Blog 4, Lineal Growth

Part A

Linear Growth
Good Afternoon class, I am unable to attend this lecture on linear growth in person, so I am going to attempt to educate all of you on 'Linear Growth' in this document.  I am first going to describe what it is, I am going to show examples, lastly I am going to give sample problems you can educate yourself and try for yourself on.

What is Linear Growth?
Linear Growth occurs what you have a quantity, that grows by the SAME absolute amount in every unit of time.  In other words (you are getting older every day by the same growth rate of how old you are, so for every 365 days your age goes up by one number.)

Linear growth example
In order to calculate linear Growth, imagine that a graph shows your hight change from the age of 5 years old to 15, making that 10 years of hight growth.  If the graph shows an upwardly sloping line, you are experiencing linear growth.  Calculate the linear growth of your hight the same way you would calculate the slope of the line.  Suppose the x and y coordinates on the graph are (5,4) and (10,5).  This would mean that age of 5, you were 4 feet tall, and age of 10, you were five feet tall. Calculate the rate of linear growth by dividing the difference in height by the difference in time as follows: (5 feet - 4 feet) / 10 years - 5 years) = 1 Foot / 5 Years.

This means that you grew 1 Foot in 5 years.


Example of baby growth rate, in a linear model. 


On the left, this linear model started when the baby was 20 inches in length, wile on the bottem, you have the growth period in days. this is an example of linear growth because the growth rate is the same absolute amount every unit of time.











How to calculate linear growth
- Suppose you are putting a fixed increase in marbles in a bucket every day.

-Choose the amount of marble growth each day = 200
(Hint: choose a whole number for your growth rate, rather than a percent.)

a. Fill in the following chart:

Day (t) Population (p)
t = 0
(1) 100

t = 1
(2) 100 + 200 = 300

t = 2
(3) 100 + 400 = 500

t = 3
(4) 100 + 600 = 700

t = 6
(7) 100 + 1200 = 1300

b) find the linear equation in the form of p = mt + b (y = mx + b), which gives the marble population p,t days from 1.

Answer: p = 200t+100
Explain: using the slope intercept form, with slope=growth rate = 200, intercept = initial population = 100

c) use your equation in part b to approximate the marble population by day 25.

d) use your equation in part b to approximate how many days it would take to reach 7000 marbles in the bucket.

blog 3-- the king's chessboard

1. I chose to read the children's book "The King's Chessboard" by David Birch, illustrated by Devis Grebu. It is about a wise man in India who was summoned to appear in front of the king and he was rewarded. The king would not take no for an answer and demanded the wise man to choose a reward for his outstanding services for the king. He finally decided that he wanted a grain of rice for each square of the king's chessboard but doubled each day so for the 2nd day he got two grains of rice, the next day 4 grains of rice, and so on. The king seemed confused and the queen wanted him to ask how much rice that would be- he soon came to realize that when numbers are growing exponentially, they grow to be much bigger than would have originally thought.

2. "The King's Chessboard" demonstrates a clever way to show how to use exponential growth in a fun way and how it can be applied in real life situations. The wise man presents the king with a reward of a grain of rice, doubling with each day and chess square. This book did a super creative job of explaining this math concept and showing a real-world application of exponential growth.

3. Literature can be quite effective in teaching math concepts because it adds a level of creativity that helps people remember concepts actually very effectively. Story narratives are much easier to remember because the story makes the concept much more memorable.

Ali Shapero

Blog #3-The Math Curse

The Math Curse

1. The Math Curse, written by Jon Scieszka is a math story that talks about a variety of math principles. The story begins with a girl(unnamed) waking up only to realize that each and every daily activity of her life can be applied to math. The story goes through an entire day of her life and discusses all the "problems" (haha math pun) that just never seem to let up. When she wakes up, she has to use math for time management in order to make it to school on time. While she's eating breakfast, she ponders how many quarts are in a gallon while she pours milk into her cereal, and a plethora of other conversions. Throughout the day, she deals with simple addition, subtraction, division, fractions, conversions, and probabilities. The teacher's name is even Ms. Fibonacci! My personal favorite math issue that this girl experiences has to do with scales. The Mississippi River is 4,000 km long, and an M&M is about one cm long. How many M&M's would it take to measure the Mississippi River? When the girl returns home from school, the math does not end here. Even dinner has math in it-here she ponders logic with True/False statements. She finally gets so fed up with math that she decides it time for bed, where of course she still can't stop thinking about it! 

2. I think the point of this book was express to young children just how important and prevalent math is in our daily lives. It may seem trivial to have to learn geometric proofs, linear equations, or find meaning in learning the quadratic formula at times. I think this book does a great job of showing that math can indeed be fun and easy and that it is an important skill to have. Although this book is aimed at children ages 6-9 it definitely contains some information that is appealing to adults, like the Quadratic formula and the Fibonacci sequence. It did not discuss one single math principle in depth, rather it touched on a lot of math ideas briefly. The one that I found most relevant to what we are learning in class right now is conversions and scaling. 

3. I personally think that literature, illustrated literature in particular is an effective way to engage children in math for multiple reasons. One being that I think it simplifies math by showing children that math is not just numbers and equations and uselessness, it can be applied to nearly everything! By adding a fun story, cool pictures, and a relatable subject, kids are definitely more intrigued and attentive. Times tables, story problems, or simply just writing on a white board sometimes isn't enough for children to understand or make any sort of connection with math. As a child, I loved reading picture books-no matter the subject. I know many kids love reading as well and could perhaps like math more if they read a picture book about it. Overall, math is a very important subject for everyone to learn and understand and that's why it is important to make it appealing to children through their interests-such as reading and looking at pictures!

Blog Post 3 -->Jonathan Lencki

Blog post #3

Jonathan Lencki

The Kings Chessboard by David Birch

Part A:

         A Wiseman does a favor for the king and the king gives the Wiseman a reward for his favor. At first the Wiseman doesn’t want anything for his favor until the king persists to return the favor threatening him that if he doesn’t ask for anything he will wish he had. The Wiseman then looks towards the kings chessboard and decides on his favor. He asks that the king give him a grain of rice for the first square on his chessboard, the next day he asks for 2 grains for the next square, the next day, four grains and to double the amount of rice everyday for every square for all of the Kings 64 chess square. The king begins to think to himself how many grains of rice he would have to emit by the time the favor is over and he is totally unsure, being custom to only giving pounds of rice. The queen then suggests to the King to simply ask the Wiseman how much rice that is. Being a proud man, the King refuses to show the rest of his chamber that he cannot count deciding to not ask the Wiseman the question. The king finally grants the Wiseman his requests and his councilors erupt in laughter at the Wiseman’s strange request. The Wiseman then bows and leaves quietly. Later in the day the Wiseman is given his first grain of rice by a Kings servant in splendid dress, after receiving it he places it on the first square of his chessboard. The King, hearing of the Wiseman’s action, then places a square of rice on his chessboard. The Wiseman continues to receive the increasing grains of rice everyday until on the eighth day, instead of receiving rice from a Kings Servant, a normal rice worker appears, delivering the Wiseman’s 128 grains of rice. The King soon forgets about the Wiseman and his rice leaving the counting and distribution of rice to the Weigher of The King’s Grain: 256 grains of rice and then 512 and then 1024. The Weigher of The King’s Grain now has to spend his whole day counting rice so he begins sending the Wiseman an Ounce of rice. Four days later the Wiseman receives only 16 ounces, he takes one grain of rice for his chessboard and gives the rest to a beggar. Soon the Grain Weigher realizes that everyday he will continue to lose half as much rise as he had the following day, ultimately going to The Grand Superintendent of The King’s Granaries; when he gets there however he panics’ and is unable to tell the superintendent of the extreme loss of grain. Nine days later the superintendent sees men carrying four sacks of rice to the Wiseman’s house. Realizing how much rice is being given away he rushes to the King’s palace. The King however is away on a hunting trip so he is unable to order the discontinuation of the deliveries. Soon, the Wiseman is receiving tons of rice everyday. When the King returns he hears cheering from the town and sees full carts of his rice being taken away. The king calls the royal mathematicians to his chamber and is told that the total amount of rice after the 64 days is Five hundred forty nine billion seven hundred fifty five million eight hundred thirty thousand eight hundred eighty seven tons. Appalled by the Wiseman he demands him to make a new request because the Kings doesn’t have enough rice to get through this 64 days. The Wiseman is satisfied with his plan and then asked the King a strange question: “are you satisfied”. Seeing all the happy people in the town the King happily answers that he is in fact satisfied. The Wiseman continued to serve the King many times again but never for reward.

Part B:

Clearly this elaborate story details the function of Exponential Growth. The King doesn’t even think about how every day he would have to double the amount of rice from the last day and ultimately makes the mistake of being mathematically short sited. Through the reading of this story you gain a great perspective of the pure mass exponential numbers have especially when given such a large window of growth (64 days). The expression the represents this growth pattern is N^2 where N represents the grains of rice being doubled from the day before.

Part C:

By explaining a fundamentally challenging concept through a very basic story, the reader is able to grapple with the concept of doubling more fully then if he or she were to be simply lectured about exponents. Through the readers engagement with the story they are able to see how the mathematical concepts can function in real life, while also getting some great morals along the way.

Blog 3

1. For this blog i decided to read Lemonade for Sale by Stuart Murphy and illustrated by Tricia Tusa. The kids in this story, Meg, Matthew, Danny and Sherry (and the pet parrot, Petey) are apart of the Elm Street Kids club. They realize that their club house is pretty run down so in order to get money to rebuild it, they decided to sell lemonade. Danny said that if they were to sell 30 or 40 cups a day, they would be able to get enough money. On Monday they set up their stand and had the parrot get people’s attention by screaming “lemonade for sale!”. The first day they were able to sell 30 cups and as the days went on their sales began to increase. On Thursday however, their sales dropped because a Juggler down the street was stealing all of their customers. In order to fix this problem, Sherry came up with the idea to have the juggler, do his juggling next to their lemonade stand that way they wouldn’t lose any more customers. This plan worked and they were able to earn enough money by Friday to rebuild their clubhouse.

2. The mathematical concept that is shown in this book is graphing. Once Danny suggests they should sell lemonade, Sherry exclaims that she would volunteer to keep track of how many cups they sold each day. She says she will list the number of cups along the side of the graph (Y-axis) and the days of the week along the bottom of the graph (X-axis). As the days go on and their sales increase, Sherry fills in the bar graph to show the other members of the club how well they are doing. When sales drop on Thursday, the kids were able to physically see something was wrong, which led them to investigate and find out about the juggler down the street. The graphing was also helpful because on Friday it showed that their sales were over the top, which meant they had earned enough money to fix their clubhouse. This story does a great job of explaining how to set up a graph by discussing the x and y axis and also it also shows how helpful graphs can be when tracking items or events.

3. I think literature is effective in teaching mathematical concepts because it is different. When writing notes on a board or verbally explaining a concept can get boring and kids, especially younger kids, tend to lose focus. By putting it in a story it grabs the attention of the kids and it helps them understand the concept and how it works in a different way.

Liam Mazzara
Blog 3
11-19-15


1.
Less than Zero by Stuart Murphy & Frank Remkiewicz is a picture book about a little penguin named Perry than wants a ice scooter. He dad tells him that he can buy himself one and that they are 9 clams. At first Perry has 0 clams but from doing odd tasks around his house, Perry earns the clams he needs. He keeps track of his process through using a graph with a x-axis of days of the week and a y-axis of clams he has earned. This book shows the mathematical concept of graphing equations.

 2.
The book explains the math concept of graphing. Graphing shows the relationship between two units, in this case, days and clams.

 3.
I believe that using visual representation of what is being is explained is a very effective way of teaching. By putting a concept into the context of a story that child can see more clearly, if this happens then I do this and then if this happens, I do this. In this case, I earned this much money in one day, I’m going to graph that I made this much money in this day and now tomorrow I don't start from zero again, I start from the amount of money I made yesterday.

Blog 3

Mathematics in a story

Lemonade for Sale by Stuart Murphy
1. This children's book is about children from the Elm Street Kid's Club deciding to try to make money by selling lemonade at a lemonade stand in order to fix their falling-apart clubhouse. The kids,  Sheri, Matthew, Meg, and Danny all work together.  They set up a lemonade stand and had Meg's parrot, Petey, yell "Lemonade for sale!" as people walked by.  Matthew squeezed the lemons, Meg mixed in the sugar, Danny shook it up with ice.  After each day of selling lemonade, Sheri would keep track of the number of of cups of lemonade they sold each day on a bar graph.  For example, they sold 30 cups in the first day.  They were doing well selling lemonade until a juggler, Jed, stole the attention they had been getting at the lemonade stand.  In order to fix this problem, Sheri talked to the juggler and they agreed that the kids would set up the lemonade stand right next to Jed juggling in order to increase sales.  The plan worked wonderfully and the kids were able to make enough money to rebuild their clubhouse by the end of the week!

2.  This book introduced the mathematical concept of bar graphs. The kids calculated that they could sell about 30 or 40 cups of lemonade a day for a week in order to make enough money to fix the clubhouse.  Sheri, decided to make a bar graph with the number of cups on the y axis and the days of the week on the x axis. Every day Sheri kept track of how many cups they sold.  The first day they sold 30 cups then the second day they sold 40 cups. Each day Sheri filled in the bar graph keeping track of the number of lemonade cups they sold.  The third day they sold 50 cups.  The forth day however, their sales started to decrease and they only sold 24 cups that day and filled in the graph with corresponding numbers. By looking at the graph and noticing the decrease in numbers they realized that they had to do something in order to keep up the original rate of lemonade sales.  Once Sheri talked to the juggler, Jed, and the kids set up the lemonade stand right next to Jed, they sold the most lemonade that day then they had any other day.  Their sales were over the top of the size of the bar graph which meant that they had made enough money to rebuild their clubhouse.

3. Literature is a very useful way to introduce mathematical concepts because it makes it fun.   It is a lot easier to read an interesting story about kids and a lemonade stand in order to learn how to make a bar graph rather than trying to learn without a fun context. After a child reads this book, Lemonade for Sale, they have learned about keeping track of numbers on a bar graph without even having the intention of picking up math skills.

Carly Roggensack

“Lemonade for sale”  by Stuart J. Murphy,is about a group four kids and their side kick and their parrot Petey who have decided to sell lemonade to make money and fix up their club house. They then created a graph to keep track of their sales.For the first three days the graph had a steady increase in sales and then there is a noticeable drop in sales. They noticed that it was because of the neighbor down the street. The neighbor had been getting their costumers to come to his house by juggling for them. They came up with a smart idea, and asked the juggler to go juggle over by their lemonade stand and the sales then went through the roof. “Lemonade for sale” shows a way of graphing showing economics of a company. It’s teaching you about producing and consuming. They produce the product of lemonade and then sell it and they watch their money increase to decrease to increasing even more. It shows that your economic growth can easily go up and down. This book does a great job on explaining the way graphs relate to the real world. I think literature is an effectives way to learn a mathematical concept because it shows you exactly how the graph is being done and why it is changing. You aren’t just plugging in numbers to a formula, you are actually seeing with your own eyes. 

Blog 3

1.) Lemonade for Sale, by Tricia Tusa
     The children on Elm Street thought of the idea to make a lemonade stand to make money so that they could rebuild their clubhouse that was falling apart. Meg, Matthew, Dani, and Cheri were talking about how much money they bet they could raise within a certain amount of time. Cheri came up with the idea making a bar graph to show how many cups are sold each day they sell lemonade at their stand. They decided to put the days of the week on the x axis and the number of cups sold on the y axis, making the number of cups sold dependent on the day of the week. Throughout the week Cheri kept track of how many cups were sold. Monday they sold 30 cups of lemonade. Tuesday they sold 40 cups. Wednesday the team sold 56. But on Thursday no one came to the lemonade stand, and they were selling fewer cups. They looked around the corner to see someone else juggling on the corner. Everyone was there, so the kids went over and asked Jed if he wanted to juggle at their lemonade stand while they sold lemonade. Jed agreed and the next day the number of cups sold went over the bar graph they had made. In the end they made enough money to fix their clubhouse and Jed joined their clubhouse.

2.) In Lemonade for Sale,  Tricia does a good job of explaining how you can represent everyday data on a graph. Whether its a bar graph or a line graph we can represent our data in a way that is easier to understand and see a curve in sales or see the increase/decrease. She shows the decrease on the graph on Thursday when they don't sell many cups because of the new guy on the street. But then also shows how it can sky rocket and increase like it did on Friday. The graph helps them see how many cups they sell each day. The book shows how to use the input and output ( X and Y) on the graph and also references how to label them.

3.) Literature is a good way to explain and teach mathematical skills because you can view it in a more realistic way and puts it in better perspective for you. It applies it to real life, and sometimes people learn better than way or they learn better by seeing it in an actual picture book. They can actually picture it rather than just trying to analyze it on the board. Its a good way to use imagery to pick up on a concept.

Samantha Wright

Blog 3: Mathematics in a story

Title: Stacks of Trouble by Martha F. Brenner, Illustrated by Liz Woodruff

 


1) In the story Stacks of Trouble by Martha Brenner, it uses detailed illustrations to show a young boy named mike who needs to clean up the house before his mother gets home. His mother left a list of all the chores that he needed to do, mike attended to all of his chores except the dishes. Mike noticed the dishwasher was broken and there were very few dishes that needed to be cleaned, so mike decided to wait to wash the dishes. Instead mike spent time avoiding washing the dishes by being with his brother and sister, only to learn how fast dirty dishes can multiply when he tries to avoid them.

2) Stacks of Trouble provides a great example through detailed imagery to show the use of exponential growth and how it works in real life. In the beginning of the story, Mike started off with three rows of four dishes, totaling to the amount of 12 dishes. After mike, his brother, and sister ate lunch, mike then had a kitchen table with more dirty dishes. Mike did the calculation "2 dishes * 4 people", he then had an additional 8 dirty dishes, the number of dishes grew rapidly. This book represents an exponential growth pattern of 2^n for n greater than or equal to zero, it also presents a step by step process of how exponential growth starts.

3) I believe literature is an effective way of learning a mathematical concept because it incorporates stories into the teaching and learning of mathematics, as well as building a conceptual understanding of math skills through illustrations. It also keeps the reader engaged and motivated to want to learn and read more.

Blog #3 Hayley Pawloff

Hayley Pawloff

Goldilocks and the Three Bears
By: Robert Southey

 a) The story "Goldilocks and the Three Bears" is about a little girl who stumbles upon a house which she enters.  When she's inside the house she finds three bowls of soup- one of three is just right.  She then tries to find which chair is perfect for her of the three at the table.  Lastly, she tries out the beds in the home and tries to find the one that fulfills her needs.  To her surprise the three bears come home and see the all of the damage that Goldilock's has done.

b) I choose the short story Goldilocks because of the obvious repetition of the mathematical concept of probability. Goldilock's has found multiple sets, each with their own object in those subsets.  The concept of probability works out here because by the knowledge of knowing the first bowl of porridge is too hot, and the second too cold, it is easy to make an assumption that the third one may be in between.  Once she goes through the chairs, and ends at the choosing of the proper bed, there is enough information Goldilock's has gathered to know theres a probability that one of the things in ever subset she observes, will be just right for her.

c) I find literature to be the most effective way of me learning and remembering information.  In mathematics I've found my whole life its always easy to understand a fraction if you have six apples in front of you, and the teacher takes three (physically) away, it's easier to grasp the concept of fractions and simplification, because you could be teaching how to get to 3/6 to 1/2.

Blog 3

1 Hunter

1.     In the story 1 Hunter  by Pat Hutchins, depicts the adventures of a hunter on his journey through the jungle as he counts the different animals he sees on his journey. The story begins with the single hunter and continues to add 2 elephants, 3 giraffes and so on. The story does not use many words but the images that are shown are very colorful and descriptive in themselves.

2.     The story 1 Hunter explains the concept of linear growth. Because as each group of animals is found the original number gets added by one. The equation in other words is f(x)=x+1. X being the previous number. For example x=1 hunter, f(1)=1+1 which then results in f(1)=2, 2 being the number of elephants which follows.

3.     Literature is a very effective way to learn a mathematical concept because it allows people to understand the concept in a far simpler way and can provide visual aid to those who need it.

Blog 3

Jack Langone

Grapes of Math

1. I read the book "The Grapes of Math" by Greg Tang. This book features a different poem on each page. Each poem tells a math riddle and has a picture that relates to each riddle. This book's main demographic is obviously children, and uses pictures to teach kids basic counting principles.

2. In this book each little poem demonstrated very basic mathematical ideas like adding, subtracting, and multiplying. Greg Tang teaches kids, or anybody reading the book, that it is faster to subtract from the whole number rather than just adding each unit. You also learn that it is easy to multiply sometimes. For example, on one page there is a pizza with 3 mushrooms on each slice (there are 6 slices). So he is saying it is easier to do 3x6 rather than count each individual mushroom. The book does a great job of teaching these concepts to a younger audience using fun examples and illustrations.

3.  Math is a very abstract thing when you think about it. Putting real world examples can always make things easier, especially when you are teaching it to a younger audience. Literature uses these real world examples and pictures to represent mathematical concepts.

Blog 3: mathematics in a story

The children’s book I decided to read was the King’s Chessboard by David Birch. When the wise man refuses to accept a reward for his service to the king, the King insists and so the wise man asks for a payment of rice for each square of the King’s chessboard, and for the amount to be doubled each day. He then reaches to the end of the board in 64 days. The wise man asks for one grain of rice for the first square of the chessboard, two grains for the next square, four for the next, eight for the next and so on for all 64 squares, with each square having double the number of grains as the square before. The emperor agreed. This becomes tons of rice, and the King realizes his error. This book has a clever plot to it, and is a great way to teach kids about exponents and exponential growth.

This book is a great way to show and teach exponential growth. With the plot you are able to understand the the effects of exponential growth in a pattern and able to to describe this pattern with a algebraic expression. In the story you have to find the number of grains for the 64th day. By the end of the period the King would have given out  274,877,906,944 tons of rice.
The exercise of working through this problem is used to explain exponents and exponential growth because with 64 squares on a chessboard, if the total number of grains doubles on successive squares, then the sum of the grains on all 64 squares is 1+ 2+4+8..and so forth for the 64 squares. The number of grains on the second half of the chessboard is  232 + 233 + 234 ... + 263, for a total of 264 − 232 grains of rice (the square of the number of grains on the first half of the board plus itself).This story helps show how fast exponents like doubling, and how they are shown everywhere around us.

Margot Hudson
11/17/15
Blog 3

a) I read "Lemonade for Sale" by Stuart Murphy, illustrated by Tricia Tusa. In the story, a group of kids and a parrot make a lemonade stand to pay for a new club house. The children predict 30-40 cups of lemonade per day for a week will pay for a new clubhouse. On the last day, the children only sold 24 cups because the new neighborhood juggler was taking all of their customers. However, one of the children asked the juggler if he would juggle next to the stand.  The children sold more cups than any other day as a result.

b) This book demonstrates the concept of bar graphing. Each day, one of the children would mark the amount of cups sold to compare day by day sales. At the end of the week, each mark represented a day and the amount of cups sold, making it a bar graph.

c) I think literature is a good way to teach a concept because its straightforward and easy to understand. This book teaches bar graphs in such a simple context that it's almost impossible to not understand. It also includes more engaging material than a math class would so it's easier to pay attention.

Anthony P-Hungry Cata

The Very Hungry Caterpillar is a children book designed, illustrated and written by Eric Carle, first published by the World Publishing Company in 1969, later published by Penguin Putnam. A green baby caterpillar hatches from an egg, and from birth he experiences a perpetual craving for food. He eats through fruits on five days, one piece on the first, two on the second, and so on up to five, then experiments with a wider variety of foods. Soon enough he eats too much and nauseates himself. After recovering he spins a cocoon in which he remains for the following two weeks. Later, the caterpillar emerges as a bright, colorful butterfly with large, gorgeous, multi colored wings.

Linear growth means that it grows by the same amount in each time step. The one fruit can represent linear growth because its going up by 1 each day. whither it be the same fruit or different its staying constant through out the book.

I believe Children’s books are a great way to teach due to the many bright pictures that catch kids eyes. A picture book is a lot less boring then a textbook or a novel. Kids can’t read as well at a young age so these pictures can help the children understand the full meaning of the subject.

            

Blog 3

For this Blog I read 'Lemonade for Sale' by 'Stuart J. Murphy.' This story had a fun illustration and story line to help children learn graphing.  There was a club that neighborhood kids were into, and they  needed enough money in order to fix their club house that needs some repairing.  They were a relatively large group of kids and had used cups, water, sugar, and lemons in order to accomplish their funds for their club house.

  During their lemonade sales, they were using a graphing bar day to day showing how many cups they have sold during the week, on the left side of the bar, they had numbers going up indicating how many cups sold, on the bottom was the week days.  The graphing had helped the kids know exactly how they were doing prior to the last day, to be able to compare how their sales were going daily.  This was a good thing because at the end of a day, they had realized thank you to the graph bar, that they have sold very little cups of lemonade compared to the other days that they have sold lemonade.

In real life, The same graphing that the kids in the book had used is very useful for every day life,  Just how the kids found out that they lost sales one day, thanks to the graphing that they had used, this would be beneficial for real life decision making and tracking.  You can use it for your savings account, or your investment portfolio to have a feel how you are doing compared to the prior day.  Personally I use this for My stock investment portfolio, it helps be realize how I have been doing.  Underneath here is a example graph that can be used in many different ways.

The grapes of math

1. I chose to read the grapes of math by Greg Tang and illustrated by Harry Brigs. The book is filled with different simple math problems to teach children basic concepts for their future math careers. The book is filled with cute colorful pictures to keep you intrigued the whole time, and uses riddles to format the problems to make it a little bit more fun for the kids. The book doesn’t necessarily have a synopsis, as every riddle has it’s own story, rather than all following one plot.  The book uses creative riddles with cute illustrations like snails or shells and teaches kids short cuts to make solving math problems more efficient.

2. The most prevalent concept in this story is the counting principle. The book illustrates different counting techniques and using units. The different counting techniques are given in the instructions of each riddle. For example, “the  snail parade” teaches kids that rather than counting individually each snail, they can calculate the amount of snails that should be in the given area and then subtract how many are missing. The same concept is also shown in the “Large pizza to go!” riddle. It provides the idea that rather than counting each individual mushroom on the pizza, you can count half of the pizza and then multiply by two.

The book also teaches units by providing a different item to be counted for each riddle. By doing this it gets children in the habit of writing what unit they are counting. By jumping from snails to mushrooms, to dots on dice, they realize that writing the units of what is being calculated is important to showing the proper answer and beneficial to communicating in the math world.

3. Literature is an effect way to teach math because using words to explain numbers is more beneficial to some students, especially when explaining why we use the concepts that we do in math, and to explain the process of solving equations. Without using literature, people essentially wouldn’t be able to learn math. You need to use words to explain numbers, especially to young children.