Today — an objectively beautiful day in Boston — we took a walk along the river behind our house. It is late November; the trees have mostly shed their leaves, which only makes the brilliant blue of the sky on a day like this all the more stunning.
My 5-year-old son, N, enjoyed racing along the path, experimenting with the moves he learned in karate class. (Front kick! Side kick!) At some point, we wandered off the gravel, towards the local middle school’s playing field.
N ran back and forth, the crunch of the dry leaves echoing.
“Mama! Papa! Watch me!”
More jumps. More side kicks.
“There are so many leaves!” He mused.
After years of teaching elementary mathematics, my brain perks up at the mere hint of quantity. I’m like a bloodhound.
“How many leaves do you think there are?” I posed to N.
“Maybe… 59 hundred?” N suggested with a shrug.
“Ooooh, I like that guess,” I told him. Then I paused: “If I told you there were ten leaves, would you believe me?”
He gave me the most skeptical look he could muster, eyebrows slanted down and mouth slanted up. Sometimes, he looks just like his father. “No!”
“There’s ten leaves right here. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10!” He gestured at the leaves broadly, without specifying which ten. “There’s more than ten.”
“If I told you there were 100 leaves… would you believe me?”
N squinted and pursed his lips, considering the idea. “I don’t think so. 100 is a lot but this is a lotter.”
“Oh, sometimes we count to 100, don’t we,” I countered. There’s a book that N loves — Stop and Smell the Cookies, by Gibson Frazier — that suggests counting to 100 as strategy for regulation. In the book, the main character counts by tens. So calming.
“Yeah, 10, 20, 30, 40, 50, 60, 70, 80, 90… oooOone HUNdredDDDDD!” N announced with fanfare. Oprah could take notes.
“Okay, so you’re thinking more than 100,” I said. “If I told you that there were 1000 leaves, would you believe me?”
N squinted again. “Maybe. Or maybe 72 thousand or 100 thousand.”
“If I told you there were 1 million leaves, would you believe me?”
“A million sounds really big!” N chuckled. He has no benchmark for determining this quantity. He was already starting to run off further away, the crunch of each leaf punctuating his words. “Maybe it’s 72 thousand millionnnnn!”
If I told you… would you believe me?
In this conversation, I did not expect 5-year-old N to differentiate between what a thousand a million look like. He’s in preschool, still working on nailing every teen number when he counts.
But I like these conversations for a few reasons. Using the “would you believe me” structure allows us to play around with different quantities. We use it for countable quantities, like the number of eggs in the carton of 18, as well as the seemingly endless trails of autumn leaves. What makes sense: is ten enough? Is twenty too much?
When it’s a smaller quantity — the number of legos in a small bag — we might count them. With leaves, we let the ideas hang in the cool November air.
It is also building up some healthy skepticism and critical thinking. Should my son believe everything I, or another adult, says? (I mean, like every parent, there are times when I’m Not In the Mood to be questioned, and that this is a subtle point for a preschooler, but I do want him to grow up to be someone that respects others, values community, and also thinks critically.
In the Classroom
I use this structure at school sometimes, too. For example, students sometimes get stuck when asked to estimate, or when asked to determine whether an answer is reasonable. It’s an on the spot version of tasks that offer a fictional student’s thinking and ask the students to critique the reasoning.
45 x 82
Would you believe me if I said the answer was close to 3600?
Would you believe me if I said that (16, 16) was a point on this line?
It’s not really anything new.
…but it’s playful. It’s fun to say that you wouldn’t believe someone in a position of authority, or realize that — oh, no! — they flipped the script and actually would would believe them. That’s completely reasonable.
…or maybe it’s just a fun way to mathematize the world with a child out on a walk, on a gorgeous day in the late fall.