Stairway to Heaven
The following story was told to me by Judy White, one of the world’s greatest middle school teachers.
Using wooden cubes, Judy created a set of double stairs. As illustrated below, 2 cubes were required to create 1 step (green), 6 cubes were required to create 2 steps (green and red), and 12 cubes were required to create 3 steps (green, red, and blue).
Judy asked her students how many cubes would be required to create 4 steps, 5 steps, and 6 steps. With a little discussion, her students agreed that 20 cubes, 30 cubes, and 42 cubes would be needed, respectively.
She then asked them to generalize. “Do you see a pattern for how many cubes would be needed to create n steps?” she asked.
One boy responded, “No.”
“There isn’t a pattern?” Judy asked.
“No, Mrs. White,” the boy said, “the answer is no — n × o.”
Not well versed in algebraic notation, the boy used the letter o instead of n + 1.
How great is that?
Speaking of stairs, here’s a math joke involving stairs.
A statistician, a physicist, and an engineer die on the same day. At the Pearly Gates, they are greeted by St. Peter. “To enter Heaven,” he tells them, “you must climb these 1,000 stairs. But while you are climbing, I will read to you from Math Jokes 4 Mathy Folks. If you can make it to the top without laughing, you may enter.”
They start up the stairs. The statistician laughs when he reaches the 47th step. The physicist reaches the 125th step, but he then laughs, too. The engineer, however, makes it all the way to the top.
“Congratulations!” says St. Peter. “Welcome to Heaven!”
Upon hearing this, the engineer begins to laugh.
“What’s so funny?” asks St. Peter.
“I just got the first joke.”