# Caterpillar Math

This spring, my children fell madly in love with insects.

Ants.

Bees.

Butterflies.

We read books. We went exploring outside with magnifying glasses. We developed elaborate pretend play rituals based on insect life cycles and behavior. (They usually make me the queen. Obviously.) My two year old casually uses words like colony, pupae, and larvae. We are deep into it.

So I ordered some caterpillars off the internet.

They arrived in a jar: small, slow, and sleepy. Because these caterpillars are meant to be easy to raise, they come with a disclaimer that caterpillars may not look active until 48 hours after unboxing. It felt dystopian to talk about living things in that manner… but, also, I needed that disclaimer, without question.

### How many?

“There are 10 caterpillars,” my 4 year old daughter, S, told me.

Ever the math teacher, I asked; “how do you know?”

“There’s 5 in that jar, and 5 in that jar,” she said, indicating the two separate jars of little larvae.

How many was the obvious math inquiry for a preschooler and a toddler with a brand new caterpillar habitat. What came next surprised me more.

### Which day is it?

I took out blank books to use as science notebooks. The kids and I did some noticing and wondering. The caterpillars were black, brown, and tan. “They’re not green, like monarch caterpillars,” S the Expert announced. They looked fuzzy. They had a lot of legs that were too hard to count. Some were upside down. The food at the bottom looked like a hard syrup, “but still a little gooey.”

I opened up my notebook, and carefully wrote, Day 1.

“But it’s not day 1,” S insisted.

“Why do you say that?”

“Because they aren’t eggs. Caterpillars start as eggs because they become caterpillars and then pupae inside a chrysalis and then finally butterflies.”

Both kids have that life cycle down cold.

“So,” she continued. “You’re wrong. This isn’t day 1. We don’t know what day it is.”

“Is it okay if I write ‘Day 1’ because it’s the first day we are observing the caterpillars?'”

“No,” she replied prosaically.

I mean, she was right. My ‘day 1’ suddenly felt colonial. Who was I to ascribe my own chronology to these beautiful little bugs?

“Their day 1 was when their mother butterfly laid the eggs and then died,” S continued. “This isn’t day 1. The mother is already long dead.” Well, well, well, I didn’t know that this was our benchmark.

While I was busy agonizing over my Day 1 dilemma, S drew these sketches of the caterpillar life cycle. From left to right: happy caterpillars, j-shaped caterpillar ready to pupate and become a chrysalis, the chrysalis, and then the painted lady butterfly.

“Right now all I see in the jars are caterpillars,” I said, trying to push her towards my own definition of a science notebook. “We haven’t seen the other parts of the life cycle yet.”

S frowned. “Mama. You wrote day 1. Your book isn’t even right.”

### How can we keep track?

How long does it take for a butterfly to go through every stage in its life cycle?

Because we conveniently had 10 caterpillars, this seemed like a great time to bust out the ten frame. We have a gorgeous hand-knit ten frame (made by Tina Cardone @tinacardone). I thought we might use it to show how the caterpillars changed, modeling each caterpillar individually, over the course of the 2+ weeks of observation.

But then I remembered that I have a two year old who enjoys throwing things. There was no way that we’d be able to keep up our display for the duration of the project.

We switched over to paper ten frames and dot stickers. This prompted lots of conversation about parts of 10 — if two are now in their chrysalides, and the rest are still in caterpillar form, how many caterpillars do we have? — and also tracking how many days each stage took.

The kids and I determined that we would use a four color key to chart our butterflies’ progression through the life cycle: blue for caterpillars, green for caterpillars on the top of the jar in a J-shape — the primary sign they are about to pupate, orange for chrysalides, and red for butterflies. (We were optimistic they would all make it through.)

“There are 2 caterpillars that are going faster,” S observed.

### What do butterfly wings look like?

I bought a kit for my kids to make butterfly wings. My son N, who is 2, layered felt stickers atop felt stickers, in beautiful chaos.

Big sister S looked on. “That’s cool, baby brother.” (She’s supportive.) “But also butterflies look like…” I watched her stumble for the language. “You know, one dot over here, and one dot over here,” S said while touching opposite points on the wing. “Then then one over here, and one over here,” she said, again indicating some sort of line of symmetry.

S picked up one of our many butterfly books, and pointed to a photo of a monarch butterfly.

“Like it goes here, and then here, and then here, and then here…”

A month later, long after we had released our kaleidoscope of painted lady butterflies, S spent an afternoon noodling around with some pattern blocks. She made the following creation:

“Look, mama! I made a biiiiiig hexagon! It has so much math! Like a butterfly’s wing!”

### Going beyond “how much…”

During these ‘home days,’ several parents of my daughter’s classmates have reached out to me to ask “what math” they should be doing with their 4 year old.

Discuss, measure, and quantify. Examine patterns, including (and especially) patterns of change. Build up a mathematical lens for the world. Nurture creativity. There’s no need to create unnatural story problems right now (“Jaden found 6 chrysalides in the park, and Bo found 7 chrysalides in his backyard. How many chrysalides did they find in all?”). Have fun.

### Up Next: The Ocean

Our study of insects centered on life cycles. Next up, we’re attacking the collection of books I’ve acquired about the ocean, to examine how everything is connected. A lot of the mathematical ideas I’ve stumbled across related to this study seem, well, over the head of a typical four year old, but I’m sure we’ll find something to discuss!