Five Little Monkeys Jumping on the Bed

In Five Little Monkeys Jumping on the Bed by Eileen Christelow, a fun childhood favorite book tells the story of five little monkeys and their escapades before they go to bed.  Before they can reach their eventual slumber, they must first bathe, put on their pajamas and brush their teeth.  They say goodnight to their mama and as soon as she closes their bedroom door, the party starts! All five little monkeys are jumping on the bed. As soon as they start jumping, one falls off and bumps his head.  Their mama implores them, “no more monkeys jumping on the bed.” Once again, the group of now only four monkeys goes to bed and start their nightly ruckus, until another one falls off and bumps his head. Once again, mama tells them what the doctor said, “no more monkeys jumping on the bed.” The little monkeys continue their shenanigans until only one monkey remains.  However as soon she is alone in bed, she jumps on the bed and bumps her head.  Finally all of the little monkeys have bumped their heads and now go to bed. 

The mathematical concept that is apparent in this book is rate of change.  After their mama tells each monkey “no more jumping on the bed,” one more monkey leaves the group.  There is a constant rate of change from the monkeys jumping on the bed.  As soon as the group begins to jump, one monkey falls off, meaning one less monkey per jump.  The numbers decrease from 5 to 4 to 3 to 2 to 1 all the way to 0. 

Literature is an effective way to convey mathematical concepts as well as many different concepts in the educational world.   If a child were to read this book or another comparable book that relates mathematical concepts in a friendly way, they would be more relaxed and confident coming into a learning environment in which they were already familiar with the concepts.  I think that warming up a student to a topic they might normally find particularly challenging is a great way to familiarize them with new concepts.  Students might also relate to literature better than being taught through a blackboard and a classroom setting; all students learn differently and some respond to different mediums. 

The Grapes of Math by Greg Tang

The Grapes of Math is a clever and fruitful compilation of mathematical rhymes.  The book contains colorful illustrations and insightful riddles to help the readers solve each of the math problems. Each set of pictures has its own riddle and unique and easy ways of solving the daunting math problem. Each set of colorful pictures challenges the readers to think creatively so that solving the problems is more enjoyable.  The lighthearted tones and the adorable imagery of the book make the reader forget that they are counting large numbers!

The Grapes of Math addresses the mathematical concept of symmetry. Each illustration requires the reader to find a creative way to quickly count larger numbers. The book mainly illustrates the mathematical concept of symmetry. For example, in the pizza pie picture the riddle asks how many mushrooms there are. Since it would take too long to count all of the mushrooms, the riddle says “ Just do have and count it twice”. Since the pizza is symmetrical, doing this would take half the time than it would to count out all of the mushrooms.  By looking for patterns and symmetries, solving the problems becomes much less difficult. Since we have been discussing the symmetry of graphs lately in class, this story relates to that topic. It reminded me that even though some math concepts can be tricky, there’s always an easier way to solve them.

I think using literature to explain mathematical concepts is a great idea. Math, for me at least, is a daunting subject and I have always struggled with it. Explaining somewhat difficult concepts through colorful and fun illustrations makes math seem much easier. Sometimes younger students become disenchanted with math because it can be very difficult and the process of learning math is not always fun. Learning math through a textbook does not really help visual learners most of the time. Storybooks like The Grapes of Math appeals greatly to visual learners. For younger students learning things without knowing that you are learning them will make the students more receptive to the concepts.

Once Upon A Dime 
By Nancy Kelly Allen

Max Sherman

1) Farmer Truman Worth is busy in the middle of the harvest season. He is hurrying to pick and sell all of his produce before the first frost hits. This year is particularly good, the market prices for his apples are higher then normal. As time progresses, different factors effect the price that the market is willing to pay for Farmer Truman's apples. The reader is given an introduction to the fluctuation in commodity prices, vs-a-via the harvest yield and market price. He teaches this to his son, as well as the reader.

2) A simple explanation of the average rate of change is taught and illustrated. Different scenariois are presented in which the prices that the market is willing to pay for Farmer Truman's produce change. One example is a surplus of apples by other farmers in the area. This lowers the price that Farmer Truman can receive for his apples, decreasing his profit. Ex. 100 apple for $25, then 100 apple for $20 (25/100, 20/100) (5% change)

3) I believe that teaching mathematical concepts through a book is a great way for children and adults a like to better grasp a concept. Math can sometimes be ominous and intimating. By setting a scenario in which the numbers are used, a reader is better able to visualize the concept and is more likely to retain it for future knowledge. This is especially true for children, the vivid illustrations and relate-able story is more likely to stick with them then the numbers being drawn on the chalk board.

Pythagoras' theorem

1. What's Your Angle Pythagoras by Julie Ellis is a story about a curious boy named Pythagoras that tries to solve to questions throughout the story. The first question he had was why Saltos and Pepros, two workmen, building a temple could not seem to find the right ladder size to build the temple and fix a temple with crooked columns. They were arguing why the ladder was not fit to climb if the height of the temple was 12 ft. and the ladder is 12 ft. The second problem was to help his father create a new route that would be shorter for him to travel for work. While on a trip with his dad, Pythagoras was introduced to a builder, Neff, with a special rope that helped him build things. He was amazed at the straightness of the buildings, and was curious to see how the roped helped Neff build such nice things. Neff however, would not let Pythagoras hold on to the rope for long because it was his secret. That didn't stop him from creating his own rope and figuring out this special method that let Neff build upright things, a right triangle. He discovered that to create a right triangle the rope had to have the lengths of 3-4-5. While his father and Neff went off to fetch some supplies Pythagoras decided to play around with Neff’s tiles and lay it around his rope into squares. When Neff and his father came back they got mad at him for fooling around with Neff’s things however, Pythagoras found out a formula that created right triangles using the tiles. Pythagoras then used this method to solve the two mysteries with the temple and his father. The workers thanked him for helping them finish the temple in time. And his dad who was still upset at him for touching Neff’s things thanked him and applauded him for helping him see things from the “right angle”.

2. Pythagoras with his 3-4-5 right triangle theorem also discovered that the 3 to the 2^nd power and 4 to the 2nd power added up to be 5 to the 2nd power. Creating a^2+b^2=c^2. For Saltos and Pepros to have the correct ladder size Pythagoras used his equation and figured out that 5^2+12^2=13^2 which means that the ladder had to be 13 ft long. To solve his father’s problem he mapped out the three locations, which created a right triangle when connected together. He used his formula again to find that his father could cut across and only travel 185 miles, by using 111^2+148^2=185^2.  This book represents how when Pythagoras “graphed” the right triangles using the rope, leading him to his discovery on the formula. He also unintentionally figured a way to find the slope of something (although it wasn’t a focus in the book). The ladder for example acted as the slope for the space between the temple and the ground.

3. I think literature is a great way to teach mathematical concepts because it lets you paint a picture in your head about the problems. When you look at formulas on paper it can look confusing, but when you follow a problem with a story it is easier to understand and conceptualize. This method of learning can also apply to teaching a mathematic concept because it makes it easier for the other person to understand. It also reassures the uses of math because I feel like most of the time most people think math beyond the basic is useless in real life. But as we learn in this class and read through stories like this one, people can see that it has more real like concepts it can apply to.

Mathematics in a Story

I decided to read Lemonade For Sale  by Stuart J. Murphy. This quirky story was about 4 friends who were members of the Elm Street Kids Club. They decided to start a lemonade stand in order to fix up their withering clubhouse. One of the friends, Sheri, tracked the groups progress on a bar graph. She plotted cups sold on the y axis and days of the week on the x axis.
In the beginning business was soaring, the group put all of their effort in they even dressed up and wore lemon hats. The club mascot, Petey the Parrot was even helping to attract customers.
Until one day when business was not so good. The group was no selling anywhere near the amount they had been in previous days. They then discovered that Jed the Juggler was juggling and performing down the street from them and taking away their customers! On the Friday at the end of the week, Jed the Juggler performed his juggling next to the lemonade stand, and on this day the stand made more money than ever before.
The pictures and visuals in this book are very clear and simple. Not a lot of fuss in the background lets the students focus on the making of the graphs.

The main math concept that was presented in this book was graphing. Sheri used a bar graph in order to track the teams progress with the lemonade stand. She would plot how many cups of lemonade were sold for each day, and compare the progress. Some could even argue that you could use the bars to make predictions about future days or future weeks. Sheri and the group can easily see booming sales in the beginning and by the graph they can recognize the severe drop in sales when Jed comes to town and steals away customers. The bar graph is a good indicator of business growth and also decreasing sales. But when the two forces combine it is clear through the bar graph that the Elm Street Kids Club are back in business with booming sales. I think that picture books is a great way to both teach and learn math concepts. I know for me personally I am a visually learner and get things when I see them done out. And it helps me even more when I can see them in context in real life situations. I think that especially for younger kids which a lot of these books are aimed at it teaches them somewhat complex concepts about math easily in ways that they can understand in situations that they might actually be in, like selling lemonade at a stand!

Lemonade for sale
By: Stuart J. Murthy

        Once there was a kids’ club that need to be fixed a little and the members of the club found out that they don't have money in their piggy bank. So one of them came with the idea of selling lemonade. They were hoping to sale to sale about 30-40 cup of lemonade every day. They decided each one would be part of that sale to be succeeded. Some were selling others were making the lemonade. One of them made a bar graph of days and numbers of cups sale each day. And they started on Monday they sale 30 cups, Tuesday 40 cups, Wednesday 56 cups, so their sale is increasing so far. Unfortunately on Thursday they only sold 24 cups, and it was all because there was a boy play juggle on the other side. The kids decided to bring the boy by their sale table and make him juggle the lemonade. As far the did on Friday the sale was over the top of the bar graph that they made. Now they have enough money to rebuild their clubhouse. 

Days	# of cups
Monday	30
Tuesday	40
Wednesday	56
Thursday	24
Friday	100

 I just put 100 cup for Friday to make the table, cause in the book the graph was until 90 and the sale was above the graph. 

The author did good job to show graphing and linear function in both ways increasing and decreasing by having positive and negative slope, so on Monday, Tuesday and Wednesday the sale was increasing, but on Thursday deceased then increased again on Friday.

Wheres the Function?

I found online President Obama’s approval ratings listed every day spanning the entire length of his presidency thus far. The website is :

http://www.realclearpolitics.com/epolls/other/obama_bush_first_term_job_approval.html . This is a function because for every input, the day, there is one matching output, the approval rating. It therefore passes the vertical line test. In this case, the President’s approval rating is the dependent variable. It depends on the independent, which is time (in days). The approval ratings depends on the time because over time the President makes certain decisions that can sway his ratings. One month he may have a spike in ratings due to a successful initiative and another month he may have a drop due to a blunder, like his recent MediCare site. The function in function notation would be:

 Approval Rating=f(Time)    à time in days

This function is NOT linear, because the values of the average rate of change are not identical. If the function were linear, the slope would be consistent and create a straight line when graphed. Approval ratings are variable that depend on random, independent occurrences rather than predictable, stable variables. If the function were linear, the “changes in rating” would all be the same, indicating a steady linear relationship.

            As stated earlier, this function is a mathematical model. Although some could consider it isn’t, I argue that it is. My reason being is that in this case, time in days is not just a physical date, but it is an indication of choices being made by the President. On January 17, 2014 the President has extremely poor approval ratings following his Medicare blunder. But his ratings may have been higher following healthcare reform initiatives.

            As for relationships that are not functions, I struggled to find an example but might have gotten one. When reading about professional sport’s teams uniforms, I caught something. Functions CANNOT have the same x-values. Sure, if we are looking at New York Yankees Player, Shirt Color being (x, y), this is a function. But if we change it around to Shirt Color, Player , this is no longer a function. A FUNCTION MAY NOT HAVE TWO Y-VALUES ASSIGNED TO THE SAME X-VALUE.

The article I was looking at was:

http://sports.yahoo.com/news/top-25-uniforms-worn-professional-sports-teams-years-185100394--spt.html

The relationship I was looking at was between Professional Athletes and shirt colors.