The Number Devil Summary:
The Number Devil follows twelve dreams of a boy named Robert. Robert hates math and he is very irritated with the pretzel problems that his math teacher, Mr. Bockel, always assigns to his class. At the beginning of the book it describes how much Robert hated dreaming at times he would dream of being swallowed by a big fish or he would slide down an endless slide. Other times he would dream of things that he really wanted, such as a mountain bike, and when he woke up he would be disappointed because it wouldn’t be there anymore. Robert started getting tired of dreaming, until one night the number devil appeared in his dream. The number devil was there to take Robert on various adventures, while he was dreaming, to help him better understand math and make it more appealing to him. Every night, when Robert would fall asleep, the number devil would appear in his dreams and create interesting scenarios to help him understand new mathematical concepts. At first, Robert wasn’t too fond of the number devil, but as each night passed by Robert began looking forward to seeing the number devil in his dreams. The number devil covered topics such as infinite numbers, prime numbers, Fibonacci numbers, numbers that mysteriously appear in triangles, and numbers that expand without end. The book uses a lot of made up words to help simplify difficult math concepts, such as using the word hopping to replace the term squaring and using the word rutabaga when they were dealing with taking the square root. At the end of the book it informs the reader that these are not the correct mathematical terms and it includes a key that matches up the correct term with the term it uses in the book. During Robert’s twelfth dream he gets invited to Number Hell/Number Heaven as the number devil’s apprentice where he gets to see a lot of famous mathematicians throughout the course of history. The book concludes with Robert going to Mr. Bockel’s math class, not in his dream, and then solving a math problem that the teacher thought no one in the class would be able to solve. So this book started out with a boy, who hates math, and then after a number devil appeared in his dreams and started helping him with various mathematical concepts he began to love math so much that he can’t get enough of it. Reviews: Overall, the whole group enjoyed this book a lot and felt it was a very good resource to use in the classroom. Some of the reasons it was so well liked was because it presented mathematics in a way it is not usually presented, was a very easy read with the large print and fun illustrations, could easily be broken up for different groups to read since each chapter was a different night, and it helped us learn things as well as get a deeper knowledge of certain topics. This book would also be a great resource for students who do not particularly like math and give them an alternative way to learn some of the material. Most students would probably enjoy this book because it is such an easy read and does not seem like a chore to read since it is exciting and interesting. As a whole, we all stayed very interested in the book and would wonder what the number devil was going to do the next night to Robert. This would also be a useful tool at home with your own children as a way to make math fun and even have them read a chapter each night at bedtime to go along with Robert's journey with the number devil. The Number Devil should be implemented where appropriate in math classrooms because it will help students realize that math does not always have to be boring book work and can actually be fun if the teacher uses this book in a good way.

Activities:

The website shown below is a chapter by chapter guide on how one teacher in particular had her students read through the book. After each chapter she would have them do a different activity. At the very end of the book she had the students pick one of the famous mathematicians mentioned in the book and do an online webquest about that mathematician to see what else they could discover about them. This would be a great end of book project for the students to do. The students are allowed to use the following websites during their research:

Creating all the whole numbers using only 1(11x11=121)

Palindromes and other symmetrical patterns created (111x111=12321)

Explore finding half of a half (1/2 x1/2) and see how far you can get with various sized objects. A post it note, and 8.5 x 11 piece of paper, 11x14 size paper etc… What fraction of the original can you get to.

Explore Palindromic Numbers. What are some other numbers that are Palindromic. ( i.e.: Dates etc... Create a short Sentence that is palindromic.

2nd Night

Roman Numerals, Importance of Zero,

Link to Negative numbers, Squared numbers & Exponents (Hopping),

Expanded Notation

Investigate Roman Numerals; 2) Roman Numeral War
Supplies: Roman numeral cards (print on cardstock)
Set Up: Cut apart Roman numeral cards.
Game: Mix up the cards. Pass out all the cards equally among all the players face down. Players keep their cards face down. All players flip their top card at the same time in the center of the table. The player with the highest number takes all the cards and adds them to the bottom of his pile. Play continues with all players laying down cards until all players, but one is out of cards. The player that ends with all the cards is the winner.

Imagine a World without zero. Write a scenario of what impact the loss of zero could have on our lives.

3rd Night

Division with zero?,

Prime Numbers (Prima donnas),

Patterns in primes

Prime Number Scavenger Hunt: Create a list of Prime numbers using the Method Described in the Chapter, Sieve of Eratosthenes. Look for the prime numbers around the classroom and record them next to the numbers. Additionally, look for the following: Name an animal that lays a prime number of eggs at a time Animal Number of Eggs_
Name a sports star with a jersey number that is a prime number Sports Star Jersey Number_
Find a person with a birthday of prime numbers (month and day) Person Birthday
Find a friend with a street address that is a prime number Friend Street Number_
Name a flower with a prime number of petals Flower Number of Petals_
Find someone with a shoe size that is a prime number Person Shoe Size_
Find a food with a prime number of calories Food Calories_
Find a city whose latitude and longitude coordinates are prime numbers City Latitude and Longitude Coordinates_

Prime Numbers and Composite Numbers are alike in some ways and different in others. Describe TWO ways they are similar and TWO ways they are different.

Explore other irrational numbers and record in your journal.

5th Night

Triangular Numbers (coconuts), any number can be made by adding triangular numbers,

Adding consecutive triangular numbers results in a square number,

Adding Consecutive triangular numbers results in the last triangular number added. (i.e. 1-12 is the 12th triangular number)

Slap Triangular Numbers, Decks of cards with numbers 1-100, Play Triangle Number Slapjack with 1 to 3 friends. Use a deck of cards with numbers between 1 and 100. Instead of slapping "jacks", the players slap triangle numbers (1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91) to win the pile. If needed, review the rules for slapjack.

Only two numbers between 1 and 100 hold the distinction of being both square numbers and triangle numbers. The first number is 1. What is the other number that is both triangular and a square number. Create a model to demonstrate your answer.

6th Night

Fibonacci Numbers and Sequences (Bonacci) 1,2,3,5,8,13,21

Explore the relationship between the Fibonacci sequence and Nature, Art and Architecture. Go hunting for the Fibonacci sequence in nature, art, architecture. Petals on a flower are often a number in the Fibonacci sequence. Rows of spirals on a pinecone are a number in the Fibonacci sequence. The branches of a tree or plant sometimes divide following the Fibonacci sequence. Now, grab a camera and head out the door. Snap a picture each time you find an example of the sequence in nature. No camera? Draw a sketch.

Write a poem with a Fibonacci pattern. The Fibonacci sequence determines the number of syllables in each line of the poem. For example, the first and second lines have one syllable, the third line has two syllables, the fourth has three, and the fifth has five.

7th Night

Pascal's Triangle relates to triangular numbers

Investigate Patterns: Create a tetrahedral number sequence by building a tetrahedron out of marbles and recording the numbers in each layer. Make a table with the headings Height ( number of layers) Triangular Number (marbles), and tetrahedral number (total marbles) What are your observations?

The number devil introduces Robert to Pascal's triangle. Examine how Pascal's triangle is used in probability.

8th Night

Permutations and Combinations,

Factorials,

Circle Diagrams,

Use of number pyramid for solving problems such as teams of 3, 4, 5, etc…

Permutation Relay: Give each student a red square of paper, a blue square of paper and a white square of paper. Separate the group into two teams. Have the teams line up for a relay style race. The first child from each team runs to the board/wall and puts up their 3 papers in a line, in any order. They run back, tag the next person who then runs to the board and puts up their 3 papers in a line, in any order except the order of the other person on their team. This continues until all six permutations have been discovered. The team that gets all their permutations up first is the winner.

The Number Devil shows Robert that to figure out how many possible ways to arrange his classmate's seats all Robert has to do is multiply the number of people by all the whole numbers below the number of people except zero. Pretend you're in Robert's class and you want to figure out the number of possibilities for arranging your classmate's seats. Describe another Real life way of using permutations.

9th Night

Number Sequences

Sum of Fraction on a number line

Write-Out Exponents Race, Help students understand how to write out exponent strings in long form through the completion of this easy, fast-paced game. Before class, write out a list of exponents to use during the game. Use exponents that are at your students' current level. Once students arrive in class, divide them into two teams. Ask one team to sit on the left side of the classroom and the other to sit on the right side. Draw a line down the chalkboard, dividing it in half. Then ask one member of each team to come to the board. Tell the class you are going to read off a number in exponent notation and they have to write it in long form as quickly as they can. For example, if you said five to the fifth power, they would need to write (5)(5)(5)(5)(5) as quickly as they can. Once the student has finished writing the answer, he needs to set the chalk down to indicate that he is done. The first person to complete the task, wins a point for his team. Continue in this fashion, calling one member of each team up at a time, until you have gone through all of your listed exponents. The team with the most points at the end of the game wins.

Write an acronym poem for the word "infinite". Each line may be one word describing infinity or an entire sentence about things that are infinite. Be creative. Use a thesaurus for help coming up with synonyms for infinite.

10th Night

Hexagons,

Fibonacci Numbers divided by them and their neighbors recurring decimals,

1.618, the divine proportion,

Platonic Solids

Testing D + S - L = 1: Choose an item to represent a line and a dot. It could be red vines and life savers or pretzel rods and banana chips or Tinker toys sticks and wheels. Create your own figures with a dot at both ends of every line, as demonstrated by the Number Devil on page 203. Record your finding

What is a quang? Who knows? It's from the Number Devil's own imagination. Invent your own measurement. Using a strip of cardstock or poster board make markings equally along the edge to show how long your measurement is. What are you going to call it? How does it compare to a standard measurement such as an inch or a millimeter (i.e.. Is it about 2 1/2 inches or 22 millimeters)?

11th Night

Proof, what's behind the rule of the game

Candy Bar Proof: Start with a candy bar that is scored into smaller bars- at least 3 sections across and 4 in length. Have students guess the minimum number of breaks it will take to break the candy bar into all the small sections. In small groups pass the candy bar around letting each student make one break until the bar is in individual sections. Count how many breaks you make along the way. How many breaks did each group make? (The number should be the same for every group). How close were the children's guesses? The proof says that there will always be one more piece than the number of breaks it takes to separate them. For example at the beginning there was no breaks and one piece, then there was one break and two pieces, and two breaks and three pieces and so on.

Write a Proof Sequence in 4 short paragraphs: 1. Create a Model 2. Convince a Friend 3. Convince a Skeptic 4. Write the Rule

12th Night

Famous Mathematicians,

History of Mathematics,

Pi

Research an Area of Mathematics that is of interest of you. Using a journal article and the internet.

Write a 2 page Paper. Include a summary of the topic, why it was interesting to you and what you discovered during your research. Include a Reference page.

The Number Devil

Summary:

The Number Devil follows twelve dreams of a boy named Robert. Robert hates math and he is very irritated with the pretzel problems that his math teacher, Mr. Bockel, always assigns to his class. At the beginning of the book it describes how much Robert hated dreaming at times he would dream of being swallowed by a big fish or he would slide down an endless slide. Other times he would dream of things that he really wanted, such as a mountain bike, and when he woke up he would be disappointed because it wouldn’t be there anymore. Robert started getting tired of dreaming, until one night the number devil appeared in his dream. The number devil was there to take Robert on various adventures, while he was dreaming, to help him better understand math and make it more appealing to him. Every night, when Robert would fall asleep, the number devil would appear in his dreams and create interesting scenarios to help him understand new mathematical concepts. At first, Robert wasn’t too fond of the number devil, but as each night passed by Robert began looking forward to seeing the number devil in his dreams. The number devil covered topics such as infinite numbers, prime numbers, Fibonacci numbers, numbers that mysteriously appear in triangles, and numbers that expand without end. The book uses a lot of made up words to help simplify difficult math concepts, such as using the word hopping to replace the term squaring and using the word rutabaga when they were dealing with taking the square root. At the end of the book it informs the reader that these are not the correct mathematical terms and it includes a key that matches up the correct term with the term it uses in the book. During Robert’s twelfth dream he gets invited to Number Hell/Number Heaven as the number devil’s apprentice where he gets to see a lot of famous mathematicians throughout the course of history. The book concludes with Robert going to Mr. Bockel’s math class, not in his dream, and then solving a math problem that the teacher thought no one in the class would be able to solve. So this book started out with a boy, who hates math, and then after a number devil appeared in his dreams and started helping him with various mathematical concepts he began to love math so much that he can’t get enough of it.

Reviews:

Overall, the whole group enjoyed this book a lot and felt it was a very good resource to use in the classroom. Some of the reasons it was so well liked was because it presented mathematics in a way it is not usually presented, was a very easy read with the large print and fun illustrations, could easily be broken up for different groups to read since each chapter was a different night, and it helped us learn things as well as get a deeper knowledge of certain topics. This book would also be a great resource for students who do not particularly like math and give them an alternative way to learn some of the material. Most students would probably enjoy this book because it is such an easy read and does not seem like a chore to read since it is exciting and interesting. As a whole, we all stayed very interested in the book and would wonder what the number devil was going to do the next night to Robert. This would also be a useful tool at home with your own children as a way to make math fun and even have them read a chapter each night at bedtime to go along with Robert's journey with the number devil. The Number Devil should be implemented where appropriate in math classrooms because it will help students realize that math does not always have to be boring book work and can actually be fun if the teacher uses this book in a good way.

Activities:

http://www.agnesscott.edu/lriddle/women/women.htm

http://www-gap.dcs.st-and.ac.uk/~history/Day_files/Now.html

http://www.maths.tcd.ie/pub/HistMath/People/RBallHist.html

http://physics.hallym.ac.kr/reference/physicist/mathematician.html

Of course, we can decide on different websites and different things to have the students research as long as it relates to the book. We can have them do group presentations on the information, or we can have them do individualized research assignments. This would be a fun way to get students active after reading this book and find out more than just what the book talks about.

Here is the website that the teacher made for these activities for each chapter:

http://mindflight.plymouth.edu/icet/2002/icet2002/projects/kearsarge/help.html

Here is a Chart which summarizes the Content from each chapter and then lists some activities that teachers can do with the students in the classroom as well as a Journal Activity for each Chapter. These can be used all together or individually.

ChapterContentActivity/LessonJournalSupplies: Roman numeral cards (print on cardstock)

Set Up: Cut apart Roman numeral cards.

Game: Mix up the cards. Pass out all the cards equally among all the players face down. Players keep their cards face down. All players flip their top card at the same time in the center of the table. The player with the highest number takes all the cards and adds them to the bottom of his pile. Play continues with all players laying down cards until all players, but one is out of cards. The player that ends with all the cards is the winner.

Name a sports star with a jersey number that is a prime number Sports Star Jersey Number_

Find a person with a birthday of prime numbers (month and day) Person Birthday

Find a friend with a street address that is a prime number Friend Street Number_

Name a flower with a prime number of petals Flower Number of Petals_

Find someone with a shoe size that is a prime number Person Shoe Size_

Find a food with a prime number of calories Food Calories_

Find a city whose latitude and longitude coordinates are prime numbers City Latitude and Longitude Coordinates_

List of Contributors:Summary:Kevin NashReviews:Kassie Sliney, Jordan Boesenhart, Rome Fiedler, Kevin NashActivities:Jordan Boesenhart, Rome Fiedler