Blog post 3: Mathematics in a story

1. I  read the book titled The Grapes of Math by Greg Tang. I chose this children's book because the titled intrigued me, as I noticed it was a play of the critically acclaimed novel The Grapes of Wrath by John Steinbeck.  Unlike the original novel, The Grapes of Math is a cheerful book, depicting colorful images of several different things that are to be counted by young readers. The book aims to provide a fun reading experience, while teaching how one can count most efficiently by using such methods as grouping, multiplication, addition, and subtraction, to speed up the process, rather than counting each item or picture individually. 

2. Each page of the book contains an image with a certain number of items, along with a short text that rhymes. The text has to do with the image, and provides a suggestion for how the items should or should not be counted. For example, the second page shows an image of two different kinds of grape bunches: 4 green bunches with 3 grapes each, and 4 purple bunches with 7 grapes each. The text reads: "How many grapes are on the vine? Counting each takes too much time." Here the text suggests the simply counting the grapes one by one would be too labor intensive. Instead, the next line reads: "Never fear, I have a hunch. There is a match for every bunch." The text is implying that the reader should count the grape bunches that have the same number of grapes, multiply the number of grapes on each bunch but the total number of bunches, and then finally add them together. So for example, one should count that there are 4 bunches of 7 of grapes, and 4 bunches of 3 grapes, so one would multiply 4X7 and add that result to the product of 4X3, giving us a total of 40 grapes (28+12). Using other items such as watermelon seeds, ants, camels, and more, the author give clever hints of which operation should be used to facilitate the counting. 

3. Books can be an incredibly fun way of learning math, especially for children, because it is much less intimidating. Instead being presented as a difficult task, a book with colorful illustrations introduces math as a entertaining activity. This can allow children to pick up essential mathematical skills and concepts without realizing they are doing math problems. This can significantly reduce the fear and anxiety many children have toward math. In addition, the math concepts used in children's books are simple enough that they do not require complex explanations, but rather can be explained through by clever means, such as rhyme. 

Blog Submission 3: Mathematics in a story

1.)
        I decided to choose “The Number Devil” by Hans Enzensberger.  The name was intriguing considering it was a book written for children.  I was curious how the author would associate something negative like the devil with mathematics in a positive way for young readers to learn.  But maybe that was the point - math is often notorious among children for being both difficult and boring, and perhaps the author wanted something to grab their attention first.

The Number Devil tells the story of Robert, a young boy who suffers from math anxiety.  When not being tormented by math problems issued by his overweight teacher, Mr. Bockel, Robert has vivid nightmares.  One night he is visited by the Number Devil, a creature possessing magical powers, a short temper, and a love of math.  The Number Devil has decided out of the kindness of his heart to assist Robert by educating him in mathematics every night, for twelve nights.

On their journey, the two learn such subjects as exponents, infinite series, and imaginary numbers.  As the lessons progress, Robert begins to understand and express interest in math, while the Number Devil learns to control his temper.  Instead of loathing his teacher, Robert gains a newfound appreciation for Mr. Bockel.  The story culminates with the young boy successfully answering a difficult question posed by his teacher.

2.)
Several mathematical concepts are explained throughout the book.  An example would be exponents: when multiplying numbers, Robert becomes intimidated by the amount of writing he must do in order to find the product of a problem, such as 10x10x10x10.  The Number Devil teaches him a trick, referred to as “hopping” (but is really just exponentiation).  He explains that whatever number the exponent is above 10 (say 10^4), all Robert simply has to do is make zero “hop” that many times to the right.  In this case, the zero hops four times to get 10,000.  Robert is then able to confidently solve problems with answers ranging in the millions.

3.)

Children’s books are designed to do two things that make for effective learning: they intrigue the reader, usually by appealing to their sense of imagination and having relatable characters, and they break ideas down into very simple concepts.  Such is the case for The Number Devil - in addition to having an imaginative and unorthodox story line for a children’s book, it also makes no assumptions about the readers knowledge of mathematics.  Subsequently, the book explains complex ideas in a straight forward and simple manner.

Blog Post 3

1. I chose The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger (German) translated in English by Michael Henry Heim. This book talks about a young boy, Robert, who suffers from a mathematical anxiety. He also often experience recurring dreams. One night he is interrupted by a creature introduced to him as Number Devil. Number Devil will teach Robert math principles over the course of twelve nights. The first night, Number Devil introduces to Robert the number one. The second night he explains the importance of zeros and negative numbers, but he also talks about hopping which exponents. On the third night, Number Devil teaches Robert primes numbers and how they can only be divided by themselves and one. The next night, the young boy learns square roots. Using coconuts in the desert, Number Devil teaches him triangular numbers on the fifth night. On the sixth, Fibonacci numbers is the theme or simply Bonacci numbers. After this dream, Robert started changing. The seventh night, Number Devil presents Pascal's triangle. On the eight night, Robert learns permutations and factorials. Finally on the ninth, tenth, eleventh and twelfth nights, Number Devil teaches to Robert respectively natural numbers, irrational numbers, mathematical proofs, and imaginary numbers. On that last dream, Robert is invited to Number Heaven where he meets famous mathematicians.

2. Number Devil refers to exponentiation as hopping numbers. The two were talking about the difference between two numbers (four and five which is one). Number Devil asked him why and explained to that it's like hopping. Numbers hop. They tried multiplying as many ones, then as many twos, then five. The numbers were growing very fast and faster if the base is bigger. He showed him that we could write that using exponents. Finally, he used the exemple of 1986 to show him how numbers hop; 1986 = 6*1 +8*10+9*100+1*1000.

3. I think literature is an effective way because they actually use words that you read to understand the meaning behing the math. It is more effective and easy language for the brain to understand and even more when there are images to give the brain a clearer view of everything. People are able to get the theorical part much easier.

Blog Post 3: Mathematics in a story

“Lemonade For Sale” by Stuart J Murphy

1) The book “Lemonade For Sale” is about the children of Elm Street Kids’ Club who need to raise money in order to build a new clubhouse as it is falling apart and their piggie-bank is empty. They decide a lemonade stand is the best way and they sell it for five days, keeping track of their sales on a bar graph. Their aim is to sell 30-40 cups a day in order to make enough money. They eventually make enough money to rebuild the clubhouse, after  cleverly asking the juggler “Jed” to juggle near their stand on the last day of sales, after having a slow sale day on Thursday. It used very detailed illustrations and explained what information should be plotted where. Overall it seemed like a great way to introduce kids to using bar graphs!

2) The mathematical model explained in this story is graphing, specifically bar graphs. This is shown by the number of sales the kids managed on a daily bases over a period of five days. The concept of X and Y axises are clearly explained and demonstrated, allowing kids to understand how to also create other graphs of a similar nature. By having a number on Friday that couldn’t be graphed, it highlights the importance of creating effective axis and sensible intervals for the numbers. 

3) I believe that literature is an effective and useful tool in teaching kids mathematical concepts, as it allows it to be explained in a way that is engaging and interesting to them. It can seem less intimidating for kids that may not excel in maths, as it presents the information in a more digestible manner. It also has the benefit of connecting mathematical concepts to real life situations, which allows a better understanding as it can be more relatable and easier to remember. 

Mathematics in a Story_Blake Keats

Summary:

In the inspirational story, A King’s Chessman, written by David Birch and beautifully illustrated by Devis Grebu, a wise man is given a tremendous gift for his service to the king. The wise man is at first reluctant to asking for any rewards for his service but is soon demanded by the king to make a request for a reward. This leads him to notice a chessboard in the room. The wise man makes the request that for the next 64 days he receive a grain of rice for each square on the chessboard amounting to double the amount on the square before that, beginning at one. Not wanting to hesitate, the king thought very little of how much rice he would really be giving away to the wise man at the end of the total 64 days. After the thirty-second day the king was becoming aware of how much rice he was giving away after he saw 16 wagons being delivered to the wise man. The king then filled with rage called upon the wise man to explain that his royal mathematicians had calculated that the king would eventually be giving the wise man 549,755,830,887 tons of rice. The wise man then explains to the king that he had been happy with just giving the king a service. The king now understands that he should not have forced a reward on the wise man and is happy yet again with another service given to him by the man.

Mathematical Concept:

In the tale, the wise man demonstrates how the reward of rice is an example of exponential growth. There is an extreme growth rate when receiving twice the amount of rice as the wise man received on the previous chess square for 64 days. Eventually the deliverer’s could no longer count individual grains of rice, but they had to count in tons leading to the 16 wagons of rice on the thirty-second day. This exponential growth can be explained by using the formula 2^x when x is greater than 0.

Effective Way to Teach/Learn:

The use of mathematical concepts in a children’s book is a clever way to keep younger students involved in the lesson and the addition of a storyline maintains curiosity about the characters while also introducing numbers and math problems. This is also a good way for students to realize that they will use math in everyday situations leading them to want to learn more about math and concepts.

Mathematics in a Story (B3) Alex Babrak

Blog 3 - Mathematics in a Story

1) The Dragon Pack Snack Attack," by Joel E. Tanis and Jeff Grooters hilariously illustrates the tactics a few dragons used in order to satisfy their hunger. In the beginning, the story depicts several young dragons who are reeking havoc on Earth. They would hunt innocent knights for food and steal their gold. One day, a Dragon named Hobart got really bored of eating knights and snatching their gold. He came up with a brilliant idea: go on a vacation to the beach. As a result, he gathered all of his dragon friends and went to the beach on a remote island. After 200 years of vacationing, Hobart was bored again. Only this time, he was also hungry. They flew off to find something juicy to eat. The dragons roamed cities after cities in search for food. They did not want to eat grown up humans because they believed grown ups were hard to chew. They also did not wan to eat young children because young children are understood to be too sweet. Suddenly, in the middle of searching for food, Hobart smelled something delicious: it was a burger! Hobart strolled to the drive through window and demanded a thousand of everything. Hobart gave the owner of the store all of the gold he earned by terrorizing Knights several hundred years earlier. After Hobart and his friends ate all of the burgers, they wanted more. Unfortunately, the dragons did not have any money. They also did not have any source of income in order to buy more burgers. The owners suggested that they work for him in order to make money. After working several days at Hutburgers, the Dragons were able to make their own profit in order to buy burgers. The dragons were amazing workers. They cooked burgers faster than anyone else, resulting in a higher revenue for the business. Everyone lived happily ever after. 

2) The mathematical concept presented in this book is profit/revenue. The Dragons in this book needed to make a profit out of working in order to purchase hamburgers. They did so by getting a job at their favorite fast food restaurant. After working at Hutburgers, the business had an increase in revenue due to the dragons' hard work. I could also make the argument, that this book presents the concept of slope. There is a positive linear function between the time the dragons spent working and the number of burgers they would be able to purchase. 

3) Literature is an effective way to teach and learn a mathematical concept because it allows you to use imagination in order to understand difficult concepts. Instead of learning through a systems of equations out of a book, it helps people unravel concepts through fun imagination. Also, learning mathematical concepts are a difficult and intimidating thing to do. By adding literature, you are easing the intimidation levels. In essence, literature is a less intimidating and efficient way to learn mathematical concepts because it allows students to use their imaginations. 

Blog Post 3: Mathematics in a Story

1.  The Librarian Who Measured the Earth by Kathryn Lasky and Kevin Hawkes tells the story of the Greek mathematician and philosopher Eratosthenes, who created the field of geography and was the first person to calculate the circumference of the Earth.  While studying in Athens, Eratosthenes became well known for his incredibly accurate chronologies of Greek history.  When he was 30 years old, he moved to Alexandria and later became the Chief Librarian of the Library of Alexandria.  Eratosthenes was determined to create the first book about geography, and more specifically, to measure the circumference of the Earth.   By using mathematical principles related to circumference, arc, angles, and measuring shadows, Eratosthenes determined the circumference of the Earth and created the first book of geography, Geographica. 

2.  Eratosthenes knew that in order to find the circumference of a circle, he could calculate the length of one arc along the circle and then determine how many arcs comprised the circumference.  To determine how many arcs were necessary, he could measure the inside angle of one of the arcs and divide 360 degrees by that number.  Eratosthenes heard that on June 21, the sun would shine directly onto a well in Syene, a city in southern Egypt, and cast no shadows.  Eratosthenes decided to measure the angle of the shadows in Alexandria at noon on June 21, and this angle would be equal to the inside angle of the arc (the arc was the distance between Alexandria and Syene).  He measured an angle of 7.2 degrees.  360 divided by 7.2 equals 50, so he knew that the distance between Alexandria and Syene multiplied by 50 would equal the circumference of the Earth.  He measured the distance between the two cities by hiring bematists, who are surveyors trained to walk with equal steps.  The distance was about 5,000 stades, or 1/10 of a mile.   Through his calculations, Eratosthenes determined the circumference of the Earth to be 24,662 miles. When the circumference of the Earth was measured using modern technology, Eratosthenes' calculations were only off by about 200 miles, even though he measured the circumference over 2000 years ago.

3. Literature is an effective way to teach mathematical concepts to children because the illustrations and story-telling show them that mathematics is not a dull concept.  Children who are visual learners are stimulated by pictures and physical explanations, and literature is effective at teaching mathematical concepts to visual learners.  Additionally, in The Librarian Who Measured the Earth, the authors write that Eratosthenes loved to question the world around him, which is what led to his discoveries.  By instilling the values of curiosity and questioning into children, literature teaches them that math is not a stagnant subject.  There are always new discoveries to be made, which makes the subject exciting.  

Blog Post 3: Mathematics in a story

Pythagoras and the Ratios by Phyllis Hornung Peacook

This book is about two boys called Pythagoras and Octavius. One day Pythagoras heard Octavius played the pipe but it sounded very awful. Pythagoras then starts making his own pipe by measuring the length and width of each pipe. He made 6 pipes in total. The first pipe measured 12 then second pipe is 15, 16,18,20 and 24. Later he compared his pipe with Octavius’s pipe, but Octavius’s pipe was twice longer than Pythagoras.  Pythagoras then tried to change Octavius’s pipe by cutting the length of the pipe. In the end both their pipes sounded very nice.

The mathematical concept of this story presented the trigonometric concept. Intervals are based on simple ratios (1:1, 2:1, 3:2, 4:3), which this creates perfection in the music. The reason Pythoras’s pipe sounded nice is because his ratio is perfect. The lengths of the pipe controls how high or low the sound is.

Literature is an effective way to teach, as it’s easier to understand the concept of the book. If there were only numbers and a few texts, some people wouldn’t understand. Also this book is easy to understand as it shows the calculation and also makes children understand how music and math is related to each other.

Blog Post 3: Shaping Our World

I chose the children's book, Shaping Our Word by Julia Wall to write about. It discusses and analyzes many basic mathematical concepts through the use of aesthetically appealing pictures that children know well and probably see often. Ultimately, the book recognizes the different shapes that each real-life object represents. For this blog post I chose symmetry as my topic because there are many pictures within the book that show symmetry on a more simple scale. The cover of the book alone, a rainbow kite, shows reflection or, vertical symmetry.

The section of the book about symmetry uses everyday objects such as clocks, balls, a lunch sandwich, and more, to illustrate the presence of symmetry in our everyday lives. It shows where the line of symmetry would be for an object of the same shape and relates the sandwich to a square and tells that it has multiple types of symmetry; horizontal and vertical. Likewise, a clock represents a circle and has the same symmetry as a square. The idea of symmetry seems very clear to me now, but I think if I were to have read this book at a young age it would have been a great way to introduce simple mathematical concepts to me.

Literature is an effective way to teach and learn mathematical concepts because it makes young kids excited to learn. Teaching math through literature is a great idea because it allows all children, not just the ones with an aptitude for math, to be excited about math and learn in an easy and fun way. Overall, literature has the ability to connect real world ideas and objects to math, a topic that may not have appeared accessible to children.

Pythagoras and the Ratios: A Math Adventure

In the thrilling sequel to "Whats Your Angle, Pythagoras", Julie Ellis and  Phyllis Hornung Peacock are at it again in "Pythagoras and the Ratios: A Math Adventure". Never have I ever been enthralled in a way similar than I was reading this fine novel. Pythagoras and his cousins want to win a music contest, but first they must figure out how to play their instruments in tune.  While trying to fix the problem, Pythagoras makes an important discovery, notes that sound pleasant together have a certain mathematical relationship!! When Pythagoras applies this ratio to his cousins' pipes and lyres, the result is the best music ever made. It is an amazing story of an amazing kid making a profound discovery and teaching us about math. 

The book demonstrates what the Pythagorean theorem is, that a2 + b2 = c2 in any right triangle. Using this formula, one can solve for any of the sides in any triangle. In the same way that the pipes and lyres on the instruments must have a certain mathematical relationship, the sides on a right triangle also depend upon one another and can be expressed through the Pythagorean theorem. 

If it were not for literature, some kids might have a tough time understanding the Pythagorean theorem (or adults). Literature serves as an important and necessary way of helping people learn complex topics through expressing it in a different medium. If every single theorem or fact I learned was purely through textbook definitions, I would not have a firm or long lasting grasp of it. However, whenever I think of the Pythagorean theorem, I now think of young Pythagoras and his cousins trying to win a music competition.

Emma Qian Blog 3

Blog 3:

Mathematics in a story-Lemonade for sale

1.     The story “ Lemonade for sale” was written by Andrew Einsprunch, and in the book, it talked about a boy who wants to buy a bicycle without enough money. In this case, he chooses to open sell lemonade to make money. In the book, this little boy uses lots of math methods to find out how much money he should spend, and how munch money he should make to buy a bike. He calculates the cost, the revenue and the profits. Finally, he raises enough money to buy a new bicycle by him own.

2.      This book uses so much math concepts to solve little boy’s problems. For example, in the book, the boy use math to calculate how much money he should make and how munch money he should spend as cost. In this case, in this book, it has lots of math words also, like revenue, cost, profit etc.

3.     I think learn math through a book is really interesting and easy, because the math methods are easy to remember and forgettable. For example, in this book, I learn how to calculate my revenue and budget, and also I know how to make money through math ways. In this case, I think it’s a good way to learn math through reading books and people will love it.

Blog Post #3: Mathematics in a story | The King's Chessboard

The book I chose to write about is The King's Chessboard by David Birch, illustrated by Devis Grebu. This book deals with the concept of exponents and exponential growth.

Summary
In David Birch's The King's Chessboard, beautiful illustrations by Devis Grebu tell the tale of a king and a wise man. The king wishes to give the wise man a reward, as the man has performed a great service. While the wise man at first wishes to receive no reward, the king demands he ask for something. Finally, the man figures out his request. Pointing to a chessboard, the man asks that each day, the king give him one grain of rice for every square on the board, doubling in amount each day. So for the first day, he would receive one grain; the second, two; the third, four; the fourth, eight-- and so on. The king, not knowing just how much rice that would amount in and being too prideful to ask, granted his complicated request. Each day, someone was sent to the wise man to deliver the rice. For the first few days, the amount of rice was expectedly little. But soon, the rice started piling up. Before he knew it, the king was sending out tons and tons of rice to the wise man. In disbelief, he called for the royal mathematicians to calculate the number of grains of rice the king had promised-- which turned out to be over 5 billion tons. The king eventually confers with the wise man, and in important lesson is learned about not letting your pride getting the better of you, because even a king can look like a fool. But beyond the moral lesson, there is math to be learned here!

Mathematical Concept
The king wrongly assumed that such little rice could add up to be such an impossible amount. This demonstrates his lack of understanding of exponential growth. As we have learned in class, exponential functions grow much more rapidly than linear ones. Here's an explanation of why:

The equation for a linear function is as follows:

y = mx + b

Because "m" is added an "x" number of times, the repeated sums result in a product.
It could also be written as:

y = b + {m + m + m + m...}

Now, look at the equation for an exponential function:

f(x) = ab^x

Now, "b" is being multiplied an "x" number of times. Which could also look like:

f(x) = a * (b*b*b*b...)

Though it can be a confusing concept at first, it's easy to see that multiplying a number results in a higher product than adding. For the story of The King's Chessboard, the equation would be 2^x, x representing the day. The story explains this complicated concept in a simple manner. This is why literature like this is so important-- and not just for children. Clearly college students can learn from it too!

C. G. Blog Post 3: Infinity and Me

Channing Gatewood
Professor Little
Applied Precalculus
22 March 2015

Infinity and Me

For this assignment, I am using the storybook Infinity and Me by Kate Hosford. This story follows a young girl who consults her friends and family in an attempt to define "infinity." She asks her friends, teachers, and her grandmother what infinity means to the, and she received a wide variety of answers in response. For example, while her best friend instantly thought of the infinity symbol, her school chef used the example of cutting a noodle in half forever -- a thought that Uma, the protagonist, had trouble fathoming. Uma remained in a state of unrest over the intangibility of "infinity," and it was not until her grandmother complimented her shoes at dinner, that she realized that her love for her grandmother was infinite, and that was what infinity meant to her. 

The main mathematical theme in this story is the concept of infinity, and that it is impossible to measure infinity with distinct numbers. Hosford demonstrates this well by using the different characters' perceptions of infinity to represent the various definitions that infinity can have. The first boy in Uma's class attempts to write it in a number, but says that infinity is a number that goes on "forever and ever," showing how there is no end to infinity.

I think that the storybook application is a great one because I could follow Uma's thought process as she learned how to define infinity in her unique way. This is a great model of how we might go through our own process with infinity, and with any large mathematical concept. While math can be very formulaic, sometimes it is best understood when we can explain concepts in a way that helps us understand. That way might be different from someone else's, but, as Uma learned, it can still be right.

Math in a story-Bianca Flores

Title of Book: Two of Everything by Lily Toy Hong

Summary:

There once lived an old, humble couple named Mr. and Mrs. Haktak who lived in a shack and were very poor. One day while Mr.Haktak was digging in his garden his shovel hit something hard, he dug deeper and out came an ancient brass pot. Mr.Haktak decided to take the brass pot home and dropped 5 gold coins and decided to put them in the pot for safe keeping. Once home, Ms.Haktak inspected the pot and accidently dropped her one and only hair pin inside. While looking inside the pot, Ms.Haktak was surprised and pulled out not one but two hairpins and 10 gold coins. Astonished Mr.Haktak decided to put his coat in the pot to see if it would also double. The coat did indeed double and from then on Mr. and Mrs. Haktak worked all night putting things in the pot. In the morning Mr.Haktak set off to the village with a basket full of coins from the pot. While Mr.Haktak was gone, Mrs.Haktak continued to inspect the pot and stood over it. Mr.Haktak kicked the door open since his hands were full, startling Mrs.Haktak. Mrs.Haktak was so startled she fell into the pot, Mr.Haktak running over to save his wife. However instead of there being only one Mrs.Haktak there were now two and in the midst of bickering Mrs.Haktaks, Mr.Haktak fell over into the pot as well and now there were two Mr.Haktaks and two Mrs.Haktaks. One of the Mrs.Haktaks saw this as an opportunity to have company and so from then on the Haktaks built two identical houses with two of everything and inside one of these houses was hidden a big brass pot that the Haktaks were super careful to never fall into again.

Mathematical Concept:

Two of Everything is a great representation of a linear function and how it could be used in the real world. At the beginning of the story, Mr.Haktak has 5 gold coins and after putting them into the pot he then finds the 5 gold coins have become 10 gold coins. Each item that is put into the pot doubles, the number of coins the Haktak have increasing rapidly demonstrating linear growth as eventually they have enough to fill a basket. The expression that represents this growth is 2N for N, the amount of items initially put into the pot, is greater than zero and is then doubled. This story is a great example of a linear function for each time a number of items is put into the pot that number is then doubled creating a constant slope of 2.

Literature is a great way to teach/learn a mathematical concept because for those who learn best visually, storylines can help in making the concept more understandable and relatable.

Blog 3: Math Story ( Ben)

1. I picked Grapes in Math as my picture book. This book consists of many interesting math stories. Each of them has a a picture and several lines of interpretations and hint to help your solve the problem. For example, there is a story called "ant attack". A group of ants are crossing the grassland and they see the picnic and scream, Now these ants on the ground form a unique geometry shape that looks like a square. The question for you to solve is to tell the total number of these ants without count them one by one. Another example is about fan. This is a colorful fan that has a combination of purple, red, green, yellow, blue and so on. Each fan leaf has a different color, Overall it looks like a Chinese traditional fan and become popular worldwide. When summer comes, ladies will hold fans like this and bring themselves breeze. This one asks you to count dots on the fan using a different route.

2. This book utilizes principles like symmetry, number combination and grouping, multiplication and so on. In the "Ant Attack" story, you find a square and calculate how many ants are in the square. There are 4 ants on each side of the square, so 4 x 4 = 16. Then you just add the 3 ants that are left behind, 16+3=19. So there are 19 ants in total. We are be able to solve this problem so easily is because the symmetry of the square. We know that each side of the square has  equal number of ants so we just multiply them. In the "It's a Breeze" story, the fan is a symmetry shape, so we know both sides of the fan have equal amount of dots. 5 x 3 =15. There are 15 dots on the fan.

3. These stories are interesting for kids to learn. Learning through pictures is helpful for people who have difficulties with abstraction and dimension, especially for young kids who are still developing their right brain.  And these interesting lines on the right side of the picture are well phrased like poems. Hints in the bottom offers a chance for kids to brainstorming a while and think about a different route to solve the problem.

Blog Post Three- Jonathan Murray

1. For my post I chose the book "Lemonade For Sale" by Stuart J. Murphy. The book is about a bunch of children, the Elm Street Kids, who are selling lemonade. They keep track of their lemonade sales using bar graphs. They need the money as their clubhouse is falling apart, and their piggiebank is empty. They say if they can sell 30-40 cups of lemonade each day for a week they could get the money to fix the club house. Sheri, a member of the Elm Street Kids, makes a bar graph with the days of the week on the X axis, and the number of cups sold on the Y axis. A graph like this:

  They each have a specific role to play when they set up shop on Monday. Each kid does something to help make the lemonade. On Monday the Elm Street Kids sold thirty cups of lemonade, so they fill in the bar graph up to thirty on the Monday column. The next day, Tuesday, they sell forty cups, so they fill up the Tuesday column on the graph up to forty. It is at this point that Petey the Parrot squawks: "Looking good. Looking good". Petey actually squawks "Lemonade for sale!" so many times on Wednesday that they get a lot more customers. That day they sold fifty six cups, they made it in between fifty and sixty on the bar graph for Wednesday, as they didn't have a spot for fifty six. On Thursday though, they didn't get many customers. On that day they only sold twenty four cups. They put twenty four on the Thursday column for the graph, scribbling in just a little before halfway between twenty and thirty. They figure out why no one really came that day, there was someone juggling down the street from them. The Elm Street Kids meet the juggler, whose name is Jed, and the kids get an idea. On Friday that bring Jed to their lemonade stand to juggle! More people came by than ever before. Their sales were through the roof! In the end, they rebuilt their club house, and invited Jed to join.

2. The mathematical model in this story is graphing. Graphing is represented in the Elm Street Kids' bar graph documenting their lemonade sales daily. In the beginning of the story the graph is empty, but as each day progresses they fill in that day's column with their number of sold cups of lemonade. In this the organization of a bar graph, and how to use it for recording are demonstrated to kids. The reason for both the X and Y axises are shown by how the days of the week are on the X and the number of cups sold on the Y. Finally they sell so many cups on Friday that they cannot even record the amount, showing how you should correctly label your axises.

3. Literature is a great way to teach mathematics. This is because it is a right brained way to teach it, and for right brained people who struggle in math, like me, it is helpful to learn it in non abstract ways. For children with math problems establishing tangible ways to express abstract concepts such as graphs can be helpful for them to get a grasp on the concept. Not only that but picture books are fun, and with that they help make math fun. If math is fun to children they will learn it easier and not struggle, which is incredibly important for them as they grow up and go through school.

Mathematics in a Story- My Lemonade Stand

Mathematics in a Story

My Lemonade Stand by Andrew Einspruch

Marisa Ewing

Blog Post 2

1. The story "My Lemonade Stand" by Andrew Einspruch is written about a boy who wants to buy a bike during his summer vacation. Unfortunately, this young boy doesn't have enough money to buy it. To make some money, he decides to make a lemonade stand to raise money to purchase the bike. He uses many different mathematical concepts through out the book to help him ultimately get his bike, including calculating the amount of materials he needs for multiple batches of lemonade, calculating how much lemonade he should sell, and how much money he will make. Eventually he makes enough to buy the bike that he wanted.

2. This book makes use of many math concepts that carry over into the business world. He uses  algebraic skills to calculate the amount of materials he needs to buy, as well as how much lemonade he needs to make. He also creates a budget using profit/ revenue functions to calculate how much money he will be making from his lemonade stand.

3. I think learning mathematical concepts through literature is very important. When concepts are presented in a lecture, it's sometimes hard to remember how the concepts work and how they can be applied. However, when presented in story form, those same concepts become much easier to remember, and it's very easy to see how those concepts can be applied. 

Blog 3: Tyler Rose Mathematics in a Story!

Tyler Rose

Professor Little

MATH-160-002

21 March 2015

Mathematics in a Story

Blog submission number 3

Due Date: March 23, 2015 by 11:59 pm Eastern Standard Time

Point value: (20 points)

Book: Farmer Will Allen and the Growing Table

Author: Jacqueline Briggs Martin

Illustrator: Eric-Shabazz Larkin

The book I chose was “Farmer Will Allen and the Growing Table”, written by Jacqueline Briggs Martin and illustrated by Eric-Shabazz Larkin.  The book discusses farmer Will Allen and how he grew up on a farm that produced enough food for more than 30 people!  They grew peas, greens, and lima beans.  As he aged, Will did not like to work and plow the land, so he moved to Belgium and played professional basketball.  After shooting hoops, Will decided to move to Milwaukie and bought 6 large plots of land in the city to grow food, like he did back home.  He did this in order to put food on the table for him and his wife.  Unfortunately, he noticed that the soil in the city was not great so he composted and was eventually able to put food on his table and other’s too.

The mathematical concept of “area” is addressed in the book because farmer Will Allen is given a certain area to grow his food (6 city lots).  At this, Will is upset that he could not feed the entire city on just the 6 lots, so he builds greenhouses on each to double his food growth!  This shows that only a certain amount of goods can be produced on an area and in order to make more.  One can buy more lots or use the greenhouses to double the growth!  All in all, the book does a nice job a demonstrating the limits of area in a “real world” setting of farming.  The book further goes on to express that the more area one has the more food could be produced.  Finally, the pictures help demonstrate the productiveness of area in farming.  The more area, the more food production! 

I believe that literature is an effective way to teach/learn a mathematical concept because it helps people conceptualize the idea discussed in another form.  In the book I studied, readers could learn about area from the words on the page and pictures.  Unfortunately, when one is learning math a teacher is not drawing a “real world” example along with the theory’s discussion, so the literature aids in the learning process.  I strongly feel that literature and math should be more integrated, especially with children, because they could gain a better understanding of things that they will learn in the future.