Blog 4 - How to find Slope

Blog post #4- learning how to factorize

Blog Post #3

A. I choose the Grapes of Math by Greg Tang. I remember reading this book in grade school, and my teacher actually had a project for us to "write" another page in the book. I believe Tang uses great visual aid for young children. It provides kids another way of counting; especially when you can count in groups.

B. In the Grapes of Math, it teaches children the concept of symmetry. Within a single group, you can count as many different types of objects. For example, on the section of Win-Doze: counting windows instead of sheep, Tang teaches the reader to instead of counting the windows that has a light in it, to count the windows that have "zzzzzz" in them. It is much faster to count the dark windows verses the windows with light in them.

C. This is one of the greatest children's book because it teaches kids how to count in a different way. I believe children learn better if they have a visual aid in front of them instead of just having someone talk about the concept. Same goes in College, I learn so much more when I have a visual to look at verses just sitting there and trying to figure it our. 

Blog post number 3

A) In grapes of math the author uses real life examples that kids would be able to relate to in an attempt to teach how to count through grouping. The reader see that there a many reasons as to why counting by grouping is much better and easier as apposed to standard counting. This includes counting ants that are moving too fast to count individually. This teaches kids that it is possible to count to much higher  numbers quicker than they ever could have imagined.

B) The concept being portrayed in this book is symmetry. This concept is when you group certain amounts of this in the same number of units. This example is best exemplified when the authors shows that counting fish in groups of four is much better, quicker and more efficient as opposed to counting each one individually. Instead of adding each fish 1+1+1+1+1 etc, it is possible to count through symmetry to count each group of fish in intervals of four.

C) Picture books are in my opinion the best way to teach kids math because it is hard to imagine something one doesn't know for someone who is so young. By seeing pictures, kids can much easily see what is being explained rather than trying to explain a concept without any visual aids. Kids this young need to see what they learn because it is the easiest way to explain what they are learning.

Mr. Archimede's Bath & Linear Functions

For this assignment I chose to focus on the children's book Mr. Archimede's Bath by Pamela Allen. This is a book I grew up reading. In the story, Mr. Archimede cannot understand why his bathtub is always overflowing and is growing sick of cleaning up the mess. One day he decides to find out where the water is coming from. Mr. Archimede fills the tub with just a little bit of water and hops in with his friends kangaroo, wombat, and goat. He cannot believe the water overflows when all the friends jump in and kicks them out one by one, blaming one after another for the mess. Mr. Archimede finds as each friend hops out, the water depth lowers each time, finally concluding that the addition of each person adds 2 inches to the height of the water.

Mr. Archimede's Bath represents a function of the number of people in the tub and the height of the water. For each input (number of people), one output is produced (height of the water). This particular function is linear because the rate of change (2 inches) is constant.

It is important to depict math in not only real life situations but children's books because it is a way to show real world application at a young age. These concepts are important to build off of in the years to come. Literature in general is effective in portraying mathematical situations because it can numbers and formulas and change them into words and situations which is helpful in understand where the numbers and formulas are derived from and how they work in the world around us.

Taylor McCulley

Anita Tjahyadi Blog 3-- "The Math Curse"

1.Once you have selected a book, read the book and write a synopsis (summary) of the book. 
       -The book that I have chosen is called The Math Curse. This book relates to math and to students in a very close matter. The Math Curse, is about a boy and his struggles in finding out that math is everywhere and in everything around him. In the beginning of the book, the little boy first hears how everyday life is basically like a math problem.The next day, he wakes up realizing that he has woken up to algebra when he starts to try thinking of the time in terms of it. As the day goes on, he begins to feel as if math is consuming his life. When everything in his life is transformed into a problem, he turns into a "math zombie". Mathematical subjects like probability turn up when a class treat becomes a fractions problem. Then when he goes to a trip to the local store, he has to deal with counting money and basic math. Finally, He is in a rut and counting the days until he is going to stop seeing math in his everyday life and feels as if he has become a math lunatic. His sister asks him what his problem is, and he responds, "365 days x 24 hours x 60 minutes." Finally, he collapses on his bed, and dreams that he is trapped in a blackboard-room covered in math problems. Armed with only a piece of chalk, he must escape and he manages to do just that by breaking the chalk in half, because "two halves make a whole." He escapes through this "whole", and awakens the next morning with the ability to solve any problem. His curse is broken...until the next day, when his science teacher mentions that in life, everything can be viewed as a science experiment.

2. After reading and summarizing the book, explain in detail the mathematical concept presented in the book.
        - There are many mathematical concepts in this book. There is probability, money counting, adding and subtracting and multiplying complicated, everyday equations in life. This book was based solely on the exploration of everyday life and algebra concepts. When the class treats were distributed, the student is confronted with a problem in fractions-- how many are left if a certain amount is take away?[5/8]?[1/4]?

 3. Explain in your own words why you believe literature is an effective way to teach/learn a mathematical concept.
       - I feel that this book is a good source for people to relate to math because it helps to give a deeper understanding in how math revolves around our world. It helps to show that you do not need to get to stressed over math because you're doing it everyday. If kids were to read this, it could teach them not to panic just because there is a math problem on the board. It could help them to be more comfortable around it and even love math a little more because now they can just see math as little puzzles for them to solve.

Blog post #3- Alexander, Who Used to Be Rich Last Sunday

1.The children book I chose is “Alexander, Who Used to be Rich Last Sunday” by Judith Viorst. In the beginning of the book the main character Alexander is talking about how unfair it is that his brother Anthony and his other brother Nicholas have more money than him. Alexander complains about his lack in money and that he only has bus tokens. Every time Alexander is rich he knows he will end up only with bus tokens, because he used to be rich last Sunday. He used to be rich last Sunday because Grandma Betty and Grandpa Louie came to visit from New Jersey. They brought gifts for everyone in the family, lox for his father, plants for his mother and they brought one dollar for Alexander and his brothers. His brothers and him love money especially him. His mother told him to save the dollar if he really wanted to buy a walkie-talkie, but saving money is hard for Alexander. After Alexander received the dollar he went and bought candy, did multiple bets, lost money, spent recklessly and when he was going to actually save the money he realize he had zero. Alexander tried to gain his money by searching in Pearson’s telephone booth for nickels and dimes that people sometimes forget, but failed. He went to desperate measures by trying to make his tooth to fall out and putting it below his pillow to get a quarter, but failed again. He gave up and told his grandpa and grandma to come back soon.

2. The mathematical concept behind the book is Finance and compound interest. Even though the compound interest formula isn't in the story, it can relate in the context of saving money. It is related to finance because Alexander doesn't know how to manage his money and struggles investing and saving money to buy the walkie-talkie. Alexander the main character starts with an amount of one dollar and every paragraph subtracts the amount he spent in that paragraph eventually leading to zero. I like it a lot because he spent little amounts of money every paragraph and it is written like if he was actually rich. It is very interesting because kids need to pay attention to every amount of money spent and it has an entertaining story with it. What also makes this math concept easy to learn and entertaining is that kids can relate to the reckless spending when their family give them money.

3. Literature is an effective way for children to learn mathematical concepts because it teaches them the fundamentals since an early age and in a fun way. If they learn math in a fun way they will relate math with fun and won’t struggle in the future like most of us do. Children will also know since an early stage i their life that math is completely related to life.

Blog Post 3

Ashley Maddox
The Grapes of Math

Part 1: In the story the Grapes of Math, author Greg Tang teaches readers how to use symmetry and grouping to count, rather than counting individual pieces or objects. Through each example, there is a reason the reader can't efficiently count the number of objects whether it be because the ants are moving to fast, the pizza is hot and ready to go, or because the eggs are about to hatch. Near the end of the story, the reader has learned that when there is a large amount of objects to count, it's better to find symmetry and multiply small groups. Finally at the end, there are answers and diagrams of how to group every picture into symmetric groups.

Part 2: Symmetry is the mathematical concept in the book. Grapes of Math explains symmetry with grouping and lines of symmetry. The most clear example of symmetry through grouping is the scallop example. Rather than counting every scallop, the answer key maps boxes around clearly 3 distinguished groups, so the reader counts 11 scallops in one group, and multiplies 11 by 3, as all three sections are symmetrical. Also the book addresses finding symmetry through lines of symmetry. For example to count bugs in the jungle, the answer key shows that the most efficient way is to draw six lines of symmetry.

Part 3. I believe that literature is an effective way to teach math skills because it gives examples beyond numbers. While someone may not be able to see where an unfamiliar shape is symmetrical, it may be much easier to understand the concept on a pizza, or group of animals. Also following a storyline can help people stay engaged and not get frustrated by number or shapes.

Blog Post #3

Book Title - Is a Blue Whale the Biggest Thing There is?
By - Robert E. Wells

1. The book Is a Blue Whale the Biggest Thing There is? takes the reader in a journey through the idea of size and area. Wells starts off talking about the size of a Blue Whale's fluke and how it is bigger than most animals such as an elephant of giraffe. Through the illustrations he shows the size of the whale when compared to the animals. Then he talks about what if we put 100 whales in a really big jar, and then stacked the jars on top of each other. Then he talks about the jars or whales being compared to Mt. Everest and how small they are in comparison. Then he stacks 100 Mt Everest on top of each other and says that it "would be a mere whisker on the face of the earth". He continues this pattern by talking about bags filled with earths, compared to the sun and then crates of suns compared to the star Antares, then Antares to our Galaxy, then our Galaxy compared to the Universe.

2. The mathematical concept explained in the book is the idea of exponential functions or growth. Each item he talks about is a certain number of times larger than the proceeding object. For example the sun is x times larger than the earth and the earth is y times larger than the whales. If one wanted to find the exponential function or growth they could find the size of the earth and have it divided by the size of the sun and the answer would give the number of times larger the sun is than the earth. Thus the growth factor between the two.

3. Literature is an effective way to teach mathematical concepts because it uses more concrete things to show the math that is being preformed. It is perhaps easier for children to understand that something is 2x larger than something else when comparing it to another object, rather than using just number. Overall it is effective because it applies the ideas of familiar objects and alters those objects using math, and it shows more clear changes.

Blog Post #3

1. Bigger, Better, Best! By Stuart J. Murphy tells the story of three young siblings, Jenny Jeff and Jill who constantly argue over who has the nicest room, belongings etc. Shortly after their family moves into their new home, each child makes the claim that they have the best and biggest room out of the three. After much argument and dispute, no one can decide who's room is superior. Finally, with the introduction of the mathematical concept of "Area", the trio determines whose room is largest and consequently better.

2. In Bigger, Better, Best! the mathematical concept of area is used to determine which child has the largest and overall superior room. In the book, each child measures their room's floor space by placing sheets of paper along the perimeter of two adjacent walls then counting up the number of sheets along each wall. Since the children's rooms are square, they find the area of their rooms by multiplying the number of sheets on each wall to determine the area, and size of the room itself. After comparing room area's, the siblings thus learn who's room is larger and thus superior.

3. I believe that literature is an effect way of teaching mathematical concepts because remembering short and simple stories is often easier to remember than complicated math lessons. Also, using literature in math enhances math concepts understandability in that it provides students with easy to use and memorable examples. And everyone could agree that making math easier is a good thing!

Blog Post #3

THE NUMBER DEVIL

1) The Number Devil is a children’s novel written by Hans Magnus Enzenberger. The Number Devil is about a young boy by the name of Robert who suffers from mathematical anxiety due to endless amounts of boredom in class. Robert experiences a continuous dream that involves falling down a slide that results in getting eaten by a huge fish. Throughout the novel Robert is visited 12 times by the number devil teaching him a new math technique each night. For example, Robert learns about infinite number, negative numbers, prime numbers, natural numbers, exponential numbers, irrational numbers and last but not least infinite numbers. After the 12^th dream, Robert no longer suffers from mathematical anxiety and is able to interpret what he learned from the math devil in class. 

2) On the second night that the devil visits Robert, he teaches him the math concept of exponential numbers through hopping numbers because they hop from themselves to another multiple. Such as 2^2= 4, then 2^3=8, the number hops from 4 directly to the number 8, when only the exponent is increased by 1.  

3) I think literature is an effective way to teach math because literature is read very closely with attention to detail. So if mathematical concepts are being used within literature, people can easily identify the concept and analyze it to the point where they understand it and how it relates to the text. It can effectively teach young children and young men concepts that are not entirely understood, or even completely teach a new concept to a young child or young man. 

Blog Post #3

THE VERY HUNGRY CATERPILLAR

1) The Very Hungry Caterpillar is a children’s book written by Eric Carle. The story begins at night with a little egg on a leaf, which then evolves one Sunday morning into a very small and hungry caterpillar. He began looking for some food because he was hungry. On Monday morning he ate through 1 apple, but was still hungry. On Tuesday he ate through 2 pears but was still hungry. On Wednesday he ate through 3 plums but he was still hungry. On Thursday he ate through 4 strawberries but he was still hungry. On Friday he ate through 5 oranges, but he was still hungry. On Saturday he ate through many things and then had a stomach ache. Then came Sunday, he ate through a nice green leaf and then felt much better. After that he wasn’t hungry anymore nor was he small, he was large and built a cocoon and two weeks later evolved into a butterfly.

2) The Very Hungry Caterpillar demonstrates constant rate of change. The caterpillar, as the days of the week go by, increases his consumption by a factor of 1 each following day. In other words, Monday he consumes 1, Tuesday 2, Wednesday 3, Thursday 4 and Friday 5. Up until Friday the book demonstrates a constant rate of change of 1. After Friday I could say that the book also partially demonstrates exponential growth because on Saturday he eats about 10 things, meaning from one day to the next he increases his consumption by a factor of 5, not 1. This book does a well job of showing a constant rate of change, then a little bit of exponential growth, to an extent.

3) I believe literature is an effective way to teach a mathematical concept because it demonstrates mathematical concepts primarily in very simple and understandable ways, such as the numerous amounts of children books. It can easily teach young children how to count, as well as older children and young men to better understand concepts that are taught in the classroom.  

Blog Post #3 - The Number Devil - Paul Hernandez

The Number Devil: A Mathematical Adventure is written by Hans Magnus Enzensberger and illustrated by Rotraut Susanne Berner. The Number devil is about a boy named Robert who is afraid to do math on his own. Robert tends to dream a lot ,and he is visited by the number devil in his dreams. Throughout the story the number devil teaches him many math terms such as prime numbers, negative numbers, natural numbers, irrational numbers, infinite numbers, and exponentiation. The number devil starts with explaining the number one to robert and gradually explores more concepts as each dream happens. Robert experiences twelve dreams where the number devil teaches him a new math skill in each dream. The number devil uses examples such as Robert's classmates to introduce mathematical concepts. It is later introduced that the name of the Devil is Teplotaxl. By the end of all twelve dreams, Robert is not longer afraid to tackle math on his own and is able to use his math knowledge and experience in class.

In the first chapter, the number devil explains the number one and how if you keep on adding ones together they will eventually make bigger numbers. He later tells Robert to multiply 1 x 1 = 1, then 11 x 11 = 121, then 111 x 111 = 12,231. This is an example of exponential growth .because the larger the numbers would create a larger outcome

I think literature is an effective way to learn mathematical concepts ,because it brings perspective to math. For example, if I were to use a story about candy to explain basic multiplication or addition it creates a world that can be visualized in order for it to relate to a student or young child. Literature can also relate math to real world applications ,so they can show their actual importance instead of just relating to math and that's it.

Grapes of Math

1) In the children s math story, Grapes of Wrath, the author takes us to many different places where you need to count quickly. to do this you need to look at the symmetry of the objects in question to see if you can find the pattern and count quickly. When you reach the end of the story you get to learn all the ways to see the symmetry and patterns in the pictures.

2) The primary concept of the book Grapes of Math, is finding symmetry to be able to make quick calculations. For example, in a perfect diamond shaped school of fish, it's easy to quickly assess that there were 4 lines of 4 fish. instead of counting each fish you can just count 4+4+4+4=16 

3)  Literature is an excellent way to teach and learn a mathematical concept because it gives a person a different outlook on the concept. In the case of children's books, the concepts are not only expressed literally but also visually in a creative way. 

Blog post #3

Blogpost #3

Ana Maria Lopez

Topic: Exponential functions

Book title:  The Kings chessboard

Author: David Birch and Illustrator: Devis Grebu

1.          Summary: In a far away land, the amazing King of India orders to his kingdom that the wise man should be rewarded for his useful services. The wise man strongly insists that he is just rewarded with just having the honor to serve the king. Yet, this was not enough for this king. After insisting, the wise man says: “Tomorrow, for the first square of your chessboard, give me one grain of rice; the next day, for the second square, two grains of rice; the next day after that, four grains of rice; then, the following day, eight grains for the next square of your chessboard. Thus for each square give me twice the number of grains for the square before it, and so on for every square of the chessboard”. Not knowing the real trick the King agrees. The wise man begins to receive large amount of bags of rice. At the end, they both end agreeing to end the rice deal but yet the wise man continued to serve the king.

2.         The mathematical concept presented in this story is the exponential function. In this case, the chessboard has 64 squares; in this case it would be 64 days. In this case, as the wise man descried, he received 1 grain on day 1, 2 grains on day 2, 4 grains on day 3, 8 days on day 4, 16 grains on day 5, 32 on day 6 and so on. In this case, the number of rice grains doubled every day for 64 days. At the beginning, it might have seemed, to the king and to many others who read the story, that the number of grans of rice was small. But as the numbers became bigger and they kept doubling the number of grains of rice, the amount of rice became really big. This situation can be modeled by the function 2^n.

3.          In this case, the use of a simple pictures and a very straightforward plot, facilitates the understanding of the exponential function. In this case, the author does a really effective job on, very clearly and basically (with simple rice grains), explaining such a complex topic. In this case, this situation of “ the King’s Chessboard” illustrates the effect of doubling. Additionally, when applying a mathematical concept to a real life situation, students in general can understand the concept even better.