2.G 2: Making Squares On Purpose (#175)


A Year in the Life: Ambient Math Wins the Race to the Top!
Day 174

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.” And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.”

Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. Today’s standard will be listed in blue, followed by its ambient counterpart.

Geometry 2.G
Reason with shapes and their attributes.
2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

It’s not clear how to get rows and columns of squares by folding a rectangle into smaller versions of itself.  I’d think you’d need to start with a square to get squares.  Aside from that though, there’s the activity itself.  Does it have a purpose, or is it busywork, as are so many of the lessons and activities imposed on children as part of a school day.  Here’s what John Holt has to say about this:


The very first Grade 2 lesson is making an oversized times tables wall chart.  A 36 inch square piece of poster paper is folded: in half twice (4 columns), then in thirds (12 columns).  Then the paper is opened up and the same folds are repeated the other way, yielding 144 same-sized squares.


The children then fill in the tables they know.  They’ve learned the 2’s, 5’s, and 10’s in Grade 1 and of course they know the 1’s.  They can be told that the 11’s are just double numbers (up to 9), and they are happy to see how much of the chart is completed!  A prompt is used to copy from, as the rest are penciled in.

After all the tables are checked for accuracy, the children color the numbers in each row a different color with colored pencils.  Many patterns are found, like the square numbers running along a diagonal line from 1 to 144.  The chart is posted in a prominent place so the times tables can be painlessly and gradually absorbed.


Many squares were made from a large square, and used for a good purpose.  This chart can used until all the times tables are learned.  Basic skills like this are the bedrock of math success and proficiency.  And the chart is created with pride and enjoyment, qualities that are so essential to any teaching and learning worth its salt.

As always, it’s movement, story, art and playfulness that win the math day! Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.

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