The Prime-Time Burglars
Page 7
“And the barking?”
“I knew the burglars were afraid of dogs since they had been scared away from at least two houses that had dogs,” Justin said. “Stephanie doesn’t have a dog, so I brought my own!” He held up his phone. “In case you were wondering, it’s a Golden Retriever. They have the loudest recorded bark, according to the Guinness Book of World Records.”
I laughed. Not only did Justin think of having a dog ready to go, he had even researched which one had the loudest bark.
I didn’t have time to ask any more questions, because Linda and Amy rushed through the basement door.
“What’s going on?” Linda asked in alarm.
“Oh, not much,” Stephanie replied.
We all laughed while Linda and Amy looked at each other in confusion
Chapter 15
The Math Kids got together again the next day. We wanted to celebrate our success in capturing the burglars. We clinked our glasses of milk together and then plowed into a large plate of Oreos.
“I still can’t believe what we did,” Stephanie said.
It was amazing. We were just kids, but we had cracked a case that even the police couldn’t solve!
Justin explained that it had been Stephanie who had come up with the plan to get Robbie to tell his dad what we had discovered.
“I thought if Mr. Colson got the credit for solving the case then maybe Robbie would leave Justin alone,” she explained. “I don’t know if that part of the plan will work, but I do know that Detective Ponnath was pretty impressed with Mr. Colson. Hopefully, having a hero for a father will make Robbie back off a little.”
Fat chance, I thought, but I hoped she was right.
“But why didn’t you guys let me know what was going on?” I asked.
Justin and Stephanie looked at each other.
“Justin said you weren’t very good at keeping secrets,” said Stephanie.
I looked at Justin.
“Don’t you remember that time in first grade when you told Mrs. Becker that I put the frog into the aquarium?” Justin asked. “Or in second grade when you told your sister we were going to leave school early to go to the comic book store. Or in third grade—.”
“Okay, okay, I get it,” I laughed. I was too happy about our success to be hurt.
It didn’t take us long to find out if the bullies were going to back off. Before school had even started the next day, Bill had knocked Justin’s backpack off his hook and onto the floor. I guessed the bullying was going to continue.
That’s when something amazing happened. Robbie got up from his desk and picked up Justin’s backpack. He brushed it off and placed it back on the hook. Justin looked on in stunned silence.
“Hey, man, it looks like you dropped your backpack,” Robbie said.
“Thanks,” Justin said.
“Don’t mention it,” Robbie said with a smile. “Happy to help.”
The day continued to surprise us. At lunchtime, when we would normally line up to head to the cafeteria, Mrs. Gouche made an announcement.
“Class, we have some guests.”
Our mouths dropped open when we recognized the two men who walked through the door. It was Detective Ponnath and Mr. Colson. Each carried a stack of pizza boxes. It turned out we were getting our pizza party after all!
“This is just a little thank-you for your classmates who helped us to capture the burglars,” Detective Ponnath said with a large smile. “Come on up here, kids. Stephanie, Justin, Jordan, and Robbie!”
Robbie?
I started to say something, but Justin whispered, “Just let it go, Jordan.”
Justin was right. It didn’t hurt to let Robbie get a little credit for talking his dad into hiding in the tool shed while we waited for the burglars. And if it would give us a little break from him and the other bullies, it was well worth it.
“What a great day,” said Stephanie as she stuffed her face with pizza.
“Almost perfect,” agreed Justin.
“Almost?” I asked.
“Well, we didn’t get that math project done,” Justin said. “Hopefully, Mrs. Gouche will give us a couple of extra days to finish.”
“Maybe we don’t need more time,” I said. I went to my desk and pulled out a neatly-stapled stack of papers. Justin started to read, flipping through the pages as he began to smile.
“You finished the project!” he said.
“Well, someone had to do the math work while you guys were wasting all your time plotting how to catch criminals,” I smiled.
“We make a great team, don’t we?” Stephanie said.
“We sure do,” Justin agreed.
“To the Math Kids!” I yelled, holding up my box of chocolate milk.
Justin and Stephanie touched their own milk boxes to mine.
As we drank our milk and celebrated our success, I couldn’t help but wonder where our math club would take us next.
The End
Coming Spring 2019! A Sequence of Events, Book 2 in The Math Kids series. Don’t miss it!
The Math Kids Club is back! After solving the case of the prime-time burglars, The Math Kids, Jordan, Justin, and Stephanie, are ready to return to the original purpose of their club: solving math problems. And the district Math Olympics is the perfect opportunity to do just that. But before they can enter the competition, they need a fourth teammate. The Math Kids set their sights on Catherine Duchesne.
Even though Catherine has been quiet in class, she knows some really cool math tricks that are sure to help The Math Kids win the competition. But when Catherine doesn’t show up for school and Jordan, Justin, and Stephanie find out her father’s been kidnapped, the group springs into action to help their new friend.
Want to Do Math
Like The Math Kids?
Adding the numbers from 1 to 100
The amazing thing about Stephanie adding up the numbers from 1 to 100 is that the story is true. Okay, there was no pizza party. There was also no calculator, since the story happened before calculators had been invented. And the teacher’s name probably wasn’t Mrs. Grouch either. So, what part of the story was true? Carl Friedrich Gauss was eight years old when his teacher gave the class that assignment back in 1785. Carl really did come up with the correct answer of 5,050 after only a few seconds of thought. The teacher—and the rest of his class—was amazed that he could do it so quickly.
How did he do it?
Well, Carl wasn’t just any eight year old. He became one of the most famous mathematicians in the world (sometimes he was even called the “Prince of Mathematicians”). One of the reasons Carl became so good at math is that he didn’t look at numbers the same way as everyone else. Most people would look at those numbers like this:
1, 2, 3, 4, 5 … 98, 99, 100
If you’re not familiar with “...” in a list of numbers, it just meansto keep going in the same pattern. It is called an ellipsis. Mathematicians are lazy sometimes, and it’s easier to write “...” than it is to write out all 100 numbers.
Carl Gauss looked at the numbers a little differently though. He thought of what it would look like if he stacked the numbers from 1 to 100 on top of the same numbers from 100 down to 1.
1 2 3 4 5 … 98 99 100
100 99 98 97 96 … 3 2 1
He then noticed a helpful pattern to the numbers when he added the rows of numbers together.
1 + 100= 101
2 + 99= 101
3 + 98= 101
4 + 97= 101
5 + 96= 101
...
98 + 3= 101
99 + 2= 101
100 + 1= 101
Carl saw that he had 100 pairs of numbers that all added up to 101, so he multiplied 101 x 100 to get 10,100. He then divided that number by 2 to get 5,050. Why did he divide by 2? Becaus
e he was adding each number twice, he knew he had to divide the total by 2 to get the right answer.
Was that the only way Carl could have quickly solved the problem? No, there are actually at least three or four other ways he could have done it. All the methods of quickly solving the problem all have something in common though. They all look at the numbers a little differently. That’s what The Math Kids series is all about. It’s about looking at numbers a little differently. In fact, it’s about looking at math a little differently—looking past adding, multiplying, subtracting, and dividing and seeing math as something that’s not boring, but actually very cool.
The Bridges of Konigsberg
The Bridges of Königsberg is a classic math problem that was given to a famous mathematician named Leonhard Euler about three hundred years ago. It involves an area of mathematics called graph theory.
The old town of Königsberg has seven bridges. Can you walk through the town, visiting each part of town and crossing each bridge only once?
There are four areas of town.
We’ll label them A, B, C, and D.
There are seven bridges.
We’ll label the bridges 1 to 7.
We can simplify this picture even more. In mathematics, this is called a graph.
In a graph, each point (A, B, C, and D) is called a vertex.
Each line (1 to7) is called an edge.
The number of edges which end at a vertex is call the degree.
There are 3 edges (1, 2, and 3) ending at vertex A, so we say vertex A has degree 3.
If we can start at any vertex and draw a line that goes through every vertex (A, B, C, and D) and along each edge (1 to 7) without lifting our pencil, we’ve solved the problem. The path that we draw is called an Euler path.
Here’s what that would look like with some easier shapes:
This shape has 4 vertices, each with degree 2.
We can draw an Euler path.
This shape has 4 vertices, two with degree 3 and two with degree 2.
We can draw an Euler path if we start at either of the vertices with degree 3.
We can’t draw an Euler path if we start at either of the vertices with degree 2.
This shape has 4 vertices, all with degree 3.
We can’t draw an Euler path. That means we can’t draw this shape without lifting up our pencil.
Euler figured out that we could tell which graphs have an Euler path by counting how many vertices have an odd degree (1, 3, 5…).
We can only draw an Euler path if the number of vertices with an odd degree is 0 or 2.
If there are two vertices with an odd degree, the Euler path must start and end at the vertices with an odd degree.
So, how could the Math Kids have quickly figured out if they could solve the Bridges of Königsberg problem? All they had to do was to count the vertices with an odd degree!
In the Bridges of Königsberg graph there are 4 vertices with an odd degree (A, C, and D have degree 3 and B has degree 5).
Since there are more than two vertices with an odd degree, there is no way to draw an Euler path.
In other words, there is no way to walk through all areas of the town and go over each bridge just one time.
Prime Numbers
Prime numbers are natural numbers that can only be divided by 1 and itself. What is a natural number? It is an integer greater than zero. These are sometimes called the counting numbers. If a number can be divided by another number (besides 1 or itself), it is not a prime. Two is a prime number because the only numbers that can divide it are 1 and 2. Four is not a prime number because it can be divided by 2. Two is the only even prime number because all other even numbers can be divided by 2.
How can we find out if a number is prime? A long time ago, a Greek mathematician named Eratosthenes of Cyrene, came up with a way to quickly find prime numbers. The method is called the sieve of Eratosthenes.
A sieve is like a strainer you use to drain the water out of a pot of spaghetti. The sieve keeps the numbers that are prime and drains out all the numbers that aren’t.
Let’s look at the first hundred numbers. Eratosthenes started with the number 2, which he knew was prime. He then crossed out all multiples of 2 (all even numbers) because he knew they couldn’t be prime.
The next number not crossed out is 3, so that is also a prime. Eratosthenes then crossed out all multiples of 3. Some numbers, like 6 and 12, are multiples of both 2 and 3, so those numbers were already crossed out when he got there.
The next number not crossed out is 5, so that is also a prime. Eratosthenes then crossed out all multiples of 5.
The next number not crossed out is 7, so that is also prime. He crossed out all multiples of 7.
The next number not crossed out is 11, so that is also prime. He found there weren’t any multiples of 11 to cross out because they had all been crossed out already. Eratosthenes knew he was done because 11 x 11 is bigger than 100. That means all the numbers that hadn’t already been crossed out were prime numbers.
Acknowledgments
Writing a book isn’t easy, and it certainly isn’t done in a vacuum.
First and foremost, I want to thank Common Deer Press for taking a chance on a guy with a crazy dream of writing a children’s series with a math theme. Thanks, Ellie Sipala, for stepping out on a limb for me. I know it was a seriously thin branch, and I will always be grateful for you sharing my vision.
Thanks to Kirsten Marion, who made the whole editing process so easy. I hope you know that I couldn’t have done this without your thoughtful ideas and your incredible enthusiasm for the story. You made this a much better book.
Thanks also to the rest of the team at Common Deer Press: Emily, Siobhan, and Anastasia. Publishing a book is a real team effort, and I couldn’t ask for a better team!
Thanks to Shannon O’Toole for her excellent artwork. You really brought The Math Kids to life and now I can’t picture them looking any different.
Thanks to all of you who read through my painful first attempts at this book and provided such great feedback.
Tom Winter, Chasity Wickenhauser, and the MathNerds@Facebook group: thanks for the early read by your kids. Their thumbs-up kept me going when I wasn’t sure if kids would like what I was writing. Special thanks for early reads by Shannon Clarkin, Stephanie Peace, and Justin Cole. I appreciate your suggestions and also that you were able to provide your criticisms without shattering my fragile ego. Thanks to my friend Mark Fauser, my writing inspiration who always reads anything I send his way. Who loves you, buddy?
To my own Stephanie, Jordan, and Justin, you are my continual inspiration. A dad couldn’t ask for better kids.
To Debbie, who deserves so much better than I could ever give her but stays by my side nevertheless. I love you for that and so much more.
About the Author
David Cole has been interested in math since was very young. He pursued degrees in math and computer science. He has shared this love of math at many levels, including teaching at the college level and coaching elementary math teams. He also ran a summer math camp for a number of years. He has always loved to write and penned a number of plays which have found their way on stage. David had always wanted to combine his love of math and writing, and now with The Math Kids, he has done just that! He feels that writing about math is a great way to exercise both sides of the brain at the same time.
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