At my school, along with Math in Focus, we use Every Day Counts (or "Calendar Math," as we commonly refer to it). The beauty of this system is its daily repetition. However kids, like all people, learn things better if they are emotionally involved. So in looking over the math Common Core frameworks for fourth grade, I started thinking about where I could fit in square numbers.
I always feel like square numbers is one of those things that is easy to forget. And what a waste that they get it wrong on their End of the Year tests or MCAS test, because it's not actually that difficult! They just need a quick reminder every so often, and they'd all be capable of getting it right.
This year I realized how easily square numbers could fit into the Every Day Counts portion of our day. It would work especially well during a month when we work on area and perimeter every day. So one day, after we looked at our improper fraction with a numerator of 9, the perimeter of a random figure we had drawn with 9 square centimeters, the geometric figures in our pattern, and the next entry in our running cash total, I wished my fourth graders a "Happy Square Day."
"What's Square Day?" They asked.
"What's Square Day? It's the happiest day of the month! You don't get brightly wrapped square presents, or eat square shaped cake or sing, Happy Square Day to You, but it's still the BEST holiday."
"Why?" They asked excitedly.
"Because it happens FIVE times every month!"
(...)
Hey, some of them saw the humor. The ones that didn't, well, their curiosity stayed piqued as I started to demonstrate how to create square numbers with one, then two, then three, and finally 4 small squares, the latter which formed a larger square. "We had a Square Day on the 4th. It's a 2 by 2 square." I continued around the first square with 5, then 6, 7, 8 and finally nine small squares that formed a square. "And today is also Square Day! 3 long by 3 wide is 9. A perfect square."
"So it's basically a doubles fact" my smart little former third graders recalled."That's right. But here's why we call it a SQUARE number. You CAN'T turn 5 blocks into a square. You CAN'T turn 10 boxes into a square. But you can with 9, and you can with 16, and you can with other Square Numbers, nice and even and neat. That's why I love Square Day!
After giving them time to draw their own squares with a partner, I challenged them; "So when is the next "Square Day's Eve this month?"
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Instead of drawing the squares on an anchor chart, I drew it on the white board so I could erase one square from each corner. "When is the day after Square Day, also known as 'Extra Boxing Day' in England?" We added a box to each corner.
Once we explored squares (as well as what it looks like right before and right after a perfect square is drawn) I challenged them to redraw their previous figures for the month. I asked them to create figures that were as compact as they could. That is, I wanted figures that are as close to squares as possible. Although sometimes it's great to draw creative, zany shapes to find the perimeter, interesting patterns emerge when the figures are more compact.
As a result, the kids started to see patterns in their work. They were noticing that the figure that is one off from a perfect square has the SAME perimeter as a square! "It's like that one square is just inside out; it goes in at the corner instead of out to fill the corner." They also noticed that the perimeter never went down as we progressed. Previously there was no rhyme or reason to how area and perimeter were connected, because many kids were drawing skinny rectangles instead of allowing for irregular figures in between squares. Now they actually had some data to analyze and draw conclusions from.
And so, in my class we celebrate Square Day, and they know that on the day before Square Day their weirdo teacher is going to be giddy with anticipation.
How do you keep square numbers fresh for students?
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