Area/Perimeter of Squares…Help.

Through my work each year with area and perimeter, I learn more and more about how I learned (was taught) math. I can work out a “proof” algebraically, however I struggle in connecting it conceptually to the problem. When this happens, I am so hesitant to reach out bc, truthfully, it is a bit embarrassing. I mean, I teach this stuff, right? But I finally hit a point, after I started blogging, when I learned that I will never learn more if I am not open to where I am. Since I encourage my students to write honestly about their understandings, I thought it only fair to throw my thoughts out there into the wonderful #mtbos. So here it is…

Here was last year’s example that I worked my way through: https://mathmindsblog.wordpress.com/2014/01/27/area-and-perimeter-of-squares-student-noticings/

And now here is this year’s: https://mathmindsblog.wordpress.com/2014/12/20/areaperimeter-my-homework-over-vacation/

I am finding the same thing is happening again…algebraically I have it, but struggling with the conceptual connection. I have a bunch of theories scattered on my papers this morning, but nothing that is satisfying me mathematically and would appreciate any thoughts….

IMG_8763_2 IMG_8764_2So when thinking about area related to perimeter in squares, I know that n^2 x 4/n = 4n, but I am stuck at that 4/n. I marked off what I thought 4/n looked like in my squares, I messes around with ratios, found some patterns, but still not seeing (or putting together) what I want. … so I went to this drawing bc the side was increasing by 2 every time…. IMG8765Then I went to this…

IMG8766 And while I would love to play with this for a bit longer, I have so many other things to do to get ready for school tomorrow! I feel like I have it somewhere here, I just cannot make a connection that works for me. Would love any pieces to the puzzle put together for me:)

Thanks!!

-Kristin

3 thoughts on “Area/Perimeter of Squares…Help.

  1. Joshua

    I am not entirely sure what type of pattern or insight you are trying to find, but here are some ideas:
    (1) Consider looking at Area/perimeter instead of perimeter/area. I know it should be symmetrical, but years of problems structured “what is the largest area for a given perimeter” + other constraints makes this more intuitive for many (maybe you?)

    (2) Explore how this ratio works for other shapes: equilateral triangles and circles would be good places to start.

    (3) Remember properties of scaling: lengths grow proportionately and areas with the square of your scaling factor.

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