Wednesday, June 22, 2016

8th Grade Math - Unit 5a: Square Numbers and Roots

This year I really changed how I taught my Number Systems Unit. I decided to teach a unit on Square Numbers and Square Roots. Then teach The Pythagorean Theorem Unit.  My goal was for this unit to give the students a foundation of perfect and non-perfect square roots and set the students up for success with the concept of The Pythagorean Theorem and solving equations by taking the square root of both sides.

Not only did I change the order of how this unit is taught, I completely changed how this concept was taught.  I only had five days for this unit and I had to make those five days meaningful. :o)

Math 8 Lesson - Square Numbers and Perfect Square Roots
The first part of the unit was an introduction to Square Numbers and Perfect Square Roots.

(Self-paced) Digital Time Tests
After learning about square numbers and perfect square roots I wanted a way for the students to practice them by doing time tests. I didn't want to give the time test as a whole class and correct it. I wanted the students to do the time tests independently and without me.

So I used the features in Showbie to create "Digital" Time Tests that the students could complete on their own and correct.

As you can see the first page they opened up in Showbie tells them to turn off the annotations (which shows the answers).  Then they are directed to set a timer for 3 minutes.

They are then directed to take the time test and complete as many as they can in 3 minutes. As you can the annotations are off.

When the time was up the directions tell them to turn back on the annotations and correct their time test.

Here are examples of students taking the "Digital" Time Test.

After the students corrected their time test they were to leave a comment in Showbie on how they did. I love using Showbie's comment feature to have the students reflect on their assignment.

Students did the (self-paced) "Digital" Time Tests every day for the week.  This really helped with their fluency of perfect square roots.

Math 8 Lesson - Non-perfect Square Roots on a Number Line
The next part of the concept was focused on Approximating Non-perfect Square Roots on a Number Line.  This was just an introduction lesson and the focus was on determining the two whole numbers the non-perfect square root falls between.  This lesson set the foundation for Estimating Non-perfect Square Roots.

Math 8 Lesson - Estimating Non-perfect Square Roots
The next part of the unit was focused on my new method for Estimating Square Roots (no calculator).

I have always taught the method using "Ghost Squares" because it gives the students a visual understanding of non-perfect square roots.  They have always liked this method.  

I realized after taking the CAASPP last year that this method was not practical for the students to be successful when estimating non-perfect square roots without a calculator.

So I decided to tweak the method and use just the number line to estimate the non-perfect square root.

For the first problem in the notes I merged the two methods to give the students the visual understanding.
Then the rest of the problems were focused on just using a number line to estimate the non-perfect square root.

The students loved, loved, loved this method.  They thought it was super easy and didn't even complain about dividing by hand.  #success

Students did a round of Recorder/Reporter and the teams collaboratively estimated non-perfect square roots. (no calculator)

iMath – Socrative (Self-paced) “Digital Task Cards”
After practicing estimating non-perfect square roots with their teams, students did my Socrative (self-paced) "Digital Task Cards" lesson on Estimating Non-perfect Square Roots.

Here is my Socrative Code. Feel Free to Use. :o)
Estimating  Non-perfect Square Roots:  SOC-20210703

I made a Estimating Square Roots Dry Erase Mat for the students to use. 
(Feel free to use)
Math 8 Lesson - Simplifying Radical Expressions
The final focus of the unit was on simplifying and solving radical expressions. The focus was on basic equations and solving by taking the square root of both sides.

iMath – Showbie “Paperless” Assignment
Students practiced simplifying expressions and solving equations in Showbie.

 iMath – Tenmarks Practice and Review
Students practiced Estimating Non-perfect Square Roots in Tenmarks.

Socrative: Estimating Non-perfect Square Roots "Team Task"
We ended the unit with my Socrative Collaborative "Team Task" on Estimating Non-perfect Square Roots, Space Race Style.

Here is my Socrative Code. Feel Free to Use. :o)  
Estimating Non-perfect Square Roots "Team Task":  SOC-20242278

Checking for Understanding
This was a really quick unit and the students did good with the concept during the unit. My goal was to keep reviewing the concept so that they didn't forget.  I accomplished this regular review by giving them one collaborative problem a week.  

The problems started out with just estimating one non-perfect square root. Once the students had confidence in solving those problems, I decided to challenge the students so I just started making the problems harder.

Here are some examples of the problems and the students working collaboratively to solve them.

The students rose to the challenge and persevered through the collaborative problems.  :o)

Do They Still Got It?
I was getting nervous in weeks before the CAASPP.  The students had learned so much this year and my fear was they were going to forget everything.

So for the CAASPP Review Week I made a Socrative "Team Task" to review Estimating Non-perfect Square Roots.

Socrative: CAASPP Review - Non-perfect Square Roots "Team Task"

Here is my Socrative Code. Feel Free to Use. :o)  
CAASPP Review: Estimating Non-perfect Square Roots "Team Task":  SOC-22817540

I loved the discussion and collaboration, but more importantly I loved that they still had it. Majority of the students could solve these problems successfully. :o)

Unit Reflection
I loved the changes I made to this unit.  Everything was well thought out and worked perfectly.  This unit could definitely use more time, but is doable in the week that I allotted. The new method is definitely a keeper.  

The students loved it and felt so successful solving these complex problems with no calculators. And teaching the students to solve equations by taking the square roots helped lay the foundation for my next unit on The Pythagorean Theorem.  :o)

Thanks for stopping by and checking out my blog. Feel free to leave feedback.


  1. Hi, I am a math teacher in Massachusetts and I recently came across your post on estimating and simplifying radicals to the nearest tenth. I have to say--YOU are a ROCKSTAR. Thank you so much for sharing such an amazing strategy. Please could you share your files with me. I would like to teach the unit on Square roots in a similar manner. I am at

    1. Thank You.... This method really helped my students... It's definitely a keeper... :o)