Kindergarten Meets Geometry

Last evening at the dinner table, my just-graduated Kindergartner triumphantly announced that a square is made by cutting a rectangle in half.

“Yep!” he declared. “A rectangle is just two squares getting close together and kissing!”

“Or two triangles,” his now high-schooler sister responded.

“No! Not triangles!” he said, knowing without a doubt that she was wrong.

“Could be,” I said, before adding, “And a rectangle cut in half doesn’t necessarily result in two squares. It could be two rectangles.”

“Or two triangles,” his sister repeated.

“Depending on how you halve it,” his dad added in.

He insisted we were all wrong and soon everyone was scrambling for a piece of paper. Luckily, we are not tidy people which meant there were already both scraps of paper and writing utensils on the dinner table. With pencil and paper in hand, I drew the following:

shape1

“Well, I didn’t know you were going to draw funny looking triangles like that!” he said, and then after a pause, took the pencil and said, “Here! Let me show you how a man does it.”

“See?” he said, drawing his rectangle and dividing it.

shape2

“Um. Technically,” I said as gently as I could, “those are two rectangles, not two squares. See? These sides are longer than these sides so they aren’t squares.”

He glared at me. I drew a more exaggerated example.

shape3

“Well, but you drew it really long and skinny!”

“Yes, but it’s still a rectangle that got cut in half and resulted in two rectangles, not two squares. You don’t always get two squares when you cut a rectangle in half.”

“Well, look. I’m going to make a rectangle out of two triangles.” He then proceeded to make an equilateral triangle and then butt another up against it. He frowned.

“That’s a parallelogram,” his brother said.

“You are never going to get to a rectangle that way,” his sister added.

He pressed ahead and eventually announced that he had drawn a circle.

shape4

“That’s a hexagon,” I said. “It has six sides.”

“Yeah, it can’t be a circle,” his sister explained. “It has edges and circles don’t have edges.”

So he announced that he could draw a different shape and he did.

shape5

“It’s a scribblegon!”

For that, we had no response. He had drawn a shape that none of us could claim was any shape other than what he had named it. Geometry lessons were clearly over and silliness had taken control.

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