by David Cole
Like I said, Joe loves to brag about how smart he is.
“Well, I guess we’ll just have to wait and see,” I said without much confidence in my voice.
Joe laughed and walked away.
Justin and I walked home slowly. We were smart enough to outwit the bullies, but could we beat Joe in a math competition? I had my doubts.
CHAPTER 8
While Justin and I were making our escape from the bullies, Catherine and Stephanie were walking home together.
“What got you interested in math?” Stephanie asked. “Your dad?”
“Well, he definitely talks about math a lot—like, all the time,” Catherine said, “but it was art that really got me into math.”
“Art? What does art have to do with math?”
“Everything,” Catherine answered. “C’mon, follow me.”
Catherine led Stephanie down a side street to a small park. Some younger kids were playing on the playground and their laughter echoed off the trees. Catherine gestured toward a bed of flowers lining the path.
“What am I looking for?” Stephanie asked.
“The math,” Catherine said cryptically.
Stephanie looked at the flowers in the bed. They were beautiful, a mixture of a bunch of different types of flowers and colors, but she didn’t see anything that looked at all like math.
“These are lilies,” Catherine said, pointing to a small patch of delicate white flowers. “Count the petals.”
“Three,” Stephanie said.
“And these are buttercups.” Catherine pointed to a clump of beautiful yellow flowers.
“Five petals,” said Stephanie.
Another point, this time to a bunch of bright orange flowers. Stephanie had to bend over to count the petals, breathing in the wonderful scent as she did.
“Thirteen, I think.”
“That’s right. Marigolds have thirteen petals. Okay, last one,” Catherine said, pointing to a white flower with a beautiful orange center. “The daisy.”
Stephanie counted the petals on one, then a second. Both came out to the same number.
“Thirty-four!” she said.
“That’s right.” Catherine smiled. “See, there’s math all around us.”
“Wait, I don’t get it,” Stephanie said in confusion. “The flowers are beautiful, but where’s the math?”
Catherine sat on a bench and opened her backpack. She removed a notebook and a sharpened pencil.
“Have you ever heard of the Fibonacci sequence?” she asked as Stephanie joined her on the bench.
“No.”
“Then you’re in for a treat!” Catherine said with excitement. “The first two numbers in the sequence are one and one. You get the next number in the sequence by adding the last two numbers. To get the third number, you add one and one to get two. To get the fourth number, you add one and two to get three. The sequence keeps going like that. Here’s what the first few numbers of the sequence look like.”
Catherine wrote the numbers in her notebook:
1, 1, 2, 3, 5, 8, 13, 21, 34,…
“Recognize any of these numbers?” she asked.
At first, Stephanie didn’t get it, then a gleam came to her eye as she saw what Catherine what trying to show her.
“The petals! The numbers of petals on the flowers are all Fibonacci numbers!”
Catherine smiled and nodded. She reached into her backpack and pulled out a sheet of graph paper.
“And that’s not all. If I make squares for each of the numbers—one by one, two by two, three by three, and so on—I’ll end up with something like this,” she said.
“That’s really cool that all of the squares fit together like that,” Stephanie said.
“Oh, that’s not all they do,” Catherine said as she pulled a red marker out of her backpack. “Look what happens when I connect the squares together.”
“Do you recognize that shape?” Catherine asked.
“It looks familiar, but—”
“Think about the shape of a ram’s horn, or a seashell, or a hurricane.”
Stephanie’s eyes grew wide. “You’re right!” she exclaimed. “It does look like a seashell. But I’m still not sure where the art part fits in.”
“I was just getting to that,” Catherine said as she pulled another piece of paper out of her backpack. “Here’s the Fibonacci sequence again.”
She wrote the numbers across the top of the paper:
1, 1, 2, 3, 5, 8, 13, 21, 34,…
“Now look what happens when we start dividing the numbers in the sequence.” She did the calculations using her phone:
1 ÷ 1 = 1
2 ÷ 1 = 2
3 ÷ 2 = 1.5
5 ÷ 3 = 1.667
8 ÷ 5 = 1.6
13 ÷ 8 = 1.625
21 ÷ 13 = 1.615
34 ÷ 21 = 1.619
“As you keep going, the numbers get closer and closer to 1.618,” Catherine said.
“So, what’s that have to do with art?” Stephanie asked.
“That number is called the golden ratio,” Catherine explained. “It’s used in geometry, architecture, and yes, even art. For example, if you look at the famous picture of the Mona Lisa, you’ll find that the length of her head is 1.618 times the width of her head. You’ll also find the golden ratio in many famous buildings, like the Parthenon in Greece.”
“That’s so cool,” said Stephanie.
“You want to hear something really cool? There are always more female bees than male bees in a hive. When you divide the number of females by the number of male bees, guess what number you get.”
“The golden ratio?” Stephanie guessed.
Catherine’s broad smile was enough to tell Stephanie she had guessed right.
“C’mon, we’d better get going,” Catherine said. “My dad will be wondering where I am.”
Stephanie walked with Catherine all the way to her house, even though it was a little bit out of her way. Jordan and Justin were nice enough, she thought, but she was glad Catherine was now a member of the Math Kids.
As Stephanie turned to walk home, Catherine came running back out of her house.
“Hey, wait up!” she called to Stephanie.
Stephanie stopped and saw that Catherine had a tattered book in her hand.
“I thought you might enjoy this book,” she said. “It’s where I learned all about the Fibonacci sequence.”
She handed the book to Stephanie with a shy smile, then turned and ran back up the porch steps to her house.
CHAPTER 9
On Monday, we discovered that Catherine was going to be a big boost to our math team. She certainly knew a lot of math, including some things the rest of us didn’t know. For example, on one of the problems we were working on, we needed to multiply 65 times 65. Justin went to the whiteboard to do the math, but Catherine just blurted out the answer.
“It’s 4,225,” she said.
Justin turned from the board and stared at her. In fact, we all turned and looked at her.
“How did you get that so fast?” Justin asked.
“It’s just a mental math trick my dad taught me when I was little,” she said.
Of course, we wanted to know the trick, so she explained it to us.
“It’s really easy,” she said, “but it only works under certain conditions. First, it must be a two-digit number, and the tens digit must be the same for both numbers. Second, the two ones digits must add up to ten.”
I checked out the conditions for 65 × 65. Both were two-digit numbers. The tens digit was 6 for both. The ones digits added up to 10. The conditions checked out.
“To get the last two numbers of the answer, just multiply the two ones digits together,” Catherine explained. “We multiply five times five and we get twenty-five.”
She wrote 25 on the whiteboard.
“Now, to get the first two numbers, multiply the tens digit by one more than the tens digit, so in this case we multiply six times seven to get fo
rty-two,” she said.
She wrote 42 in front of 25 and added a comma after the 4 to get 4,225. Just to prove it to himself, Justin multiplied it out by hand. Catherine was right!
We each had to try it out, of course. I multiplied 34 × 36 and quickly got 1,224. Stephanie went with 42 × 48 and got 2,016 in an instant. Justin, of course, had to push the trick to its limits, so he tried 93 × 97. He smiled broadly when his answer of 9,021 checked out.
“That’s really cool, Catherine,” Justin said.
Math group every day consisted of working problem after problem, trying to learn different techniques that would help us as the competition grew closer. We found that sometimes the best way to solve a problem was with some educated guessing. For example, one problem asked us to find three consecutive numbers that you can multiply together to get 15,600.
At first, we didn’t know how to even start with a problem like this. As it turned out, we were trying too hard to come up with a complicated approach when all we really needed to do was start guessing numbers.
“What if we just tried some numbers to see if we can narrow it down?” Stephanie suggested.
“That could take forever,” Justin protested.
But it actually didn’t take long at all. We started with multiplying 20 × 20 × 20 and got 8,000. That told us that 20 was too small. When we tried 30 × 30 × 30, we got 27,000, so we knew 30 was too large. We tried 25 × 25 × 25 and got 15,625. We were close. Since we needed three consecutive numbers, we tried 24 × 25 × 26 and got the answer we wanted! This was one of those cases where it was easier, and much quicker, to try out some possible solutions and see what we got.
This method, of course, didn’t sit too well with Justin, who liked to be very logical when it came to solving math problems. To him, the thought of guessing answers seemed wrong. We tried to convince him that we really had taken a logical approach. We found an answer that was too small, then one that was too large, and then narrowed it down until we found the right one.
He was much happier about how we solved the next problem. We had to find five consecutive even numbers that added up to 320.
Justin started by dividing 320 by 5 (since there were five numbers to add) and got an answer of 64. We decided that 64 must be the middle number, so we found two even numbers on both sides of 64 and added them. Our decision was correct:
60 + 62 + 64 + 66 + 68 = 320
Just like that, we had the answer.
“Now that’s the way to solve a math problem!” Justin declared. “No guessing needed on that one.”
We all agreed, but we also decided that sometimes guessing wasn’t such a bad way to solve some problems.
While things were going really well with our preparations for the math competition, the rest of fourth grade went on pretty much as usual—unfortunately.
The bullies were back in action, doing their favorite tricks, like knocking things on the floor when they passed our desks, and tripping us when we passed by theirs. More than once I saw a spitball whiz by my head when Mrs. Gouche wasn’t looking.
“Why do those guys always pick on you?” Catherine asked as we ate lunch in a corner of the cafeteria.
“It’s not their fault,” Justin said.
I looked at him in amazement. “How is it not their fault?”
“You’d be mean, too, if you had to look at their ugly faces in a mirror every morning,” he replied with a grin.
We all laughed. A little too loudly, unfortunately, because it caught the attention of Robbie and Bill two tables over. Robbie looked around to make sure there weren’t any teachers nearby and then stomped his way to our table, with Bill following closely behind him.
“Now, isn’t this cute,” he said. “There must be a loser convention in town.”
Bill laughed like it was the funniest thing he had ever heard.
“I could find a better insult than that in a bowl of alphabet soup,” Catherine said quietly as she stared straight at Robbie.
“What did you say?” Robbie yelled as he began to turn red with anger.
“Let me explain,” Catherine said. “I’ll try to say it sloooowly so you can understand.”
“You better shut up, or, or, or—” Robbie stammered in anger.
“Or what, Robbie?” asked Coach Harder, who had come up quietly behind him.
“She was picking on Robbie,” Bill said.
“Is that true, Robbie?” Coach Harder asked. “Is she picking on you?”
Catherine smiled sweetly at Robbie, making him even madder. But with Coach Harder standing right there, he was helpless to do anything.
“I didn’t hear you, Robbie,” Coach Harder said. “Was she picking on you?”
“No,” Robbie said meekly.
“Then I suggest you and Bill get out to the playground,” he said.
Robbie gave a furious look in our direction, then turned and walked away. When he was gone, Stephanie gave Catherine a high five.
“Nicely done, Catherine,” she said.
It was amazing what a little confidence had done to Catherine. In just a few short days, she had gone from not saying a word to standing up to the bullies. Unfortunately, that meant Catherine was now on the bullies’ bad side, and I knew from experience that their bad side was not a good place to be.
CHAPTER 10
The math competition was only five days away, and I was starting to feel like we had a pretty good chance to beat Joe Christian and his team. Joe was smart, but we were really starting to click as a team. We were working well together, with everyone helping to solve problems. Justin might get us started with a good idea, then Stephanie or I might come up with the next step, and then Catherine might finish the solution. The next problem, we would all contribute in a different way. Best of all, we were having a lot of fun!
And then it happened.
Tuesday morning, Catherine wasn’t at school. We still managed to solve problems during our math group, but it was much tougher without her. On Wednesday morning, she was gone again. When Thursday morning came, and she still wasn’t back at school, we started to worry. We couldn’t seem to focus on any of the problems.
“Where could she be?” Stephanie asked.
“Probably sick,” I guessed.
“She seemed fine on Monday afternoon after school,” Stephanie said.
“Maybe she has food poisoning,” Justin said.
“Or was hit by a car,” I added.
Stephanie looked horrified. “Don’t even think that!” she said angrily.
“What are we going to do if she’s still missing on Saturday morning?” I asked. “Will they let us compete with just three people?”
“Well, I’m going to go by her house after school and see what’s going on,” Stephanie said.
Justin and I agreed to go with her, and we all met at the side door when school let out. We had only made it twenty feet from the door when I heard a screech of bike tires on the blacktop. I turned, and there they were—Robbie, Bill, Bryce, and Sniffy—the whole gang of bullies.
“Nowhere to go, is there?” Robbie taunted.
It was one of the few times Robbie was right. There wasn’t anywhere we could run. They were between us and the school, and there was no way we could outrun them on their bikes.
“Where’s your little friend?” Bill asked.
“Who are you talking about?” I asked innocently.
“You know exactly who he’s talking about!” Robbie shouted. “She thinks she’s pretty smart, doesn’t she?”
“Actually, she is pretty smart,” Stephanie said. “A lot smarter than you, that’s for sure.”
“That’s not saying much,” Justin said quietly.
“What did you say?” Robbie asked, filled with anger.
“I said it’s not saying much to say Catherine is smarter than you,” Justin said defiantly.
I was always amazed to see how brave Justin was. He sure wasn’t letting his size stop him from standing up to one of the biggest kids in
the entire school.
I could see that the bullies had had enough. They were closing in on us, and we were running out of time. I had an idea. I didn’t for a second think it would work, but it was at least worth a shot.
Robbie was raising his fist in front of Justin, but he paused when I spoke.
“Don’t you want to know where Catherine is?” I asked.
“Who cares?” Robbie answered.
“She’s really sick,” I said dramatically. “She might even die.”
Now I had the attention of all the bullies.
“She might die?” asked Bryce.
“We all might,” I answered.
“What do you mean?” asked Robbie.
“She has a rare tropical disease,” I said.
“Yeah? How’d she get it?” asked Robbie.
“Her uncle brought her a parrot from South America,” Stephanie said quickly. “He didn’t know that parrots carry lots of diseases.”
I could tell that a few of the bullies were starting to buy the story, but Robbie was still a little skeptical.
“So why would her disease affect you?” he asked.
“Once someone has the disease, anyone around them can catch it,” Justin said. “We’ve probably got it since we hang around her.”
“And the more time you spend around us, the more likely you’ll get it, too,” I added.
I walked toward the bullies. Sniffy, Bryce, and Bill rolled their bikes back two or three feet. Robbie stood his ground, but then he backed up, too, as Justin stepped toward him.
“Ah, you punks aren’t worth the time,” Robbie said with a sneer. “Come on, guys.”
Robbie turned his bike and pedaled away quickly, followed closely by his little gang. Justin waited until they had gone around the corner of the school and were safely out of sight before he raised his hand to me for a high five.
“Nicely done, Jordan.”
“A deadly parrot disease—that was your plan?” Stephanie asked.
“I just said deadly disease. You were the one who came up with the parrot,” I said. “And it probably wouldn’t have worked with anyone else, but those guys aren’t the brightest light bulbs in the box.”