Solving for M

by Jennifer Swender

  This is a work of fiction. Names, characters, places, and incidents either are the product of the author’s imagination or are used fictitiously. Any resemblance to actual persons, living or dead, events, or locales is entirely coincidental.

  Text copyright © 2019 by Jennifer Swender

  Cover art copyright © 2019 by Jim Tierney

  Interior illustrations copyright © 2019 by Jennifer Naalchigar

  All rights reserved. Published in the United States by Crown Books for Young Readers, an imprint of Random House Children’s Books, a division of Penguin Random House LLC, New York.

  Crown and the colophon are registered trademarks of Penguin Random House LLC.

  Visit us on the Web! rhcbooks.com

  Educators and librarians, for a variety of teaching tools, visit us at RHTeachersLibrarians.com

  Library of Congress Cataloging-in-Publication Data is available upon request.

  ISBN 9781101932902 (trade) — ISBN 9781101932919 (lib. bdg.) — ebook ISBN 9781101932926

  Random House Children’s Books supports the First Amendment and celebrates the right to read.

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  Contents

  Cover

  Title Page

  Copyright

  Dedication

  Unit 1: Estimation

  Unit 2: Time

  Unit 3: Measurement

  Unit 4: Place Value

  Unit 5: Real and Rational Numbers

  Unit 6: Equations and Inequalities

  Unit 7: Fractions

  Unit 8: Sets and Subsets

  Unit 9: Advanced Computation and Order of Operations

  Unit 10: Surfaces and Solids

  Unit 11: Real-World Problems

  Unit 12: Representing and Interpreting Data

  Unit 13: Probability

  Acknowledgments

  Author’s Note

  About the Author

  About the Illustrator

  For Becca

  Fifth grade at the middle school should make perfect sense.

  Elementary school is first grade, second grade, third, and fourth. (Okay, I know I’m leaving out kindergarten, but stick with me for a second.) Then middle school is fifth, sixth, seventh, and eighth. High school—ninth, tenth, eleventh, and twelfth.

  Twelve grades divided by three schools gives you four grades per school, with middle school smack dab in the…well, middle. Everything nice and logical.

  But now, on the first day, I’m not so sure.

  First of all, we have to keep a journal…in math?

  Dan P. raises his hand. “Aren’t journals supposed to be for language arts?” he asks with a smirk. “Or Gothy kids who want to be poets?”

  I know Dan well. He was in my class last year.

  Mr. Vann, the math teacher, doesn’t say anything as he writes on the board: Bring in spiral notebook for your math journal. This step is mandatory. Then he turns back around to the class with a dramatic flourish.

  Mr. Vann reminds me of some kind of wacky magician. A cape and top hat would not seem entirely out of the question. He wears these thick glasses that make his eyes look very big and very far away at the same time. And he’s left-handed, which means he can write on the board with his left hand as he erases the board with his right. The letters look like they’re running to fill up the newly emptied space.

  I’m not exactly sure why we need a math journal, but it’s not the kind of question I’m going to raise my hand and ask on the first day of middle school. I’ll leave that to Dan.

  “Why do we need a math journal?” Dan calls out.

  “Keeping a math journal will help us transparently tackle innovative problems,” Mr. Vann begins. “Keeping a math journal will let us embark on reflective discussions of relevant math issues.” He underlines math journal on the board every time he says it. “Keeping a math journal will allow us to explore, justify, argue, wonder….”

  Well, okay then. I guess that’s why you need a math journal. Mr. Vann seems very excited by the whole idea. I bet when Mr. Vann was in fifth grade he kept a math journal without even being asked to. Maybe he invented the math journal.

  It’s not that I have anything against math. I’m just not much of a math person. It doesn’t seem like something to get that excited about. Numbers are numbers, right?

  My mom says she likes numbers because you always know what you’re going to get with them. She’s an accountant, so I guess she should know.

  And it’s not that I have anything against journals, either. I have like twenty blank books at home. Some are full; some are empty. Some have pages torn out; some have pages stuffed in. But those are for art, not for math.

  “Keeping a math journal will allow us to dare to color outside the lines,” Mr. Vann adds. Then he spins back around to write something else on the board: Bring in colored pencils and/or markers for your math journal. This step is optional.

  I guess he wasn’t kidding about the coloring part. And I can get excited about anything that involves colored pencils and/or markers—drawing, doodling, sketching. I can do horses really well, and I’m pretty good at people, too. I have a book that shows how to draw things in a certain number of steps. You just follow the directions and everything turns out the way it’s supposed to.

  “What do we need colored pencils for?” Dan asks.

  “Patience, please, my dear Watson,” Mr. Vann says. Then he opens the top drawer of his desk and takes out a box of matches. I’m half expecting him to light a pipe. But instead, he reaches into the drawer again and takes out what looks like a white tea candle.

  Is he allowed to have candles and matches in school? I’m pretty sure that’s got to be against the middle school rules.

  Mr. Vann dramatically strikes the match on the box and lights the candle. “Remember, dear thinkers,” he says. “Math may be exact.”

  Then he blows out the candle, pops it into his mouth, and eats it.

  “But life is mostly estimation.”

  * * *

  —

  Before anyone can say anything, the bell rings (although the middle school bell sounds more like a horn), and Mr. Vann dismisses us to the auditorium. There’s a welcome assembly for the fifth grade.

  Am I the only one thinking that first thing this morning might have been a better time for a welcome assembly? Anyway, we all file in and find our seats.

  Principal Mir walks to the microphone. You can hear her shoes going click, click, click across the shiny floor.

  Principal Mir is a small woman, but she has the look of someone you do not want to mess with. She’s wearing a matching plaid skirt and jacket and very sensible shoes.

  “Welcome to Highbridge Middle School,” she begins. “Pride of the Upper Hudson Valley. We hope you had no trouble finding your pods this morning.”

  I should explain that a pod is a team of teachers, all in the same hallway. My mom says they put the fifth graders into pods to make the middle school feel smaller and less overwhelming.

  I suddenly get this funny picture in my mind of all of us fifth graders as space aliens who have just arrived on this strange new planet called Highbridge Middle. Luckily, we have our home pods to make us feel safe and cozy.

  Across the auditorium, I see Ella, my best friend from fourth grade. I wave to her, but she’s whispering to the girl sitting next to her and doesn’t see me.

  I’m in Pod Two. Ella is in Pod One. I guess we can still probably eat lunch together, but
besides that, we’re on totally opposite ends of the building for the whole day. So even though the pods are supposed to make you feel safe and cozy, they mostly make you feel like your friends are far away.

  Principal Mir goes on and on about middle school rules, and how the rules are there to keep us healthy and safe. I wonder if she has any idea about the fire hazard that just took place in Grade Five Pod Two Math Block C.

  Then she explains about A-days and B-days, and twice-a-month early-dismissal days, and once-a-quarter late-start days. “Fifth graders have physical education every other day,” she tells us. “Remember proper footwear, please. That is, unless you are a member of the chorus or the jazz band, of course. Then you will always have physical education on Tuesdays and Thursdays, unless there’s an impending concert or unusually inclement weather.”

  Should somebody be writing this down?

  “Upon dismissal from assembly,” Principal Mir continues, “please return to your Home Pod Block C, which is the class you would normally have directly following lunch, for immediate dismissal to the buses.”

  I’m starting to think that fifth grade at the middle school might not make very much sense at all.

  * * *

  —

  “I still don’t know about having fifth graders at the middle school,” Mom says as she takes my backpack from me. I can’t believe she walked out to the corner to wait for my bus. She’s the only parent here.

  “Everybody else’s parents let them walk home alone,” I whisper.

  “Good thing I’m not everybody else’s parent,” she says, ruffling my hair. “That would be exhausting.” It’s one of my mom’s favorite comebacks. “So?” she asks in her trying-not-to-be-nosy way. “How was it?”

  “It was fine,” I say. “A little weird. I mean, it wasn’t a normal day. They changed the schedule all around. We had a welcome assembly last thing in the afternoon. And we have to keep a journal in math. And Ella’s in Pod One.”

  “I’m sure you’ll make some new friends,” Mom says with extra corny sauce added for good measure. I give that comment an exaggerated eye roll.

  “And of course, Dan P. is in all of my classes,” I tell her. Mom gives her own eye roll back.

  “Nothing a little time won’t help,” she says, sounding like a very reasonable television psychologist. “I’m sure it will sort itself out.”

  I guess she’s right. Maybe it’s something you have to get used to—all these different people in different combinations at different times. In elementary school, it was always the same kids, same teacher, all day, every day. And at home, it’s just Mom and me—same combination, all the time.

  “Just the girls,” Mom likes to say. Or “Just the two of us.” Then she starts singing that sappy song: Just the two of us. We can make it if we try! We can’t even have a dog or cat because my mom is allergic. I had a goldfish once, but it didn’t last very long.

  My dad has always not been around, so it’s never seemed like that big a deal. My parents got divorced before I was even one. “That decision was set in motion long before you were on the scene” is my mom’s go-to line on that topic.

  My dad lives in Florida with his new wife, Katie, and their dogs. I go there for two weeks in the summer, and he comes to New York for work meetings and stuff a couple of times a year.

  Sometimes I think Mom and I were like his rough-draft family—the same way we have to write rough drafts in language arts. Then he went through the revision process and moved someplace warmer.

  Math Journal Entry #1

  Karina is 11. Her mother is 38. Karina says that her mother is approximately 40 years older than she is. Is her statement reasonable?

  Explain your thinking using words, numbers, and/or pictures.

  “Who would like to share their answer to the first math journal challenge?” Mr. Vann asks on approximately the sixth day of school. A couple of kids raise their hands.

  I’m starting to learn the names of the kids in this class and every other class. And it’s a lot of kids. Our school district has four elementary schools, each with three fourth-grade classes. Then we all get mixed up for fifth grade. Maybe Mr. Vann should make a math journal “challenge” out of that.

  A girl named Chelsea raises her hand so high it looks like she’s going to pop her shoulder right out of the socket. Chelsea’s in my art class and my gym class. She raises her hand a lot, even in gym, and she keeps all of her notebooks organized in the biggest three-ring binder I have ever seen.

  Chelsea reads from her math journal very slowly. “Karina’s mother is twenty-seven years older than she is.” Then she looks up. “It’s pretty easy subtraction. You don’t even have to borrow.”

  “Regroup!” Mr. Vann shouts, snapping his fingers on both hands. “Neither a borrower nor a lender be, please. Elementary school, Chelsea?” he asks with raised eyebrows.

  I can see that Chelsea is confused. I can also see that she’s not used to not getting the right answer.

  “Pardon?” she says.

  “No, don’t tell me.” Mr. Vann paces in front of the board, with a dry-erase marker stuck in the corner of his mouth. “Mrs. Henneberry at Montgomery Hills,” he announces, holding the marker high above his head.

  “She was my teacher last year!” Chelsea says, all bright again.

  “Yes, she was,” says Mr. Vann. “And you have given us the correct answer, dear Chelsea.”

  Chelsea takes a deep breath to settle down her popped-out shoulder. Now she’s really smiling.

  “The correct answer,” Mr. Vann continues, “to the wrong question. Who would care to elaborate?”

  Dan P. raises his hand.

  “The correct answer is that Karina is totally unreasonable,” Dan says with a smirk. “I think she might be a little crazy.” He circles his pointer finger in the air by his ear.

  Everybody giggles. I can tell that Dan is waiting to see what Mr. Vann will do.

  “I asked for elaboration, not psychological evaluation, Mr. Pimental. When you receive your doctorate in psychology, we will revisit the question of our dear Karina’s mental health.” Mr. Vann gets the bigger laugh.

  “Why do we even need to know?” someone mutters from the back of the room.

  Mr. Vann’s shoulders slump. “Dear thinkers,” he says like he’s suddenly very disappointed in all of us. “It is always better to know. Now, who would care to share?”

  A kid named Miles raises his hand and explains how eleven rounds down to ten, and thirty-eight rounds up to forty, and how you subtract one from the other, and that Karina’s statement is, in fact, not reasonable.

  Mr. Vann listens and nods as he walks through the rows of desks. I’m pretty sure he’s walking around the room with his eyes closed. I don’t understand how he’s not bumping into things. Then he stops behind Miles’s shoulder just as Miles finishes talking.

  “And yet, Miles,” Mr. Vann responds, “in your math journal, I see only the number forty, a sign indicating subtraction, the number ten, a sign indicating equality, the number thirty, and the word No.

  “People!” Mr. Vann practically shouts as he runs to the front of the room. “I am giving you an opportunity—the invaluable opportunity to explain your thinking.” He knocks on the board under the words Explain your thinking.

  “You will find that it is an opportunity not that often granted. Seize it.” He clenches his hands into fists and gets very quiet. “As did our dear Mika.”

  I look up, surprised by the sound of my name. I’m also surprised that Mr. Vann pronounced it correctly. (The first syllable sounds like “me,” but sometimes people say it like “my.”)

  It’s not like I solved the problem in some super-interesting way. Maybe Mr. Vann liked that I mentioned his candle trick. Or maybe he liked that I explained my thinking using words, numbers, and pictures. I used my How to Draw
People book to get the mother and the daughter just right.

  Truth is, I haven’t had a chance to do much drawing in any of my other classes lately, not even art. Mrs. Poole, the middle school art teacher, has explained several times that the fifth-grade curriculum does not include drawing. Whenever she says the word drawing, she makes those fake quotation marks in the air with her fingers. Instead, the fifth-grade curriculum focuses on found materials. We’re currently making collages out of things we find outside.

  But wait a second. How did Mr. Vann see my math journal entry, anyway? All I can think is that he saw it when he was walking around the room with his eyes closed.

  “So, why do we estimate?” Mr. Vann asks next.

  Chelsea pops her shoulder up again and starts talking before she’s even called on. “Key words for estimation are about, approximately, and to the nearest.” She smiles.

  “I cannot argue with you,” Mr. Vann begins. “And yet I wish you would refrain from answering the question you think I am asking in favor of the question that I am asking.” He doesn’t say it meanly, more like a polite request. I can’t help laughing a little, but Chelsea doesn’t seem to get it.

  Then Mr. Vann starts erasing the math journal question with his right hand as he writes with his left hand: We estimate when…

  “You are going to work in groups to complete this statement,” he announces. I end up with Miles, Chelsea, and a girl named Dee Dee. I stay quiet as they talk about what our group should say.

  Math Journal Entry #2

  Last year, Maxwell Elementary had 68 fourth graders, Garcia Elementary had 77 fourth graders, Montgomery Hills had 71 fourth graders, and Bishop Street School had 77 fourth graders. Assuming that no students moved in or moved away, approximately how many students are in this year’s fifth-grade class?