Square Centimeters or Centimeters Squared

The same subjects keep coming up!  The girls are totally confused about the concepts of square centimeters and centimeters squared, and still mildly confused about length and area.  We cut 1 cm squares and made shapes.  This came up because I asked them to do a drawing 2 square centimeters.  Failing that we went back to 1 square centimeter.  You see, when I asked for 2 square cm, I got a square 2×2, which was really 4 sq. cm.  They were working on a principal or pattern of a square of 2 cm sides so you square  the 2, namely 2 squared, but that’s 4 square cm, and not two.  We made progress, I hope.  I like the creative design which was right as another way to get six square centimeters.  We also talked about tiles on the floor, how wide the table was, and then if we wanted to put all the books in a box we had to give it height, add another dimension.

the girls cut up pieces of graph paper in 1 cm squares and used them to create areas of different sizes and shapes/

Putting together square centimeters

We talked (I talk and hopefully they nod and when I asked what they thought they answered in centimeters).  I don’t know what stops them.  They are smart kids and I said I wouldn’t be spending these hours with them if I didn’t think they were able to get it.  They freeze, the deer in the headlights I wrote about last week.  Today the image was of children crouched in a burning house, afraid to come through the open door.  They are so afraid of getting it wrong they can’t think straight.  It’s not about language because they had the same problems when they were learning in Bengali.  But then last year when they were still learning in Bengali their math teacher was confused about length and area.

WAIT!!!!  I just Googled the title of this post, and guess what, it’s not just my girls who are confused!!!!   This is from a 2001 question in a math forum. http://mathforum.org/library/drmath/view/57209.html

My wife is a teacher and we have had a disagreement over the 
definition of meters squared. She says that a rectangle 3 meters by 4 
meters equals 12 meters squared. I say it is 12 "square meters," and 
that 12 meters squared would be a square measuring 12 meters on each 
side (or a total of 144 square meters). Who is right? This is 
important because she doesn't want to incorrectly advise her students.

 The answers are confusing and there seem to have been some changes in the 50 years since I studied math.  There is some difference between the symbols used for squaring and the words.  HMMMMM as Ganga would say.  I'm really glad I decided to write about how confused the girls are, since I'm now confused.   But, the concept, the squares, the area, how you build area and then cubic space -- those are the fundamentals we need to keep working, and meanwhile I'll have to find some help on the symbols.  As I pointed out to the girls, if we are going to get tiles for the dining room floor it really matters whether we have  64 sq feet in our 8x8 room or 64x64 sq feet, which is 4096  sq. ft, and a bit out of our budget.  

1 Comment (+add yours?)

  1. Arun Debnath
    Aug 13, 2012 @ 12:08:46

    It’s my turn to join Ganga and the girls to be confused – I still haven’t got it I’m afraid! I will catch the Mathematicians in the house at the right moment and come back with a suggested answer. Love to all of you at Shishur Sevay.
    Arun from London



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