One Pizza, 32 Pieces, and the Best Classroom Moment of My Life

Or how I learned to teach fractions

Hailuo AI image created by the author (who never had that much hair)

It was 1985 and I was teaching 6th grade math in South Central Los Angeles. My students were having a miserable time trying to understand fractions.

The math specialist suggested I try using manipulatives. She showed me tiny plastic pieces that looked like shiny blue pizza slices and fit together to make a circle. I thought this might work so I asked her for 30 sets of them for my lesson.

I was surprised when she let out a bitter laugh. “The school doesn’t have any. This is my own set I brought from home, but I can show you how to use them on an overhead projector so all the students can see it.”

This made me mad. Manipulatives were supposed to be, well, manipulated. Using them properly brought a concept from theoretical to touchable. Using them in a glorified slide show reduced them to visual models. Of course the Math Specialist was only trying to help, so I just said, “No thank you.”

She did give me an idea. What if, instead of those blue plastic triangles, I bought the class some real pizza? Not the soggy, lukewarm, no-cheese, crap they served in the cafeteria, but Dominos.

I had twenty minutes left in my lunch break so I went to see the principal and outlined my plan.

It was his lunch too but he managed to bellow with half a mouthful of bologna, “How much is this going to cost the school?”

I waved him off. ”I can get 5 pies for $40 and it’s on me.”

He shook his head, pulled two twenties out of his own wallet, and motioned me to use his phone.

After a quick stopover at the cafeteria, I got to my room just in time to beat the bell, greeted my students at the door and watched them all begin the DO NOW on the board… is what I’d say if I taught in Fantasyland!

In reality, most of them did get to work. Darnell still stared at the ceiling. I made a mental note to ask him if there is anything up there.

We started to go over the DO NOW. Sometimes these warm up problems were hard, today’s was beyond easy. I had simply written the numbers 1, 2, 3, 4 on the board. The questions were:

1. What is the biggest number? Smallest?
2. As we move left to right what is happening to the numbers?

I was smiling as every kid had their hand up, even Darnell, who correctly answered both questions with a satisfied smirk. Of course Shaniqua, my smartest student, added, “The numbers aren’t just getting bigger Darnell, they are growing by one.”

With perfect timing, there was a knock on the door, and through the small glass window in the steel door I could see the blue and orange uniform. I gave the delivery guy the two twenties and a five dollar tip and set the pizzas on my desk.

I lifted one cardboard corner from each pie until I found the special, uncut one. Tilting the open box a little, I showed the class the uncut pie.

Darnell blurted out, “That’s a big piece mister. You eat that and you’re gonna get fat…ter.”

This got some laughs but I soldiered on. “You’re right Darnell, this is a big piece. Let’s see how big.”

On the board, where I had written the number 1 for the DO NOW, I drew another 1 on top and a slash in between them, so it looked like 1/1.

“So, class. This pizza represents one whole pizza. We write it as…?”

The collective screamed back: “ONE OVER ONE!”

“Good. Now watch.”

I placed the pizza on the counter and brought the pizza wheel I borrowed from the cafeteria down through the center. The room went silent. Not the fake silent like for a quiz, the real kind, the kind that happens when twelve-year-olds witness something beautiful.

“One slice,” I said, holding up half the pizza. “How much of the whole is each piece?”

Shaniqua raised her hand so fast her desk tilted. “One half!”

“Write it down,” I said, walking to the board. I wrote 1/2 in big red letters and circled it. “One divided by two. The top number, the numerator, tells us how many pieces we’re talking about. The bottom number, the denominator, tells us how many equal pieces the whole was cut into.”

I sliced each half again. Two cuts now. Four pieces.

“Four equal pieces. What fraction is each piece?”

“ONE OVER FOUR!” they shouted in unison like a cult that worshipped math.

I wrote 1/4 and circled it.

Darnell, still staring at the pizza with the intensity of a dog watching a steak, said, “The pieces are gettin’ smaller.”

“Thank you, Darnell. That is a profound observation and exactly the point. As the denominator gets bigger, each piece gets smaller. The pizza doesn’t change. The whole stays the same. We just keep cutting it more and more ways.”

Shaniqua, who I was beginning to suspect had been eating fractions for breakfast her whole life, added: “And the number of pieces doubles every time.”

“Write that down too,” I said. “That is the most important sentence in this lesson.”

I sliced again. Eight cuts. Sixteen pieces.

“Mr. Styles,” came a voice from the back. It was DeShawn, who had spent the entire semester convinced that math was a government conspiracy to keep kids off the basketball court. “If you keep cutting it, you gonna have really tiny pieces.”

“You are absolutely right, DeShawn. At some point they’ll be so small that the pizza doesn’t really exist anymore in any meaningful way. That’s why we stop at a reasonable point.”

He nodded, satisfied.

I sliced again. Thirty-two pieces.

I held up one slice and placed it on a napkin. The napkin was now supporting what could generously be called a crumb. The class stared at it.

“THIRTY-TWO EQUAL PIECES!” I announced, pointing at the board where I had written the progression: 1/1 → 1/2 → 1/4 → 1/8 → 1/16 → 1/32.

I stood back and looked at what I had created. Thirty-two tiny triangles spread across a cardboard box like a sad geometric mosaic. A reasonable person might have questioned the pedagogical value of reducing a Domino’s pizza to something smaller than a playing card, but I was committed.

“Now,” I said, “who can tell me what fraction of the whole pizza this is?”

Every hand went up. Even Darnell, even DeShawn, even that kid in the back who was absent so often I still didn’t know his name. They were all staring at the pizza with the desperate focus of someone who understood, for maybe the first time in his life, that this tiny piece still meant something, that it was one out of thirty-two, and that’s a real number.

Shaniqua, predictably, raised her hand the highest. “One thirty-second! Thirty-two equal pieces. Each one is one thirty-second of the whole.”

I picked up one of the thirty-two slices, held it between my thumb and forefinger, and ate it.

Thirty-one left.

“You see,” I said, chewing, “when you eat one slice, you’re not subtracting a pizza. You’re subtracting one-thirty-second of a pizza.”

DeShawn looked at the pile. “Can we eat the rest?”

Nodding, I gave everybody one teeny slice and as they eagerly wolfed them down I said, “OK. The other four pies are for me.” I let the kids’ disappointed sighs go on for a minute, then added, “‘Just kidding,” and gave each student a full size slice.

That was the last thing I said before the room erupted into the kind of joyful chaos that would have gotten me fired in any classroom management training video ever made. It was loud. It was messy. Darnell got sauce on his shirt. Someone dropped a slice and someone else picked it up off the floor and ate it anyway, which in 1985 in South Central LA was basically a sign of good character.

Shaniqua, being Shaniqua, asked if she could write the fraction on the board. I handed her the marker. She wrote 31/32 next to mine and added a little asterisk. Next to it she wrote: remaining.

I gave her extra credit.

That was the best fractions lesson I ever taught. Not because of the overhead projector. Not because of the Math Specialist’s plastic blue triangles that I never actually got to use. Because of the pizza. Because it was real, and it was messy, and every kid walked out with grease on their fingers and a number in their heads.

The math specialist heard about it and asked me the next day how the lesson went.

“Pretty well,” I told her.

“Did they understand fractions?”

I thought about Darnell, who finally stopped staring at the ceiling. I thought about DeShawn, who now firmly believed that math was not a government conspiracy but rather a pizza distribution problem. I thought about Shaniqua, who I suspect already knew everything I was going to teach for the next three years and was just being polite.

“Yeah,” I said. “I think they did.”

Thanks for reading. Here’s a funny one about teaching

[embed]Ten Shocking Truths About Education From A Sarcastic Retired 35 Year Teacher Most are funny, or sad, or bothmedium.com

Write for your writing family on Medium, It’s All Good

[embed]How To Write For Us All Styles. All Genres. No Rules.medium.com