Monday, May 20, 2019

Perfect Squares

     Hi!  This week I am going to look at Perfect Squares and how they are taught in Elementary Mathematics.  I currently substitute teach in a public middle school in Upstate New York, in grades 6 through 8, and in the last two weeks I have been in both the 7th and 8th grade math classrooms, and as luck would have it they were both working on perfect squares.  What I found interesting is that at both levels I heard the same questions:  What is a perfect square?  How do I simplify one?  What is a square root and where did you get it from?  The 8th grade class asked, how is exponential math the inverse operation of a radical sign? 
     All of this got me thinking, what have these students been taught about perfect squares before 7th grade?  What will I be teaching my students in elementary math that will help prepare them for this topic when they get there?

Engage NY

Looking through the Engage NY website, I found that in second and third grade, students are expanding their ideas of geometry.  They are working with two and three dimensional geometric shapes and learning how to describe their size and shape.
 
https://www.engageny.org/resource/grade-2-mathematics-module-8-topic

https://www.engageny.org/resource/grade-3-mathematics-module-4-topic-overview


 Manipulatives and Posters


GeoBoards

Teachers are using geoboards in the classroom to experiment with shapes while having the ability to measure and define that shape. 



Image result for geoboard clipart Image result for geoboard clipart





Classroom Posters 

 Classroom posters are a great visual way to represent the topics that you are teaching.  Teachers can refer to them as they introduce a topic and teach how to use the information on the poster.  Students then have a strategy in place to help them when they get stuck.  They know where in the room to find the information they need in order to solve their problem. 

 Image result for how to teach square numbers          Image result for how to teach square numbers


Conclusion

 Students start their work on perfect squares early in elementary school.  They learn how many blocks it takes to build a perfect square or how many cubes are inside their rubber band.  They are playing with the model of what a perfect square looks like. How does this concept continue to grow from blocks to a mathematical expression, 2² = 4 and ⎷4 = 2? 

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3 comments:

  1. SarahMay 23, 2019 at 4:57 PM

    I remember geo boards! I loved your exploration here. I think we used geo boards to show different shapes and compare sizes and lengths of sides. While I remember learning about squares vs. rectangles early on, I don't remember using the geo boards to recognize that the units that make up a square illustrate what a square number, or a number squared, is. In other words, I don't recall the geo board being used to connect shapes and side lengths and what it means to be a square to square numbers and square roots. It's clear from your research and the poster you posted that this is now introduced at a really early grade and it's interesting to see how the concept of geometry and measuring sides and perimeter/area can directly connect to square numbers, square roots, etc. I know for my 7th graders they had no idea what squares were or what square roots are and I will now forever remember the square root symbol as the Vans logo, as one of my students eagerly pointed out. --Sarah Avery

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    Replies
    1. MarleeJune 25, 2019 at 1:23 PM

      Hi Sarah! I enjoyed your feedback on Jill's post! I didn't know the Vans logo was a square root! -Marlee

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  2. Veronica Speaks VolumesMay 24, 2019 at 12:37 AM

    Posters are great informative ways to help your students review guidelines to problems that they may not be able to grasp. Posters are also a good way for students to memorize strategies.

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