Does That Point Work?

In Geometry class, Dylan’s teacher was using students – human-sized objects – to demonstrate a concept.

He asked two students to stand on opposite sides of the room. They did.

“This,” said Mr. F, “is an imaginary straight line. The distance between these two students is a line. Can everyone imagine that?”

“Yes,” the class said in unison.

“Okay,” Mr. F said. “I need someone to come up here and show me a space that is equal distance from each of the two end points.”

He called on a student to be the third “point.” The third student walked to the center of the classroom – directly between the first two students, and basically on the line itself. He stood almost exactly equal distance between the first two “points.”

“Does that point work?” Mr. F asked.

“Yes,” the class agreed.

“Great,” said Mr. F. “Who else wants to try?” No one answered, because the classroom is full of teenagers who only reluctantly volunteer to do anything.

So Mr. F called on a fourth student, who reluctantly volunteered. But he was confused. He was sure there was only one midway spot, and someone was already standing in that spot. So the fourth student got as close as humanly possible to the third student, and just stood there next to him – almost midway between the first two “points.”

“Does that point work?” Mr. F asked.

“Yes,” the class agreed.

“No,” argued Dylan, loud enough for the whole class to hear him.

All heads turned and looked at Dylan.

“Why not?” asked Mr. F.

“Because he’s not really the same distance from both points,” Dylan said.

“Do you want to show us a more accurate point?” asked Mr. F.

“Okay,” Dylan said.

Dylan got up from his desk, looked around, then went to the back of the room and stood there. He was nowhere near the original line – and yet, he was equal distance from both of the first two “points.” In fact, Dylan probably created a pretty nice triangle.

Much of the class was visibly confused. So Dylan stayed standing as the teacher explained that, indeed, Dylan was equal distance from both points.

He just wasn’t standing on the original line. Dylan was, instead, thinking completely out of the box.

I love that he stood up for what he knew to be right. I love that he went against the entire class to prove it. I love that after two years of struggling with algebra, he seems to be perfectly suited to geometry. But most of all, I love that his brilliance just shines sometimes.

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