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Resource Guide The Number Devil

Book Synopsis:

Summary: Amid Robert’s strange dreams one night, the number devil-an “elderly man the size of a grasshopper” who is a math whiz-comes along. Robert is not excited to meet the number devil because Robert does not like math very much, especially because of his current math teacher. The number devil tries to win Robert over and eventually succeeds by showing new approaches and insights into the world of mathematics. Throughout several nights, Robert learns about making numbers hop, prima donnas, taking the rutabaga, vroom!, unreasonable numbers, coconuts, handshakes, Bonacci numbers. These concepts of math are explored through practical and relatable applications. Robert develops a better understanding of these concepts in mathematics and even stuns his teacher with the correct answer to a problem in his math class.

Contextual Rationale: The Number Devil creates an engaging, contextualized, and fun way to learn about challenging topics and concepts in mathematics. Students can learn practical and relatable applications of concepts, such as Algebra, Problem Solving, Geometry, and Numbers and Operations, along with Robert. Additionally, The Number Devil utilizes creative and various approaches to explaining a concept and the language used is exciting and vivid. An example would be the word “vroom!,” which in a textbook would be seen as the word “factorial.”

Things students need to know:

Students should have a general understanding of simple math concepts, specifically addition, subtraction, multiplication, division, as well as whole numbers, decimals, and fractions. However, a in-depth understanding is not required because the number devil explains topics as if there is little to no previous knowledge of the topic.

Writing for understanding and Vocabulary Integration:

Vocabulary Integration:

• Have the students create a knowledge-rating chart with the vocabulary used in the book which is on the next page. The students will rate each term as 1) I’ve never heard of the word before, 2) I’ve heard the term, but I don’t know how it applies to mathematics, or 3) I understand the meaning of this term and can applying to a mathematics problem.

• Make Frayer Models as a class to make sure the students understand different vocabulary words from the book. The model will include the definition of the word, facts about the word, examples, and non-examples. These Frayer Models can then be displayed in the classroom creating a word wall for students to reference.

• Create a number sort with three categories, prime, Fibonacci, and triangle numbers. The students will be given around 20 numbers that they will have to identify and place in the appropriate location of the number sort. This will ensure that the students have an understanding of different terms by being able to classify numbers in the three different categories.

Writing for Understanding

• Have the students create a dream journal about every chapter. The prompt for each journal will be “Explain to your parents what the dream was about.” Use your own words in these journals and explain the ideas assuming your parents do not understand the concepts. This will ensure the students have a good understanding of the chapters and can explain the ideas in the own words.

Context of concepts:

• Gum: The idea that there are infinitely many ways to split a piece of gum and there are infinitely many pieces of gum.

• Handshakes: The number of ways everyone in a room can shake the hand of everyone else without repeating a handshake with anyone is the idea of making combinations without repetition.

• Rabbits: The reproduction of rabbits is just like the Fibonacci sequence.

• Roman Numerals: History relied heavily on roman numerals until the number zero came around and then zero became a very important number.

• Place Value: Money

• Division: Dividing things among friends, such as dividing a bag of candy among so many friends

• Fractions: percents and sharing something with other people, such as a pizza: How much of a pizza will you get?

• Square Roots: Jobs that deal with triangles, like architects, construction workers, carpenters, and engineers; it is building block to further math

• Pythagoras: Utilized in constructions, such as determining how tall a ladder must to reach the top of a particular building

• Shapes: Everything in nature has a shape

Discussion Generation: Themes/ideas/issues raised by the story:

Themes sorted by NCTM Standards covered in the book:

1. Number Sense:

• Infinite Numbers

• Importance of the number one

• Roman Numerals and the number zero

• Place Value

• Prime (“prima donnas”) and composite (“the garden variety”) numbers

• Irrational Numbers (“unreasonable numbers”)

• Perfect Squares

• Triangle Numbers

• Fibonacci Numbers (“Bonacci numbers”)

• Even and odd numbers

• Infinite quantity of odd and ordinary numbers

• Imaginary numbers (“imaginative numbers”)

2. Algebra

• Exponents (“making the numbers hop”)

• Division

• Fractions

• Square Root (“taking the rutabaga”)

• Factorials (“vroom!”)

3. Geometry

• Series

• Shapes

• Circles

• Pythagoras

• Pi

4. Problem Solving

• Ordering and Arrangements

• Combinations (“handshakes”)

Related Books:

• G is for Googol by David Schwartz- This is a math alphabet book that explains various important terms and concepts that are relevant to mathematics.

• - This is a fun colorful site that has over 600 definitions of math related terms. This can help the students in understanding the definitions that are being studied which helps build an understanding for the concepts.

• - This website has links to tutorials, homework help, worksheets, and most importantly games that students can play to help them develop a stronger understanding of the concepts.

• This website has links where students can find help with homework, practice problems, tutoring, and games that will all help them better understand different concepts in math.

Pre-Reading Activities:

1) Before starting to read The Number Devil, the students will take a pre-assessment that will also be administered at the conclusion of the study. This will not be a formal grade.

2) Begin class by showing a video clip of the first night from the number devil: .

After the clip, there will be a discussion about the video. Ask the students what they thought and if they have any questions. Tell the students that for this unit the class will be using The Number Devil as the primary text. Then read the first chapter as a class. Stop ever so often to make sure the students understand what is being read. Then discuss the ideas from the first chapter. The questionnaire will be handed out at the end of the first class of this unit.

3) Give the students a questionnaire to gauge their current interest and level of understanding of math. This questionnaire will also be given out at the end of the novel to see if answers have changed. (Refer to the attached questionnaire.)

During Reading:

The students will read a majority of this book individually. Select chapters may be read in class, for example the first chapter may be read in class to give the students an introduction to the story.

During-reading activity:

1) Have the students create a concept map of one of the nights in the number devil. Assign students different nights so as thought concepts come up, those students can help lead the discussion of those concepts.

2) Make a group summary on hopping numbers (exponents). This will include a description, patterns, uses, and interesting facts.

3) Think, pair, share: Make a list of the words used by the number devil (i.e. vroom!, hopping numbers, prima donnas, etc.) Have the students think of what these words would mean in mathematical terms. This is a way to introduce the students to the language.

4) Have the students complete a guided reading note sheet along with a chapter from the novel.

Group discussion:

Read, write, pair, share: While the teacher is reading part of the book out loud, the students are writing down their impression or reaction to what is being read. Possibly create a question the students would respond. Pair and then share as a whole class, leading to class discussion.

Post Reading:

1) Have students create a 13th night that the number devil would visit Robert. Assign students different topics that were previously learned in class to base their chapter around. This will serve as an assessment because it requires the students to understand different topics of the class and the number devils approach to math.

2) The dream journal that they will start when the book is started will be completed throughout the study revolved around the novel. This dream journal will be a form of assessment to gauge the understanding that the students have developed.

3) The same assessment that was administered at the beginning of the study of The Number Devil will be administered again. However, this will not be a formal grade.

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