Want to teach a simple math lesson to your 6th graders? Nothing is simple with 6th graders, as you'll find out in this excerpt from Finishing School.
I walk to the front of the room and welcome my students to class. “Today,” I tell them, “we are going to work with one of the arithmetic operations and see how it pertains to word problems.”
“Which operation?” Sophie asks.
I notice that Monica is doodling with her gel pens on her spiral notebook and consider asking to put them away, then think better of it.
“My uncle had an operation,” says Tony. “I think it was his girl bladder.”
“Gallbladder!” Monica corrects, and I smile.
“Let’s stay focused on math,” I say. “Before we begin our lesson, let’s do a warm-up.” I gesture to the problem I had written on the board earlier.
“What the heck?” says Nick from the door.
Turning to face him, I say, “You’re late,” mostly because I can’t say what I really want to.
“Yeah,” he agrees. “My sister wouldn’t get moving this morning.”
“Well, take care of locker business and get to your math class,” I say briskly.
“I like your math class better,” he says. “Can’t I stay and finish my breakfast?” He holds up a McDonald’s bag and cup for my inspection.
“Can I have some?” Monica asks.
“No,” I say firmly to Nick. “Go to class. You can ask about your breakfast in there. Now go.” Nick sets his breakfast on his desk and then goes out to his locker. I can hear it open and close and then he comes back in, depositing some books alongside the bag on his desk and picking up his math book and spiral and a pencil.
“Come on, can’t I stay?” he asks me again. I shake my head and he turns to leave. The McDonald’s bag is still where he left it on his desk. I’m guessing the thought of testing Mr. Harper this morning was too much, even for Nick.
Monica says, “I guess he wasn’t too hungry.” The smell from the bag permeates the room and I am tempted to dump it into the trash can across the hall in the break room. Instead, I walk to the back of the classroom, pick it up and place it just outside my door. Then I close the door and walk back to the front of the classroom.
From his perch at my reading table, Morris is scribbling away on his clipboard.
“So,” I say brightly to my students, “back to our warm-up problem. How do we go about solving it?”
“We can’t,” Sophie says. “It’s missing part of the problem.”
“Yes….” I say. “But what do you see that could help you with that?”
“Nothing?” Darin suggests, and Kiernan snorts from his seat by the window.
“What do you think, Kiernan,” I say to him, smiling. “Do you agree that there’s nothing that can help us solve the problem?”
He shakes his head. “Part of the answer is given.”
I nod. “Yes, it is. So what does that mean?”
Aaron raises his hand. “Yes, Aaron,” I say to him.
“You can work backwards,” he says quietly, a sly smile on his face. I meet his smile with one of my own.
“You can, indeed,” I tell him. “Any suggestions?”
“This is dumb,” says Tony. “Why would we ever do this?”
“We wouldn’t,” Kiernan says, putting his gaze on something he is holding in front of him, hidden from my view by his desk. I have a feeling it’s his tablet, and if so, it’s in plain view of Gary Morris. I am torn between making an issue of it and pretending I don’t notice. I decide on the latter for the sake of moving things along.
“Why do you say that, Tony?” I ask him. “Don’t you like using your brain?”
He shakes his head.
“You play football, don’t you?” I ask, remembering something I heard him say to Ken earlier this week. He nods, interest now settling on his features. “Well, then,” I continue, “You do like using your brain. You have to do it a lot for football, don’t you.” He nods again. “I mean,” I say to him, “you have lots of plays to memorize. And if something happens during the game that you don’t expect, you have to think of something to do…quick!” Tony is now nodding and grinning. “So, how do you think you are able to do that?”
“That’s different,” Tony says. “Football isn’t a math problem with numbers missing.”
“But it is math,” I tell him, “along with other brain functions that you probably don’t even think about. And the exercises you do for your brain by solving problems like this,” I point to the problem on the board, “lend themselves to many other areas of your life.”
I speak to the entire class now. “Back to the problem on the board. When you see something that looks impossible,” I look across the room, meeting the faces of several students, “or even just very hard,” some of the students giggle a little, “start by deciphering what you do know as you look at the problem.” I return my attention to Aaron, pointing to the ones place in the problem. “For instance, Aaron,” I say, “we do know the answer to ‘seven minus what equals one’, don’t we?”
Aarons grins at me and nods. “It’s six,” he says. I write a red six in the blank space in the ones column.
“What next?” I address the whole class.
“Nothing minus nine equals two,” Sophie says matter-of-factly.
“Really?” I ask. “Something must work. Otherwise, why would this problem be in the book?” I grin at my students. “Did the editors of the book make a mistake?”
“Yes,” says Tony. Sophie is frowning at the problem. Mandy
quietly raises her hand.
“Yes, Mandy,” I call on her.
“Put a one above the nine,” she says softly. “And borrow from the four.”
“A one!” Sophie exclaims. “Borrow!”
I write in the one that was suggested by Mandy and put a slash mark over the four to show changing it to a three, concepts that all of these students have done since third grade.
“Now what do you think?” I say generally to the entire room.
“Three minus three equals zero,” crows Aaron. “And you’re done.”
“But the answer’s not a three-digit number,” complains Sophie. I finish writing in the last missing digit and turn to her.
“Do you get it now?” I ask. She studies the problem for a moment, and then recognition dawns in her face.
“Oh!” she says, “now I do.”
“I still don’t see why we have to do this kind of stuff,” says Tony.
“Because it’s good for you,” I tell him, “and fun.” I smile at my class. “Now, what do you say we turn our attention to the problem of what to do when we need to divide a quantity into equal groups?”