Every week my daughter divides the artwork she brings home from elementary school between what she will take to her father’s house and what will stay with me. After unloading her backpack into a big pile on the couch, she sorts through and makes her decisions. It is because of me that she lives in two houses, not one, meaning it is because of me that she must choose.

Recently she brought home a picture of a fish that was divided into parts, each including a math equation she had to solve. The solutions corresponded to a color key: five for green, eight for yellow, and so on. The result was a beautiful fish made from her math.

I longed for that fish. I wanted to display it on our refrigerator, send photos of it to my parents and after a time put it in the box where I keep all the other precious things she has given me. But she set aside the fish to give to her father.

I hate this weekly division of property, a feeling I try to hide from her, but I’m sure she notices.

“Is that OK?” she’ll ask when she indicates what she plans to give to him.

I always say yes. It never is. No matter how many times it feels like she is choosing him over me, it doesn’t hurt any less.

There are parts of divorce you can’t predict, don’t know to anticipate. It’s not something you can fully comprehend unless you’ve experienced it yourself — much like motherhood.

If I had known how divorce was truly going to be, would I have tried harder to stick it out? Obviously, I thought about how hard it might be on my daughter, how hard it might be living on my own after five years of marriage and 10 years together. I even thought about how I would never again have the delicious Thanksgiving stuffing my ex makes with the golden raisins.

What I didn’t realize is how often I would be texting him on my nights with her, asking if he could talk on the phone because she wanted to. I didn’t understand how strong their bond was — he had stayed at home with her during her early years — and how outside of that I could feel. I didn’t know how difficult it would be to miss my daughter’s first haircut when he ended up taking her.

There was just no way to conjure, ahead of time, all the firsts I would miss out on, the pain of being not chosen, the ways my life would feel too empty when she was gone and too full when she was here, an ebb and flow I still struggle to navigate.

The other morning, on a snowy day, my daughter and I squished onto our sofa to read a book about polar bears, her longtime favorite animal. She has slept with a stuffed white polar bear since birth, which I named “Mama Bear.” Mostly she just calls this bear “Puffer,” which I try not to take personally.

The captain on her favorite TV show, “Octonauts,” is also a polar bear. His name is Barnacles. She calls him Barney. He is kind, confident and brave. It’s a good show. She makes up her own adventures involving the Octonauts. In many of her imaginings, she and Barney are married.

Monomaniacal in that way children can be, she knows all about polar bears, and now, I guess, so do I. Over time, I have checked out every book from the library with a polar bear on the cover. Polar bears, I can tell you, live on land but spend a lot of time hunting in water. Their favorite food is seal, though they will eat just about anything if necessary, including fish, berries and nuts. Their breath stinks. Their skin is actually black. They have long necks for poking into holes. Their feet are large to help distribute their heavy load on thin ice. They usually have two cubs at a time. They like to be clean — “Fussy,” my daughter says, “like you.”

I laugh because she’s right, I am fussy, but I also take it as a rebuke.

She knows that the polar bears’ existence is precarious, that their home is being destroyed.

In the book we have checked out most recently, “The Ice Bear,” a polar bear cub is separated from his mother, transformed into a boy, and raised for many years by human parents. The mother bear cries over the loss of her cub and the tears etch scars onto her face. I almost can’t read this part aloud.

One day, when he is 7, the same age as my daughter, the boy gets lost in the snow and is reunited with his bear family. His human father tracks him down. The boy then must choose: “He felt that his heart was torn.”

He loves both his father and mother, so eventually he decides to spend half the year as a human and half as a bear. The soft peach glow of the sunset, the flowing fluorescence of the Northern Lights, only make the pain of his choice, of his parents’ loss, even sharper.

When I finished reading, I put the book down and said to my daughter, “I would be so sad if you spent half the year away from me. I would cry just like the mama bear.”

And then a horrible realization washed over me: My daughter does spend half the year away from me. Our divorce agreement gives me 50 percent time with her. It may not feel like six months because she goes back and forth every few days. But in the end, it’s the same. For half of the year, I am separated from my little cub.

There are problems in adulthood that are harder to solve than those of a first-grade fish. How to divide up a marriage — not just the stuff, but the entangled life that was woven together for a decade? Am I considered a single parent now? What’s the correct terminology? I wonder, along with divorced friends: Would staying under the same roof, drowning but united, have been better for our children?

The three of us — me, my daughter and my ex — don’t do much together these days. Three is a tough number, even among people who like each other. There’s always one who is left out. I used to go to a therapist who encouraged me to consider the advantages of being on the outside. It was a good prompt. In better moments, I brainstormed. But most of the time I just thought, self-pityingly: I’m the one who doesn’t get the fish art.

My ex and I try hard to get along, sending each other photos and funny stories from the days when we have our daughter. We can still laugh together. But so much of the work of parenthood I must do while alone: arrange for schools, dance classes, doctor appointments. I devour every parenting book I can get my hands on, just as I devoured books on marriage and then books on divorce. I give her an allowance to teach her about money, set up play dates, take her to birthday parties, helped her learn how to ride a bike. I talk with her about where babies come from, about death.

When she is with my ex, he of course does all these things with her, and more. And we work together on many of them. But none of that mends the divide in our family, for her or any of us.

I was 32 before I found the strength and sense of self to separate from her father and take on a view of life that was exclusively my own. Leaving my marriage felt like emerging from a fog, or like taking a long, deep breath on the surface of the ocean, after being in the murky depths for far too long.

My whole life, I have loved swimming, loved being near water — seas, rivers, trickles of streams. My daughter still doesn’t know how to swim, which bothers me. I encourage her to be brave like Barney, a strategy recommended in one of those parenting books, but that doesn’t seem to help.

Books can’t prepare you.

They don’t tell you what to do or how to feel, for example, when it’s time for the small warm body pressed against you on the sofa, toes ice cold, to get up, take her beautiful art, and go.

Emily O. Gravett teaches religion and works in a professional development center at James Madison University in Harrisonburg, Va.

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