. The videos cover several examples. They are engaging, not dry and there is also a “theme song” to the videos. I feel that these videos can sever as a great addition to lessons as extra help to the students.

D.1 What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?

The following story was first told to me in a calculus one course. While the telling of the story was to serve as amusement and did not directly relate to the topic of the day, it stuck with me. It comes to mind frequently when working with the Pythagorean theorem and with irrational squares. And when given this assignment, I saw square roots as an option, this story again came to mind. I think having an interesting story cross my mind makes a problem overall more fun. I would want to give that to my students. The article “The Dangerous Ratio” by Brain Clegg does a wonderful job of telling the story, its implications, and gives a mock dialogue so reads can work through the logic. At the end of the article, there is a link to an activity about the proof that the square root of 2 is irrational.

E.1

How can technology be used to effectively engage students with this topic?

I really like the idea of a flipped classroom and hope to be able to practice it in my classroom. While a completely flipped classroom will take some time to implement, videos such as Math Antics’ “Exponents & Square Roots” will be a great place to start.

This particular video address a previously learned topic, namely exponents and relates it to the new topic. It provides definitions and visuals to remember how the terms relate to each other and how to read the symbols. It goes through several examples of varying level and shows the viewer how to use technology such as calculators to solve hard problems. In addition, the video addresses some common misconceptions such as mistaking the root sign and the division sign. Moreover, it ties everything together with a quick review at the end.

One of my favorite aspects so of flipped classrooms, is that the student can review the video over and over. Math Antics does an excellent job of talking the math out to the viewer. The animations are amusing yet helpful. While a lot of information is covered, the video is not dry.

Resources:

“Estimating Square Roots To the Nearest Tenth by Hand” by Fort Bend Tutoring – https://www.youtube.com/watch?v=bUh7Hj-3dkw

“The Dangerous Ratio” by Brian Clegg – http://nrich.maths.org/2671

“Exponents & Square Roots” by Math Antics –https://www.youtube.com/watch?v=C_iKTTI1E34