Tonight marks the start of Ramadan! To honor it, I went to my daughter’s first grade class to read the book *The Gift of Ramadan*, written by Rabiah York Lumbard and illustrated by Lauren K. Horton. Because I am forever a teacher, there were lots of deliberate pauses to notice and wonder, or to quickly examine where the Ramadan traditions shown are similar to or different from the holiday traditions for the families of S’s classmates.

In the book, a young girl named Sophia wants to help her grandmother prepare the *iftar* (the meal that breaks the fast) for their family. They had made 5 individual pizzas: one for each member of the family. It seemed like the perfect plan, until…

*When the oven buzzed, Sophia jumped up from her chair. The pizzas were finally done. But when Grandma opened the oven, smoke billowed out.*

“Okay, so there were five pizzas,” I reminded the class. “And the top three pizzas are perfect. The ones on the bottom? Burnt to a crisp. How many pizzas are burnt? Show with your fingers,” I directed the class. I saw a mix of responses: five, three, and two. I quickly modeled with my own fingers.

“So there were five pizzas.” Five fingers up. “And three were perfect.” Three fingers down. “And now…”

“Two!” They called out, just as I realized that I was modeling a part-part-whole situation (“how many of each“) with a take away action. Well. We continued.

In the book, Sophia offers to help her grandmother fix the problem: they need pizza for *everyone*, not just three people. And how do they solve it?

Spoiler: she cuts it up into slices.

“Ohhhhhh!” Two girls in the front row called out in chorus.

“How did she know to do that!” Another girl shouted out.

I assume that this child meant, “how did she figure out that she could cut the pizzas up,” but I chose to capitalize on this moment.

“Hmm! I wonder how Sophia and her grandma decided how many slices to cut it up into. Do you think everyone had a fair share?”

I continued reading the book — since we were through the lens of Ramadan, not a math lens — but, when S and I arrived home shortly after, I pulled the book out.

“I couldn’t stop wondering about this page,” I confessed. “I wonder if everyone got a fair share, and how they decided how many slices to cut each pizza into…”

“That sounds like a math problem,” S said.

She was right.

## How many slices are there?

S furrowed her brow as she began to count.

A long pause, then S said: “I think it’s 13. But it’s hard to tell with all the slices on top of each other. Is that even three pizzas?”

“Hmm, yeah, I don’t know if those slices would go together to make full pizzas.”

“But, anyway, it’s 13.”

“Okay, so how do you think the pizzas were cut up to make these 13 slices?”

“One could be six, and one could be seven,” she suggested.

“Let’s draw it.” I got out a paper and a blue marker, and drew two circles for her. Inside, she wrote 6 and 7.

“I wonder what those cuts might look like…”

“Oh, but actually there’s three pizzas,” S remembered. We seemed to be having parallel conversations, so I tried to respond to what she was saying, rather than direct where I wanted to go.

“So how could we have cut the pizzas then?”

“Do you think that’s enough for the family to split the slices evenly?” I drew three circles.

“It’s 4 + 4 + 5,” S said.

“Oh, I notice that the numbers you chose are next to one another,” I said. 6 + 7, 4 + 4 + 5… it was like she was trying to divide equally, but the primeness of the 13 just wouldn’t let her.

“Yeah, so it’s more even.”

S paused, and then added, “but I guess you could do something else. How about 5 and 6 and… hold on.” Her eyes rolled upwards, as if looking at something playing in her brain. “That’s 11 and 2 more. 5 + 6 + 2.”

## Will it be fair?

“Will everyone get an equal number of slices? Will it be fair?”

S scrunched her nose, before breaking into a wide smile. “Oh! 15 would be equal! Like 15 would be a 5 and a 5 and a 5.”

“Would that be more fair?”

“Yeah, then everyone will get three slices.”

“Let’s try to draw that, to see. what the slices all look like…”

But, again, I was nudging S in a direction she did not want to move towards. Instead, she said, “wait! What if there were really more slices, like 20, but the artist wasn’t paying attention to this fact!”

“What fact?”

“That things should be fair. So they drew 13 but they should have draw 15 or even more. They might not have been thinking from a math perspective.”

I smiled. “Probably not.”

“And what if someone was too full before they could have another slice? Maybe it doesn’t even need to be fair. I bet the little brother doesn’t need the same amount as the papa.”

Solid point.

“Oh, did I just solve it, mama?” S asked eagerly. She must have sensed how amused I was by all of her ideas.

## Extending Ideas

When I read this, through my own mathematical lens, I started to think about the **actual cuts** made to make the slices. What would those **fractional** pieces look like? Five equal-size slices are a challenge: because you can’t cut directly across, partitioning the pizza into halves, you would end up slicing towards a center point. Cutting radii instead of diameters.

Cutting each pizza into 10 slices would work nicely, with every guest’s portion now equally 6 slices, or of a pizza. It’s the same portion, but so much easier to cut. (Just ask Personal Chef Mike Neylan about cutting a pizza into ten slices! So simple!)

This had me thinking about **multiples** and **factors**. The lowest common multiple for 3 and 5 is 15, but, again, even numbers are easier to cut, and thus we look for the lowest common multiple of 3, 5, and 2 (30). Sixty would also work, but cutting each pizza into 20 slices sounds like a beast of a chore.

And what if we don’t need equal size pieces? What if we cut two of the pizzas into 6 slices and one into halves? What portion would everyone need? What is equitable, rather than merely fair?

## Using a Mathematical Lens

It’s great that I have my own mathematical lens, but when engaging with conversations with the kids, it’s important to nudge them within their own framework. S had such interesting things to say about how to share things out, both involving additive decomposition of a number and also some multiplication and division. Just because I’m thinking of factors doesn’t mean she needs to be. Just as there can be multiple reads of a book, there can be multiple audiences.

A few months ago, I wrote about the book * Mathematizing Children’s Literature*, by Allison Hintz and Antony Smith (Stenhouse, 2022). I wrote about three disruptions to my then-thinking about using children’s literature to engage in mathematical inquiry.

- The First Disruption: The Book Doesn’t Need to be Super Mathy
- The Second Disruption: Read with Multiple Lenses
- The Third Disruption: Center Student Ideas

I think the conversation S and I had this afternoon shows how powerful the first and second disruptions can be, and how I’m still working on this extremely critical third disruption. Centering student ideas is very natural to me in the classroom, and also it can be hard to put aside my agenda with literature. I’m excited about the math that I see! And I spend a lot of time in my work nudging students towards more specific learning goals. Sometimes, mathematizing children’s literature does not need to take us down a specific path. It can give us a **window into what students are thinking**, and how they apply these ideas, rather than assessing a specific content area. It can be a generative experience.