On Taking Up Space
Unit: Measuring Volume by Displacement
Lesson 1: Everything is either a solid, liquid, or gas.
Mrs. Klein shifts from one sensibly shoed foot to another. She turns and writes “volume” in loopy script on the blackboard under the laminated “Mrs. Klein’s 5th Grade” banner. Plastic cylinders and a rainbow of objects we’ve used for math exercises line a round table. She has planned this lesson carefully, a repeat of last year and the year before.
I am poised with pencil in hand. Brandon, the boy who sits across from me, kicks my shin. I let out a yelp. He smiles wide enough to show me his canines.
Mrs. Klein lofts her rehearsed opening question over Brandon and I: “How would you measure this bear’s height, length, and width to measure it’s volume?” She holds the yellow plastic bear in question between her index finger and thumb, turning it over as if she’s never seen it before.
Brandon turns his attention from me and yells out a guess: “A ruler!”
Mrs. Klein picks up the ruler she set up in reach and attempts to measure the bear
“Look at all the irregular sides! My ruler isn’t getting all the little curves of it’s belly and ears. What else class?”
Rachel, who sits in the back and zips and unzips her glitter pencil bag, guesses: “Ask an adult?”
“Yes, Rachel. Sometimes that is a good solution to a problem. But how would you measure this bear?”
Sadie, who’s light up tennis shoes I covet, guesses: “You could look it up!”
“That might be possible, if we had the right information, but today we will learn how we can measure the volume of any irregular object.”
Rachel always suggests asking an adult. I heard her dad works at city hall. Since we started doing dictionary drills, Sadie always thinks we can find the answer in the dictionaries we keep under our desk. Even Brandon’s reasonable answer is wrong.
This is how Mrs. Klein begins every new unit.
Lesson 2: A solid holds its shape. Liquid takes the shape of its container.
Mrs. Klein begins to distribute a single sheet of misaligned copies. The word “NAME:” is half missing at the top left. I write my name in tiny print so it will fit on the line next to it.
“Today, we will be dropping these cute little bears into cylinders filled with water and logging measurements of the water before and after. The difference will be the exact mass of the object. This way we will be able to measure our bears without using a ruler or measuring tape!”
Brandon kicks me again before he realizes Mrs. Klein is approaching behind him with the materials for our two person table. I turn toward her and silently plead that she will see what’s happening before I have to say anything.
She takes my gaze as appropriate attention to begin her sequence of instructions.
“Ok Table 3. You have a cylinder of water, two bears, and your worksheet. Do not move the cylinder from the paper towel I’ve put it on. Follow along on your worksheet. Brandon, don’t forget to write your name.”
She’s turning to move on. A panic is rising in my throat.
“Mrs. Klein, Brandon kicked me.”
She spins back around to face us. Brandon sulks. This isn’t a new accusation, but it is the first from Table 3.
Last week Mrs. Klein separated our tables of four into tables of two. After we’d settled into our new seats, she lead us in a call and response of the class rules printed on the wall next to the window.
I WILL BE RESPECTFUL. Iwillberespectful.
I WILL ALWAYS DO MY BEST. Iwillalwaysdomybest.
I WILL RAISE MY HAND. Iwillraisemyhand.
I WILL KEEP MY HANDS TO MYSELF. Iwillkeepmyhandstomyself.
Now, at Table 3, she issues a repeat of a dozen times before. It is a half hearted, “Brandon. Keep your hands and feet to yourself.” She moves on to Table 4.
Lesson 3: All objects take up space. The measure of this space is an objects volume.
Brandon and I write down 1.3 on the line next to BEGINNING WATER. He drops the bear in and the water molds around it. Brandon pulls the cylinder toward him, situating the hexagonal base halfway off the paper towel.
We write 1.7 next to WATER WITH 1 BEAR.
Mrs. Klein issues a reminder from the back of the class, her tone as regular and clear as a church bell. “Remember our states of matter we learned? What state of matter is the water? What state of matter is the bear?”
Her reminders correlate to questions at the bottom of the worksheet. I write down my answers in silence.
What state of matter is the water in the cylinder? liquid
What state of matter is the bear? solid
Brandon taps my desk with the end of his pencil. He’s torn off the eraser and bitten the metal to a point.
“What are you writing? You’re skipping.”
I erase my answers. He drops another bear into the cylinder from an inch above the opening. The bear knocks the side of the plastic with a soft thoink before splashing into the water. I watch the water rise dangerously close to the top.
Brandon brings the cylinder off the paper towel to look at it closer.
“It’s at 2.1” he says confidently.
He writes 2.1 next to WATER WITH 2 BEARS. I write the same.
Lesson 4: Measure the volume of a solid object by measuring its ability to displace liquid.
We are back to the section on states of matter. I retrace my previous answers carefully. Brandon kicks me again. I don’t look at Brandon.
“The first one is liquid and the second one is solid.”
Maybe I’m confused. I’m not entirely sure my answers are right enough to be on both our papers. I’m always remembering the sting of the red mark.
Maybe I’m embarrassed. Based on what I know, he either really hates me or like-likes me. Both are equally embarrassing.
Maybe I’m afraid. Not for my safety but of a social scenario, a boy, a confrontation.
Maybe I’m afraid of his solidness.
I hook my feet around the metal chair legs. The downy hair on my ankles bristle against the cool. I read the next section out loud.
“THINK: Why does the water rise when the bears are added?”
Brandon looks at me expectantly. I don’t look at Brandon. I begin to write. The bears are solid and the water is liquid.
Brandon swings his legs moving the air under my desk. I wind my legs tighter around the chair.
“What are you writing?”
I turn my paper toward him and pick up the cylinder to put it back on the paper towel. It leaves a wet ring on the faux wood.
He writes my answer carefully. He spins my paper back to me, catching the corner in the water.
Brandon shoots up his hand and twists to find Mrs. Klein.
“We’re done!! We finished!”
Mrs. Klein stands behind him and moves an uncapped purple pen down his page.
Check. Check. Check. Check.
She flips the page over. Another set of questions run down the page. I flip my page over. The page too thin to read in the soggy spot.
“You have quite a ways to go, Brandon. You know the states of matter, that’s good, now we need to get back to measuring that bear.”
She pivots over my desk and turns my page back over.
“Be careful with the water. You won’t get another worksheet, Allison.”
She marks four purple checks and walks back to her desk.
I untuck my legs and sit side saddle on my chair. Two pink marks bisect my shins.
Brandon leans back in his chair and taps a kid behind him. I can only see the back of his head but from his audience’s stifled laugh I can tell Brandon is making a face.
Brandon turns back to me. He’s folded his eyelids so the pink shows in a small crescent above each pupil. I turn my lips into a smile. I am afraid of Brandon.
I rewind my feet around the chair legs and read the next question silently.
IN YOUR OWN WORDS: What does it mean for liquid to be “displaced”?
Liquid moves because of the solid.