Author:
Tracy Rains
Subject:
Mathematics, Algebra
Material Type:
Lesson Plan
Level:
Middle School, High School
Tags:
Exploring Real Numbers, Exponent, Radical Symbol, Radicand
License:
Creative Commons Attribution-NonCommercial 4.0
Language:
English
Media Formats:
Downloadable docs, Interactive, Text/HTML, Video
Square Roots

Square Roots

Lesson Overview

In this seminar you will explore square roots and see how they are used throughout mathematics.  You will see how “squaring” a number and “taking the square root” relate to each other. Also presented will be how to estimate square roots when given a number. You will have plenty of opportunity to try practice problems, review, and even create a short presentation. You will apply techniques you have learned involving estimating. You will use the techniques learned in this seminar to solve problems involving square roots moving forward and ultimately be able to verify solutions. When working with square roots, you will identify the patterns in perfect square numbers, as well as in techniques such as squaring and cubing numbers.  By the end, you should have a better understanding of what a square root is and how to handle expressions that involve square roots.

Standards

CC.2.1.HS.F.1

Apply and extend the properties of exponents to solve problems with rational exponents.

CC.2.2.HS.D.6

Extend the knowledge of rational functions to rewrite in equivalent forms.

Task 1: Engage

Introductory warm-up activity.

no calc.PNG

Now try to figure out the square root of each of these two numbers, 100 and 27, without a calculator.  Is one easier to find than the other? Why is that?

Task 2: Explore

Read or watch the resources to learn about this concept, then do the practice activity.

Read

Watch

Do

Let’s start out with a simple Introduction to Square Roots. There are practice problems to try at the bottom when you are done reading. Pay attention to the part about negatives. This will be important to understand moving forward and is a common mistake in algebra.

Also go to Radicals: Introduction and Simplification to go a little more in-depth on this topic.  Sometimes you need to Estimate square roots, click this article to learn how.


Simplifying and Multiplying Radicals will introduce you to how to tackle square roots in algebra problems.

Watch this Introduction to Square Roots video for just that. Then head over to Math Antics: Exponents & Square Roots to pull together how exponents and square roots relate. Watch this video on Estimating Square Roots when the numbers you are given are not perfect squares.  Grab your math notebook and write down any new information. Don’t be afraid to hit pause if you need to copy an example or review something that is stated.

You can find some Square Root Tricks here!

Try some practice on taking the Square Root  of certain numbers. Also try some Equations with Square Roots & Cube Roots. Do your best on the cube roots, but concentrate on the square roots. This link will give you practice on Estimating Square Roots. On each of these links you can click the “Stuck” button if you need some help or a hint. Don’t be afraid to use it!

 

Task 3: Explain

Discuss your ideas / opinions / understandings.

Get with a partner and watch this short problem: A Real Life Problem of a Square Root Function.  Now let’s say that the area is of that pasture is 62,500 sq. ft. How much fencing does he need to go around the 3 sides? Work through the problem together, explaining why you are taking each step that you are. If you get stumped, watch the video again and follow along with her, but using the number given. Can you think of another real life example where square roots are used? Create one (with answer key!) and share with your partner.

Task 4: Evaluate

Now it is time to self-check how much you have learned about this topic.  If you do not know as much as you thought, go back to the “Explore” section of this seminar and reread, rewatch, or redo the activities listed.  See your facilitator if you have questions.

Click here to take the quiz online. You do not have to log into the quiz site in order to take this quiz. If a window pops up asking you to sign up for the quiz site, just close the sign-up window and start your quiz.

Task 5: Elaborate

This is a task or project where you can show what you know.

In this section you are going to watch a number of videos to go deeper into this topic. Please pay attention to each, as you will need to complete a short assignment after watching them.

Short videos list to watch: (Please watch all of them)

What is a Perfect Square and How do you find the Square Root of a Perfect Square?

How Do You Simplify Radicals Using the Product Property?

What is the Product Property of Square Roots?

What is the Quotient Property of Square Roots?

Choose any one of the topics above and create a short presentation involving square roots. It should include at least 16 slides. At least 10 of the slides should fully explain the concept in words and examples and the final 6 should be at least 3 examples and an answer key slide for each.

Task 6: Express

Complete this wrap-up activity where you reflect on your learning.  

How do Square Roots connect with the other topics you have been learning about?  What part of square root are you still struggling with? How can you overcome this struggle?