Imagination and Math

The King's Chessboard by David Birch tells the story about an exotic king and an old wise man. The wise man provided the king with a  service, to which the king wanted to reward him. After much disagreement over whether to accept a reward the wise man finally concedes and decides to ask for a grain of rice on the first square on the king's chessboard. With each day that passes the number of grains of rice on the previous square will be doubled. It does not take to long for the king to realize that he has been outsmarted by the old man and his knowledge of exponential growth that requires elephants to carry off the amount of grains of rice. The power of math is shown in this story along with the wisdom of completing the calculation in your head before you agree to a deal, as the king should have done.

With each day, we move to a different square on the chessboard. The first square shall have but one grain of rice on it. The second square shall have two grains of rice, the third would have four and the fourth should have eight. This is an example of the exponential growth of doubling. At first it starts off but a small increase until it starts to reach large amounts rather quickly. By the tenth day there are already one hundred grains of rice on the one square.

The imagination is a powerful instrument, some would argue even more powerful than your logical and conscious mind. Most children are not lacking in terms of imagination but suffer when it comes to grasping mathematical concepts. The power of words transports them to a land where their imagination runs free and they are faced with an adventure in which they must rely on their wits. Allowing them to benefit from using their logic to excel. By using literature to relay mathematical concepts both sides of their brains are being put to use, therefore allowing them to better recall theories in terms of stories. Words open up the imagination while math enhances them.

Shahad Nejaim

P. Bear's New Year's Party: A Counting Book by Paul Owen Lewis

P. Bear's  New Year's Party: A Counting Book by Paul Owen Lewis

The Story talks about a polar bear that decides to have a New Year's Eve party and send several invitations to several of his friends. So at 0:00(12) no one arrives. At 1, one whale arrived. And and 2, two horses arrived.

According to this story, I can relate the amount of friends in an equation. I can say that the first point  is 0,0 which means that at 0:00 or 12, no body arrived. Then the second point is (1,1) which means that at 1, 1 friend had arrived. Then the third point is (2,2), which means that at 2, two more friends arrived. Using all this information we can set up a linear equation and we can find the slope of such.

Slope:
 (1-0)/1-0) = 1
(2-1/2-1) = 1

All these mean that according to the book, there is a linear relationship between time and the amount of guests that arrive which is expressed by the equation F=T, which means that the amount of friends is the amount of time(hours).

3) literature is a very effective way to teach a mathematical concept, because mathematical concepts apply to the world today, and a person can easily relate mathematical concept to real life situations and scenario, due to their familiarity, where ones imagination can be helpful in comprehending such concepts. Giving examples of real life stories gives a person a better way to understand things by the use of logic sense. This logic sense, and easy organization of ideas that stories bring out, makes it easier for people to relate or understand in terms of mathematical concepts. This overall makes it a great effective way of learning.

Lemonade For Sale

“Lemonade For Sale” by Stuart J. Murphy is a story about a group of kids who decide to sell lemonade to earn money for their club. The group of kids wear funny hats and have a parrot who attracts customers to buy the lemonade. At first the lemonade sells very well but as the book progresses competition arrives in town, forcing the kids to reassess their business model. The story has very cute images and makes the math seem easy and fun. The math in this book is very simple. The concepts focus on basic tables and graphs. The mathematical examples in this book are real life situations that happen everyday, which is good when introducing the subject in this way. It makes kids and regular individuals more invested in the topic when they realize it can be used in everyday life. 

Lemonade For Sale

 I choose the story Lemonade for Sale. The story is about when four kids and their sidekick, Petey the Parrot, run a lemonade stand whose patrons include all kinds of wacky neighbors—even a juggler. They create a bar graph to track the rise and fall of their lemonade sales. Author Stuart Murphy and illustrator Tricia Tusa make understanding bar graphs a breeze with lively art and a warm story. When members of the Elm Street Kids' Club decide to sell lemonade to raise money to fix up their clubhouse, they do it in style. Dressed in special "lemon hats," with Petey the Parrot, the club mascot squawking, "Lemonade for Sale!," business booms at first. Sheri keeps track on a bar graph, plotting the number of cups sold against the days of the week. But suddenly sales drop when Jed the Juggler comes to town. The kids have to Gather, chart and compare data is an important skill for assessing progress and making predictions.It's an entertaining story with learning important concepts involved, such as the bar graph.


The mathematical concept presented in this story is based around the bar graph and how to graph a real life situation. The lemonade sold is put on the graph and it is recorded. The money and the lemonade makes the kids see how good they are doing with the selling of the lemonade. Business like this happens everyday in the real world so it's nice the kids can have a head start on it before they grow up.This is a great opportunity for kids to have a head start and have fun reading a fun book at the same time.

I think for people to really learn something the should see it in different ways. With these kids books it puts the the math in a different perspective. I think its great to be able to see the math in picture books, it adds a different way of learning which is great. 

Divide and Ride by Stuarty J. Murphy.

Book :Divide and Ride
By: Stuart J. Murphy

In his Book, 11 kids are going to a carnival. When they got to the carnival, the decided that they were riding a roller coaster which is name: "Dare Devil." This ride has 6 seats and each seat can have two children. Because there are only 11 kids, the last seat is missing one kids in order for all the seats to be filled. To fulfill the last seat, they ask a kid they didn't know in order for all the seats to be filled.

For this story, I am relating this into domain because there is a limited amount of seats for this ride. This means that realistically speaking the roller coaster cannot seat more 12 kids. So the domain for this roller coaster is (0,12).

I can also relate this to the slopes at different points of the roller coaster's spins and heights. Of course there are different slopes at different time in the roller coaster.

I believe that literature is effective because it not only uses one's reason or logic to develop and solve a problem. It involves detailed information about a problem that enables not only your logic but more parts of your brain in order to solve the problems.

By David Varela

Family Reunion

1.) The story “Family Reunion” by Bonnie Bader begins with a young boy (the main character) being woken up by his mother at 7:00am on a Saturday and he is wondering why she is waking him up so early even though he doesn’t have any school. His mother reminds him that this Saturday in particular was the Graff Family Reunion and he doesn’t want to go at all! He tries to come up with numerous excuses but none of them work with his mother. They arrive at Aunt Molly’s house for the Reunion. Trying to avoid his family he looks around for a spot to do his homework. He finds a spot under a tree to do his math homework about graphs! While his mother and his aunt discuss the temperature for the reunion he finds the idea for his first graph, the temperature and time.  After his mother tells him to enjoy the party a little he gets his idea for the second graph which is how many people take certain types of food. He counted how many people take Potato Salad, Coleslaw, or Macaroni Salad. While he began to get his own food his mind began to race again for another graph. This time he would graph how many people used napkins, their sleeves, or the back of their hands. Ignoring his family as he continued to work on his graphs some of his cousin’s come up to him. They also love math and join him in his graph making adventure. They deicide to then graph the hair colors of the family. As he finishes up his graphs his mother tells him its time to go and he’s really bummed! Even though he didn’t want to attend another Graff Family Reunion he ended up not only getting to know his family as a whole better through his data collected but he also got his math homework done!!

2.) The mathematical concept presented in "Family Reunion" is the idea of graphs. Not only is it the idea of graphs but the book provides starting with the idea for the graph, collecting the data, maintaining the data, then finalizing it into an appealing final product. The main character begins with an idea such as how many people will take a certain food at the reunion. He then collects his data by watching his family members take certain foods. Then after he collects and maintains his data he finally put it all into a graph with his coloring utensils. This book did a very good job at exemplifying and illustrating the process of making a graph in a very easy way with a story line along with it.

3.) Literature is a good way to explain a mathematical concept because of how easy it is to attach a storyline to a concept like graphing. I believe literature is an easier way of explaining a concept rather than a bunch of numbers on a board you can apply the concept to a real life situation which makes it easier to understand.

Lemonade for Sale

1. I chose the children's book "Lemonade for Sale" by Stuart J. Murphy. This story is about when members of the Elm Street Kid's Club decided to sell lemonade to raise money to fix up their club house. Dressed in special 'lemonade hats' and their club mascot Petey the Parot squeaking "lemonade for sale", business begins to boom. One of the members of the group, Sheri, keeps track of their sales on a bar graph, plotting the number of cups sold against the days of the week. 

2. "Lemonade for Sale" shows the effectiveness in graphing information in the business world. each day they would sell a different amount of lemonade and by graphing their sales, the kids could see whether or not their business was going well.

3. Children's books are being used more frequently to teach mathematics. With literature, children are able to experience the wonder of mathematics in the same way they appreciate the wonders of a great story. This is why literature is a great way for kids to learn math concepts; they are able to put more meaning to the concepts and practices of math rather than just learning the numbers. 

The Cat in Numberland

SUMMARY:

At Mr. and Mrs. Hilbert’s Hotel Infinity, the resident cat is puzzled by how the hotel can be fully booked, yet the rooms are full of Odd and Even Numbers, and guests continue to arrive. The odds and evens live happily together, playing games like addition and subtraction until Zero comes to call. 
When Zero tries to check in, there is a giant room switch so that he can stay, even though Mr. Hilbert insists he’s not really a Number. Mr. H refuses to admit him on the grounds that, "Zero is not a Number-Numbers serve to count things." His wife disagrees, and she offers 10, 100, and 1000 as cases in point. Defeated, her husband agrees to give him a room, moving everyone one room up. 
Zero tells the others about a place called Alphabet where the Letters live. "They cannot play the games we know, but they know others that are very interesting-." When they invite the Letters for a sleepover, Zero proposes that he move to Room 26, and the others follow suit. The Letters begin to arrive and everyone still has a room, even though no Numbers have left. No matter how many guests arrive or depart, the hotel accommodates them all, and is always full. But when the Fractions arrive, demanding rooms, real chaos threatens. But Zero seems to have all the answers. 

CONCEPTS: 

The book explained many mathematical concepts, but one of them that comes to mind is domain and range. When learning about them in class, we learned that some of them could be infinite, real number, integers, etc. This book tackles this subject. When Zero comes up with the idea of moving up all the odd and even numbers one room to make room for himself he found his place on the number line. Finding a room for fractions in between the even numbers and odd numbers as well. It grasped the concept of infinity, when it comes to domain and range. The idea the hotel is full, yet can admit more is similar to the domain and ranges. 

LITERATURE?

I think literature is an effective way to teach mathematics because it approaches and explains math problems in a way that can be applied on simpler terms. Instead of it being explained by rules and steps, we understand the significance of such math concepts, and can now apply it to other situations. 

The Doorbell Rang by Pat Hutchinson

     The title of the book that I read was "The Doorbell Rang" by Pat Hutchinson. The story is all about grandma's cookies and how no one else can make cookies the way that Grandma can. The story starts out with two children who have been given twelve cookies by their mom that their grandma sent over for a snack. Throughout the book, pictures illustrate how more and more friends come over and they keep having to devise a plan for all of their friends and themselves to get the same number of cookies. The number of children that come over for grandma's cookies starts to get unreasonable and after the cookies are all gone, all of the children are still hungry for more cookies since they had to keep distributing them equally. In the end, everyone is upset about how many cookies they didn't get to eat, but grandma shows up by surprise to bring everyone an entire batch of cookies for everyone to fill their stomachs with. The illustrations in the book help the reader to understand the changing emotions of the kids as they all start to get less and less cookies as more friends show up.

     The main mathematical concept covered in this book is division of real numbers. It is a skill used in many algebra problems when trying to solve for a single variable and many other real life situations. This book is all about the children who all want grandma's cookies, and figuring out a way to spread the cookies equally among the two kids and all of their cookie-hungry friends that all want a share of the cookies. The story begins with two children who are tasked with scarfing down twelve cookies, which meant each of them would get six cookies to themselves. Then more and more kids start to come and it is more difficult for the children to divide the cookies up evenly. It gets to a point where there are 10 kids who all want cookies, and they figure that since you can't divide twelve cookies evenly for ten kids, they can each only have one. This book does a very good job of illustrating basic division skills and how when you there is no even solution to a division problem, then you have to round up or down depending on the situation. The expression used in this story is simple, depending on how many friends were over is how much you would divide by twelve.

     I think that literature is a very effective way to teach more simple mathematic concepts because most of implement pictures and easy and very readable language to teach children these simple concepts. They match up a story to help children when they are faced with these situations in real life and when in the classroom with real math problems in front of them. If kids read these books and remember how they are set up and how the story explains the math then it is much easier for them to memorize how the problems are meant to be solved.

Seeing Symmetry

Seeing Symmetry by Lauren Leedy discusses symmetry in a simple way for kids to understand. Even the front and back covers are symmetrical! It is a picture book, comparing symmetrical items from quilts to kites! Leedy makes connections to not only math, but art, nature, and science as well with her comparisons. She delves deeper than most children's discussing symmetry because she analyzes and explains not only bilateral (line) symmetry, but also goes on to explain rotational symmetry in a way kids can comprehend.

As stated in the title, the mathematical concept analyzed is symmetry. Leedy uses things like cupcakes to explain bilateral symmetry and things like wind turbines and flowers for rotational symmetry. I think that literature (especially picture books) is a good tool for learning a mathematical concept because it simplifies the concept greatly. This is underscored for the concept of symmetry, as through pictures it is far easier explained than just through words. Literature also makes it easier to understand math depending on how you learn, as some probably prefer to have it explained in words than just see and equation laid out in front of them.

If I Had A Car

1. Summary of the book
I choose a book "If I Had A Car". As you can assume from the title, it is about a car.  A main character of rabbit, he is wondering whether he wants to have a car or not.  He thinks that if he uses a car, he will use a lot of gas, which costs a lot of money and also it makes environment pollution.  He can use buses instead of using a car. At the end, he decided to not to buy a car, and he uses buses and bicycles.


2. Mathematical concepts in the book
At first, the bunny was wondering get electricity car or regular car. Electricity is clean, but two times expensive compare to use gas. However, gas will cause a lot of air pollution. Bunny considers those negative parts and he decided to buy bicycled instead of buying a car. I think this story tells about a concept of fixed costs as we did in the section of  the function. This story makes the reader think which choice is beneficial to the bunny.


3.  Explain in your own words why you believe the literature is an effective way to teach/learn a mathematical concept.I think learning mathematical concepts of literature is an effective way to acquire them, because  mathematics always somehow related to our daily life. The book, "If I Had A Car", I think it is a typical situation we face in daily life. Personally, I like to study something which connects to my daily life or something I might use in the future.  And literature also makes us easy to understand mathematical concepts more easily rather than explain by complicated mathematical theory. 

The Number Devil

I read the book, The Number Devil by Hans Magnus. At the beginning of the story, a boy named Robert explains his dreams and how they are meaningless; he particularly talks about a fish that always gobbles him up. But one night, he has a different dream, and in this dream contains a tiny red man named the number devil. On the first night, the number devil explains the significance of the number 1 and how, if Robert ever gets confused, he should always think back to the most simple number. Then the number devil explains the concepts of infinity and fractions using chewing gum as an example. He also explains how all numbers come from the number one by showing Robert the products of 11x11, 111x111 and so on. Over the next twelve nights, many mathematical concepts are explained including Roman Numerals, exponents, square roots, prime numbers, decimals, and much more. The author comes up with creative names for some of the mathematical concepts; he refers to exponents as “number hopping” and prime numbers as “primma donnas.” Robert realizes that he truly enjoys math and is able to use the skills that the number devil, whose real name is Teplotaxl, teaches him in his math class. 

This book explained many mathematical concepts, but one that I thought was most clever and well thought out was the idea of “hopping” numbers and “rutabaga” numbers. The number devil explains how complicated the number system would be without the number zero, and how zero allows us to “hop” between numbers. Robert says how large numbers make him feel jumpy, so the number devil explains how a large number, such as 5x5x5x5x5=3125 can easily be wrote as 5^5. He then explains “rutabaga” numbers by calling them the opposite of “hopping,” which is an interesting way of putting it; I think that this could help a child understand the concept. It makes the reader think of the actual roots of a plant. 

Literature is effective in teaching new mathematical concepts because it puts things in different words than a teacher would. This gives a different perspective that could help someone understand a concept more easily. Literature, such as these children’s books, also has really helpful visuals that add to the explanation and make it that much easier to understand. This book also gave many examples for each concept, while sometimes in class there is only time to give one example; having two or more examples gives the reader the ability to compare and form a deeper understanding of the concepts.