Through the Red Fence
by Jeff Valure
www.mathprose.com
Author's Notes
This is the first appearance of the trio. I think they worked well as their personalities are just beginning to emerge. They should be making more appearances. This is one of my earliest stories.
I am an absolutely firm believer in discovery learning and try to offer as much opportunity for it as possible. Let the students work with this for a bit. It's not too hard if approached systematically. As for high school students, they shouldn't have much of a problem. These are good problems. They are real world and somewhat "messy" but doesn't that make them better? Life is not comprised of integers.
Here are the NCTM Standards utilized for this story:
Emphasis on nonroutine problem solving and varied strategies.
Model situations using concrete, pictorial, and graphical methods.
Discuss mathematical ideas and make convincing arguments.
See geometry as a means for describing the physical world.
Extend the understanding and use of measurement.
Special permission is given to remove the Author's Notes before distributing to a class.
Read the story and answer the questions that follow. As in life, there may be many answers and many forms of those answers. Use the knowledge you have to answer the questions, and where you find yourself lacking the skills, search out the answers in books, friends, teachers, parents; look anywhere you can to find what you need. Above all, enjoy yourself and please, learn something.
Teachers may print and copy this story, intact, in the interest of educating our youth.
All Rights Reserved.
Through the Red Fence
Outside
Tommy didn't know what compelled him to stop along his normally short walk home from school. His friends certainly wanted to keep going.
"Come on, Tom. Batman's going to start."
"Yeah, we're all supposed to watch at my house today."
That was Mike and Jamie. They were always complaining about something. It seemed that they were in a rush; they were always in rush. As soon as the dismissal bell rang, they were out the door and waiting at the big oak on the corner.
Mike got there first because his locker was at the end. Jamie, however, has to weave his way through half the kids in school before he could get out. He had tried to switch lockers in the beginning of the year but the good ones are like gold and no one would trade even when he tried to sweeten the deal with a '96 Maguire card. It didn't matter much anyway, he had gotten pretty good at getting through the crowd and met Mike at the tree seventy-eight seconds later (Mike had timed him).
Tommy trailed a far third. There was this girl he liked and he waited in the hall until she passed by and smiled at him. His friends didn't know that was the reason he was so late. They just thought he was slow. Tommy preferred it that way. The teasing for being slow was a lot easier to take than what he would get if they new the real reason.
They met at the old oak where they first became friends. They were going to carve their names in it but Jamie's dad works for some environmental agency and he taught his son well. From that tree they started the walk home. It usually involved jumping puddles or throwing hats into trees and of course, many races and dares. Today was no different.
Mid-race Tommy stopped and hooked his fingers through a chainlink fence. Of all the barking dogs vying for attention, for that chance at adoption, one caught his eye. It was this little red dog, its coat still glossy with youth. He had passed that place a thousand times before but this time there was that one dog that he hadn't seen before. The sun hitting his coat made him shine like a little red beacon beckoning Tommy to come take him from this place.
By the time the other boys got to the mailbox they had designated as the finish line, they were huffing and puffing pretty hard. Jamie sat on top of the mailbox as Mike was bent over, hands on his knees. The argument about who came in first and who came in last was about to begin when they saw Tommy still standing with his face pressed up against the fence.
"Tom, Batman is starting now!" Jamie called as he looked at a watch too big for his wrist.
"Guys, look at this," Tommy yelled back.
Through the sort-of diamond shaped holes in the fence, and past all the other dogs, the three of them stared at the poor little puppy. The funny thing is that they felt like the poor ones. Like kids without a bike or a ballglove, a boy just wasn't a boy without a skinned knee and a loyal companion. Tommy had wanted a dog for the longest time but his parents always gave the typical adult answer, "Maybe when you're older." Tommy had decided he was old enough and told his friends so.
"I have to get that dog."
Mike and Jamie chorused, "Yeah."
They ran the rest of the way home. Mike's house was the first stop. He opened the front door, threw his bookbag in and slammed it shut. "Sorry, Mom, bye!" he yelled as he raced down the porch stairs. He knew he was told a thousand times not to slam the door and he would probably hear it for the thousand-and-first time that evening.
The plan had been Batman at Jamie's and then maybe some kickball in his back yard but plans change. They made a detour at Jamie's to tell his Mom that they would be over at Tommy's instead. As Jamie opened the door, ready to make the same racing exit, everyone's mood suddenly sank.
"Hi, Grandma."
Grandmothers are great. We all love them and not just for the candy they always give their darling little dears, but they had one thing and one thing only on their mind. It was to get their bikes and to get a dog that would chase alongside and bark. They would ride to the park and throw a tennis ball around until it was almost too dark to see their way home.
As Jamie kissed his Grandmother, the other boys talked to his mom.
"Mrs. Rich?"
"You gentlemen look like you're in an awful hurry."
"We're going to go over to Tommy's today instead."
"Did you tell your Mom, Michael?"
She always called the neighborhood kids by their full names and was a stickler for manners but she was okay. She let her son's friends keep their bikes in their shed and always had a pitcher of lemonade in the fridge.
Jamie poked his head around the corner, "We set?"
"You're set," his mom smiled to him.
"I'll call my house from Tommy's, Mrs. Rich. Thanks, bye."
They were out the door.
Inside
Mike and Jamie sat uncomfortably upright on the livingroom chairs. The room was clean, cleaner than a hospital, but without the smell of starched sickness. You would never have known that that was a kids house. There were no toys on the floor, no crayons in the couch, no greasy fingerprints on the coffee table, not a single sign of childhood pleasures. This was strictly a "company room". It was for relatives and bosses and anyone who might pop in unannounced.
Tommy kept his pigs in the family room just two short doors away. Directly above the family room was Tommy's room. His mother joked that the ceiling sagged beneath the weight of all of his junk on the floor, at least he thought she was joking. For Christmas he had asked for a fireman's pole so he could slide down from his room whenever he wanted. That time it was Tommy who was thought to be joking.
Tommy looked out the window, his mind on a million other things than the task at hand. The puppy was far from approved but he was already out romping through the snow covered stand of pines out behind their house. He heard the crunch of the snow under his two feet and Red's four. Yep, he had the little guy named already. Red was a good sturdy name; it would suit him well. Only thing now was to get someone to say that one little word: yes.
"What about when Spring comes and you start baseball after school?"
Tommy's Mom was not going to give in easily.
"A dog needs exercise. And constant attention."
His Dad was holding strong, too.
"We can take him to the field with us."
"Coach Russo is not going to like having a dog disturb his practice, especially since you were so close to being state champs last season."
"Then we'll put him in the yard."
"Tommy's yard was big enough for a dog to run around in," the boys thought, "we'll play with him before and after practice. No problem."
There was a problem though. "Tommy, the yard's not fenced in. You can't let the dog run loose through the neighborhood." His dad had a point; his mother had a better one. "If you boys think you're responsible enough for a dog, then I think you can handle a fence first."
"Who am I? Tom Sawyer?!" Jamie cover Mike's mouth before he blew everything with one stupid comment. "No but you'll be a huckleberry if you don't shut up!" Tommy shot at him under his breath.
"Okay, a fence. No problem." Tommy would have agreed to anything, after all, Red was waiting and daylight was fading.
His parents looked at Mike and Jamie. They nodded and the deal was closed. A fence for a dog, it seemed like a good enough trade.
"Okay," Mike jumped up, "let's go get that dog." The boys followed him to the door, all of them tumbling like dominoes when they ran into Tommy's dad's chest.
"We have more to talk about, boys."
"Oh, what?" Didn't they know that waiting is agony for a twelve year old?
"Caring for a dog costs a lot of money. There's vet bills, leashes, collars, toys, bowls... The list goes on and on."
Tommy's eyes widened with every word. His allowance was five dollars a week. It wasn't even enough to see a movie. It costs him almost a month's worth if he got popcorn and soda, never mind the jujubees he couldn't live without. His dad couldn't possible expect him to pay for all those thing. Luckily he didn't.
"What I'm really concerned with is dog food. That's yours. I will take care of the rest. After all, you are my only son." His dad knocked his hat off and tousled his hair. Tommy thought, "Yeah, great, thanks. Just his food will cost me a fortune. I'll only get to the movies once a year now."
"And to help you out, we'll raise your allowance by one... okay two dollars a week. Deal?" Mom jumped in to ease the pain. Finally, the deal was closed.Outside
The boys walked the perimeter of the yard single file, Tommy, then Mike, then Jamie. There were many decisions to make and, on top of that, they had to get the fence up before they could even step foot into the pound.
With a couple of phone calls, the boys managed to get 80 feet of chain link fencing. It mostly came from Mike's uncle, the carpenter. They promised to mow his lawn for two months free of charge in return for the fence. So now all they had to tackle was the simple task of using those 80 feet to fence in the most room possible. After all, no one wanted Red to be cramped. He was going to be big when he grew up.
Mike grabbed a shovel. Tommy grabbed a pencil. "First things first."
The Questions.
1. The boys decided that if they built the fence against the house, they would get more interior room from the same amount of chain link. So the house, itself, would be used as part of the enclosure. Smart thinking. Now it's your turn for smart thinking. The back of the house, use the illustration, is 60 feet long. How would they build the fence using only the 80 feet of chain link available to them to get the greatest area? What is that area?
Advanced: The number of upright posts they can use is unlimited.
2. If the market price of gold is currently $290 per ounce, what would the cost be for a 3.4 pound locker made out of gold? Please note that gold is measures in troy ounces; the conversion rate is not 16 oz per lb.
Advanced: The value of gold has increased by 1303 % over its 1934 market price. What was the value of a troy ounce of gold in 1934? Also, what would the same locker have cost then?
Extra Credit: Our common use of the term "ounce" refers to what system of weight?
3. The brand of dog food Red is going to be fed recommends, per day, two and one-half cups of food for an adult dog (two to eight years of age), one and one-quarter cups for a puppy (up to two years), and one and two-thirds cups for a senior (over eight years old). If the dog food costs 46 dollars for 20 pounds, and a pound yields 9 cups, then how much money can Tommy expect to spend if Red lives to be 15 years old?
Advanced: If inflation causes the price of dog food to increase 1.6 % per year, how much will Tommy end up spending?
4. The above question told us that 1 lb (16 oz) of dog food yields 9 cups, and that is perfectly reasonable. But it is common knowledge that there are 8 oz in a cup just as there are 16 oz in a pint. How can you explain this paradox?
5. Will the two extra dollars of allowance per week ever fully cover the cost of Red's food, at any of his life stages? Prove your answer.
©Jeff Valure
www.mathprose.org
All Rights Reserved
![]()