On Monday I tried to thumb a ride to Atkins Corner. I waited fifteen minutes
without seeing anyone even look in my direction. So when Jill Ellis pulled
up, I was relieved.
“
Hop in, Buzz,” she instructed. I was too lame to hop, but I pulled myself
into her SUV.
The drive to Atkins Corner took longer than I remembered. Maybe that was
because she spent the entire time talking about Susie. I really wasn’t
interested in Susie’s French vocabulary, her short attention span, or
her good memory for historical facts. Mrs. Ellis concluded her rambling monologue
with a sigh. “It’s just math that stymies her.” She looked
over at me. “I’m not sure that you can help, Buzz, but since Anita
Carswell recommended you, I’m willing to take a chance.”
I was glad when we finally got to the library, a squat, white building
with small windows. As I got out of the car, Mrs. Ellis said, “Tell
Susie to come straight home when you’ve finished.” I just nodded
and headed into the building.
Eventually Susie walk in. She was giggling, with a cell phone glued to
her ear. Even after she saw me, she didn’t hang up. I cursed her, her
mother, and Anita Carswell under my breath. She pulled out a chair and sat
down. I hoped she had her math textbook.
“
Time to get tutored,” she whispered into the phone with a small giggle. “Gotta
go. Bye.” She deposited her phone in a hot pink backpack. “So,” she
said, straightening up, “what are we supposed to do now?” Her
voice was louder and belligerent, different from how it had been on the phone.
“
Take out your math book,” I said. “I need to see how much you
understand.”
“
Great!” she announced sarcastically, extracting a heavy textbook from
her pack. She dropped the tome on the table in front of me. “There it
is,” she said. “‘Chapter 5, Fractions’. And I don’t
understand anything!”
It turned out that she wasn’t exaggerating. Not much anyway.
“
Do you know what a fraction is?” I asked.
She shrugged. “If you cut something into four pieces they’re quarters.
That’s how you turn a piece of notebook paper into money.”
“
What?”
“
Never mind,” she replied, staring into the space over my left shoulder.
“
Well, you’re right. If you cut something into four equal pieces, each
piece is a quarter.”
“
Equal?” she said, looking perplexed.
“
Yeah,” I replied impatiently. “If they’re not equal, they’re
not quarters.”
“
Whatever,” she mumbled dubiously.
“
No, not whatever. Look!” I took out a piece of paper and drew a circle. “Let’s
say this is a pie,” I began.
“
Let’s not,” she mumbled again, rolling her eyes.
“
Let’s say this is a pie,” I repeated a little louder. The librarian
frowned at me. “If you cut it in half like this,” I continued,
drawing a line through the diameter of the circle, “but then divide
this bottom half into three pieces like this, you don’t have quarters,
do you?” I divided the bottom of the circle into thirds and waited for
her answer.
She was cleaning her nails. When she realized I wasn’t going to say
anymore until she answered, she said, “If you say so.”
I was getting annoyed. “No, not if I say so. Listen, Susie, if you went
to a restaurant and paid for a quarter of a pie, you’d be getting ripped
off if you got a tiny piece like this, wouldn’t you?
She shrugged and mumbled, “I wouldn’t mind. I hate pie. It makes
you fat.”
Obviously I needed to give up on the pie metaphor. “Okay, okay, forget
about pie,” I conceded. “Here! Take this piece of paper.” I
handed her another sheet from my notebook. “Now fold it in half lengthwise
and then in half the other way.”
She grumbled but did as I asked.
“
Okay. Now open it up and tell me what you have.”
She shrugged and said, “Duh! I have a piece of notebook paper with two
folds in it.”
Exasperated, I shook my head. “Are you usually this dense or are you
making a special effort to bug me?” I demanded.
She shrugged again. “You asked. I answered. What did you want me to
say?”
“
Tear the paper along the folds, Susie!” She rolled her eyes but complied. “Now
what do you have?”
“
Four pieces of paper,” she replied.
“
Right!” I said. “And what’s the relationship of those pieces
of paper to each other?”
She laughed and said, “Second cousins?”
I ignored the wisecrack. “Good,” I said.
She looked at me as if I were crazy.
“
Now what’s the relationship of each piece to the entire sheet?”
She sighed. “Smaller. Each piece is smaller than the entire sheet.”
“
How much smaller?” I demanded.
“
A lot.”
We went back and forth like this until I felt like pulling out my hair.
I tried another tack. “If you have four pieces and pick up one of them,
what fraction of the four have you picked up?”
She stared at me, then at the pieces of notebook paper, then at me again. “I
dunno. Three?”
“
No, three are still on the table,” I replied.
“
But if you pick up one, you have three left,” she insisted, looking
confused.
“
You’re not paying attention,” I scolded.
“
I am too! This is just stupid!” she hissed.
It was hard to resist telling her she was stupid, but I bit my tongue.
“
Do you know what a half is, Susie?” I asked.
She glared at me. “Of course I know what a half is. When you cut something
in half, you have two halves.”
“
And can one half be bigger than another?” I asked.
She seemed perplexed for a moment, then replied, “Yes. Half a big thing
is bigger than half a small thing.”
“
That’s true,” I admitted, “but it’s not what I meant.”
Her eyes narrowed. “Well, how am I supposed to answer your stupid questions
if you don’t say what you mean?” she demanded. “You’re
as bad as my teacher.”
I pulled out yet another sheet of paper and tore it into two very unequal
pieces. “Are these halves?” I asked.
She looked hard at them for a long time, then shook her head. “No, I
don’t think so.” She pointed at the larger paper fragment. “That’s
too big and the other is too small.”
I grinned. “Cool!” I said, trying hard to summon up some enthusiasm.
She smiled hesitantly at me. “So when you say equal, do you mean the
same size?”
Before I had a chance to reply, she continued, “Are you trying to get
me to say that two halves of one thing have to be the same size?” she
asked.
I nodded. Then she nodded. “Well, they do. Everyone knows that.”
Yeah, right, I thought, but I smiled at her. “Great! So would you tear
this piece of paper in half?” I said, handing her yet another sheet.
She hesitated.
“
Please?” I added.
She nodded. “Can I fold it first?”
“
Do whatever you have to do,” I replied.
She quickly folded and tore the paper. “There!”
“
Okay, so if you tear these halves in two, what happens?”
“
Can I do it?” she asked.
“
Go ahead.”
“
You get four pieces, all the same size,” she said, but she looked confused.
“
Right,” I said, “so what’s the problem?”
She sighed. “I remember that four pieces the same size are called fourths,” she
said.
“
That’s right,” I said, “and another word for fourths is
quarters.”
“
No,” she said sharply. “A quarter is money.”
“
That’s true, but it’s also another word for a fourth,” I
repeated.
“
How come?” she asked.
“
How come what?”
“
How come another word for a fourth is a quarter?”
I shrugged. “I think it’s from Latin,” I replied.
“
Huh?”
“
A lot of English words come from Latin,” I said, “and ‘quarter’ is
one of them.”
“
Like French ‘quatre’?” she asked.
“
Yeah, that’s right,” I answered. “French has even more words
from Latin than English does. It’s a Romance language.”
She started to laugh uncontrollably. “Sherry Evans reads romances,” she
said between giggles. “I think they’re stupid and gross.”
I nodded. “So do I.”
She stopped laughing. “I have a question,” she announced.
“
Go ahead,” I replied.
I could see that she was trying not to start laughing again. “If a quarter
is called a fourth, how come a half isn’t a twoth?”
I stared at her uncomprehending for a second. “A twoth?” I repeated. “There’s
no such word as ‘twoth’.”
Then the giggle fit began for real. After what felt like an hour, she coughed
and said, “Boy, are you dumb! No such word as ‘tooth’? What
do you think you have in your mouth?”
It was a perfect trap and I’d walked right into it. I grinned at her. “Very
funny!”
She looked pleased with herself. “I know another word that’s related
to ‘quarter’,” she announced. “‘Quart’!
And there’s four of them in a gallon.”
“
Susie,” I said, “for someone who doesn’t understand anything
about fractions, you understand a lot.”
She blushed.
“
So how about thirds?” I ventured, hoping I wasn’t pushing too
hard.
“
How about thirds?” she replied. She thought for a moment. “Three
pieces of something, all the pieces the same size?”
“
Got it on the first try!” I said, more pleased with my teaching ability
than I probably had the right to be. We played around with halves, quarters,
and thirds.
“
You know,” Susie said after a while. “I think that what confused
me was the word ‘equal’. I knew the word, but only in a social
studies way, not a math way.”
I must have looked blank because she explained. “You know, ‘All
men are created equal’? Only they’re not the same size.”
I nodded. “Can we try one more thing?” I asked.
She smiled. “Sure. Suddenly I’m feeling smart.”
“
Okay, if you cut your fourths in half, what do you get?”
“
Eights,” she said promptly.
“
Eighths,” I corrected her pronunciation. “You got that right away
without cutting up any paper. Did you remember it from school?”
She snorted. “No way! I just figured it out. If you cut one and get
two and cut two and get four, then if you cut four, you should get eight.”
I was impressed. If she could see patterns that easily, she probably wasn’t
a hopeless case at all.
“
I have another question,” she said. “How come the numbers get
bigger when the pieces get smaller?”
I nearly swallowed my tongue. This from a kid who was failing math? She’d
just offered the perfect opportunity to talk about mathematical notation for
fractions, so I did.
It was getting late.
“
Okay, Susie, time to pack it in!” I announced. “I’ll see
you on Wednesday.”
Her grin was, broad, genuine, and infectious. She was one happy kid. “This
was a lot better than math class,” she said, picking her backpack up
off the floor. “I don’t feel stupid at all.”
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