7. The Number Devil: A Mathematical AdventureUse this thread to discuss The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger.http://www.scientix.eu/c/message_boards/find_category?p_l_id=&mbCategoryId=6011072019-09-17T21:22:45Z2019-09-17T21:22:45ZScenarioRumjana Angelovahttp://www.scientix.eu/c/message_boards/find_message?p_l_id=&messageId=6053452017-04-30T20:30:03Z2017-04-30T20:30:03Z How to be a teacher, who inspired yours students?!! How to create an emotional situation to teach Mathematics? How to show …? How to expline...? How to organise the lessons, the activities?<br /> Most of the educational approaches are inspired from examples and books.<br />“The Number Devil” – this are at liest 12 great ideas!<br /> This scenario presents an example of teachers view. First, this teachers view is a key factor in improving classroom motivation to learn mathematics. Second, this is a vehicle for increasing knowledge from research into classrooms.<br />How I organise the lesson?<br /> In the role of the Devil of the numbers comes in a student, who is in a larger class than the others.<br /><br /><br /><strong>“Rabbits and numbers”</strong><br /> <br />The Number Devil tells: "A young couple of rabbits after one month becomes an elderly couple and after another month they have a generation and become two…. 1; 1; 2; 3; 5….<br /> <br /><strong>"Jumping" Numbers</strong><br /><br />High on the walls, around the room - there is a line with Fibonacci Numbers on it. The Student, who plays the rolle of the Devil of the numbers shows two consecutive numbers. When they hold hands and jump together the rest of the Students have to find which Number they make. <br />1;1;2;3;5;8;13;21;34;55;89;144;233;377;610;……..<br />And then the Devil shows a number of Fibonacci and after then two Students jump. 610=<img src="" height="25" width="32" />+<img src="" height="25" width="29" /><br /><br /><strong>“Other properties of Fibonacci numbers”</strong><br />The Devil shows with magic stick two consecutive numbers – first the larger then the lesser, and he says: “Divide them! How much is it? ”<br />O-oooooooooo Golden Ratio!<br /><br /><br /><strong>Math factor</strong><br />The competition regulation is a follows:<br />- Every participant, within 3 minutes has to present one chapter of the book in attractive and popular way. <br /> <br />This activities show how the stories of the book (12 chapters) are based on an in‐depth analysis of science and mathematics education, as well as how those modules structure the motivation development of the students. Finally, we provide an overview of the evaluation of the book - the students expline yours favorite numbers .<br /> <br /> All students will follow the seven phases below for their participation:<br /><ol style="list-style: decimal outside;"><li>Read the book and decide on a project type.</li><li>Develop an initial plan.</li><li>Have the plan approved by the teacher.</li><li>Create the first draft of the plan.</li><li>Have the first draft approved by the teacher.</li><li>Create the final draft.</li><li>The final presentation will then be evaluated.</li></ol>Each project will be rated on its own merits based on the requirements detailed above. The grade will ultimately be determined according to the following chart.<br /><table><tr><td><strong>Factor</strong></td><td><strong>Weak ---- Strong</strong></td></tr><tr><td>Creativity<br /></td><td>0 1 2 3 4 5<br /></td></tr><tr><td>Difficulty Rating<br /></td><td>0 1 2 3 4 5<br /></td></tr><tr><td>Math Content<br /></td><td>0 1 2 3 4 5<br /></td></tr><tr><td>Presentation<br /></td><td>0 1 2 3 4 5<br /></td></tr><tr><td></td></tr></table> Creativity is a measure of originality. The difficulty rating is based on the type of project that is chosen. Math content is a value determined by the amount of subject matter that is within the project. Presentation is determined by the report that is given in front of the class.<br /> <br /><strong>Objectives:</strong><br /><strong>-</strong> <strong>to rise the students awareness of their own style in the classroom and to enhance their natural abilities in giving positive feedback and understanding Mathematics;</strong><br /><strong>-to increase students’ confidence in their skills;</strong><br /><strong>-</strong> <strong>to promote the use mediation and learning through theatre;</strong><br /><strong>-to enable students to find at least 3 methods and techniques for their own context to inquiry the world of the numbers;</strong><br /><strong>-</strong> <strong>to develop the students competences of ensuring harmonious group building and transforming the class as a group into a team by usage of non-formal group dynamics;</strong><br /><strong>-to direct students to reading;</strong><br /><strong>-</strong> <strong>to share best practices and transfer practical knowledge on classroom management and mathematics teaching.</strong><br /> <br /> <br /> <br /> <br /> <br /> Rumjana Angelova2017-04-30T20:30:03ZRE: Share your classroom ideas hereMaria Melniciuchttp://www.scientix.eu/c/message_boards/find_message?p_l_id=&messageId=6053142017-04-30T19:49:26Z2017-04-30T19:42:55Z<p style="text-align: justify">I read this book for the first time and I think it could be easily read and understand by students beginning from 6th grade. The number devil explain in a fun and informal way a lot of Maths concepts and I think that will engage children.Because I teach Informatics I will suggest some activities based on the book which are related to the subject I teach: prime numbers, triangular numbers , Fibonacci numbers.The students will write the algorithms and code in a programming language for the next requirements:</p><ol style="list-style: decimal outside;"><li><p style="text-align: justify"> Giving a number <strong>a</strong> (a>1) find the prime numbers in the interval [a, 2*a]</p></li><li><p style="text-align: justify"> Write the number <strong>a</strong> read from the keyboard (a>5) as a sum of prime numbers: if the number is even it will be the sum of two prime numbers and if the number is odd it will be the sum of 3 prime numbers.</p></li><li><p style="text-align: justify"> Write in the file<em> sum_prime.out</em> the prime numbers used to decompose each number from the <em>number.in</em> file . <em>These 3 requirements are based on the third night discussions that Robert had with the Number Devil.<br /></em></p></li><li><p style="text-align: justify"><em></em>Write all triangular numbers in the interval [a,b].</p></li><li><p style="text-align: justify"> Write each number from the file <em>number.in </em>as a sum of triangular numbers . <em>Requirements based on the 5th night discussions.<br /></em></p></li></ol><p style="text-align: justify"><em></em>6. How many rabbits will be at the <strong>x</strong> hour rabbit's clock (take care that you will deal with a lot of rabbits so <strong>x</strong> must be a little number). <em>The students are previous informed by Fibonacci sequence and the story with the rabbits as in the sixth night. This is a short and funny chapter so it's better if students will read it by themselves and the teacher will clear the misunderstandings.<br /></em>7. Calculate the factorial of a number <strong>x</strong> read from the keyboard.</p><p style="text-align: justify">8. For each number from the number.in file write it's factorial in the factorial.out number. <em>(Take care which number will be in the number.in file as the factorial numbers are bigger and bigger as you observed in the 8th night meeting with the Number Devil)</em>.<br /></p><p style="text-align: justify">For ICT classes I'd like students to create <em>presentations</em> about remarkable mathematicians as seen by Robert in the 12 th night (Teplotaxl, Lord Russell,Euler, Fibonacci...) and of course in the end they will create a diploma for a <em>Maths apprentice</em>.</p>Maria Melniciuc2017-04-30T19:42:55ZRE: Share your classroom ideas hereBosiljko Derekhttp://www.scientix.eu/c/message_boards/find_message?p_l_id=&messageId=6053032017-04-30T19:46:20Z2017-04-30T18:29:15ZHi,<br />I`m a math and physics teacher from Croatia.Well..<br />First, book was very interesting to me, I`m a math teacher, it would be strange if it was not ;)..<br />Second, It was so interesting to me that I have decided to associate and cooperate with language teachers in my school(Yes, it is not tanslated into Croatian!!), in trying to translate parts of particular chapters.<br />I like the "new" names that are designed in the book, because math language is too often sterile, boring and over-complicated for our students(sorry math teachers-it`s true). There is no room for humor in math at all..<br />In Croatian schools there are lesson called: Binomial theorem-as you know already- it is hard to learn for students(as well as everything else).<br />(a + b)^n=???<br />Basicaly, it is hard to remember the coefficients in equation, in its disaggregation, as well as everything else connected to this devilish theorem.<br />Somethimes teachers use Pascal`s triangle, in clarification, but mostly not..The seventh chapter of this book mentions it, but in a different way..starting with the triangular numbers. In this way number get new"dimensions", they become closer to the students-they can see the simple intuitive side of mathematics. Everything in math has its meaning. Nothing came down-fall from the heaven, or form down below...you know..in HELL.<br /><br />The school hour/hours, in which the binomila theorem is thought in school can be done as a workshop for students. This workshop will cover and connects different school subjects.<br />Foreigh language-each student will translate part of the text. <br />Craft: prepare small balls or small cubes that will be used for "making" triangular numbers(numbers get 3D)<br />Art: every triangular number/number in Pascal`s triangle get his own design-so numbers get extra personality (I like this expresion"numbers with extra personality")<br />Music: they could design musical composition-numbers are associated to notes-if you do not see-then you can hear sound of numbers and this numbar patterns.<br />The hisorian and chemist can tell the story of Pascal-he was not just a mathematician..he was so many more..Just like me..I`m also not just math teacher..I`m a father, healer, rock star..;)<br />Eventualy, this workshop could become a whole project day, and at the end of day students/mathematicians would finaly get a Pascal`s triangle and binomial theorem(and also the Fibonacci numbers-hiden inside Pascal`s triangle)<br /><br />The Number Devil would help all students to adopt the binomial teorem<br /><br />Best <br />BosiljkoBosiljko Derek2017-04-30T18:29:15ZRE: Share your classroom ideas hereNely Stoyanovahttp://www.scientix.eu/c/message_boards/find_message?p_l_id=&messageId=6051522017-04-30T16:50:38Z2017-04-30T16:50:38ZHello. My name is Nelly Stoyanova. I am from Bulgaria and I am a teacher in Mathematics, Informatics and Information Technologies. The book "THE NUMBER DEVIL" provokes many ideas for working with students. I will share some of them I hope you will like them.<br />When I told my students about the characters in the book The number devil, some of their reactions were "I also want to have a devil of the numbers," "Let's go hunting for devils," "This book is very cool," " Are there Devils in Physics and Chemistry? " I was delighted by their desire to study and the fact that they liked the idea for the devil, but my ambition was not to find a devil, but to provoke them to become the devil of the numbers.<br />I used different options to get them to take on the role of the devil. I divided them into pairs - Robert and the devil, into teams - devils and boys (Roberts), one Robert and all the others - devils and etc. In the role of Robert, the kids "called" or "waited" the devil for the numbers to help them with a particular material.<br />I really liked the suggestion of one of the devil children. He said that when he was a devil, he first wanted to get to know his Robert and then explain to him the mathematical issues, exactly with examples from the things Robert likes or likes to do.<br />His "Robert" is an athlete and has many medals in racing. He is also interested in cars. He said he had problems with circles. Using this information, the devil linked the circle to the shape of the tires, rims and the shape of some of the medals. He sat down in a chair, grabbed one end of his shawl, handed the other end to Robert, and made him walk around the chair by holding the shawl stretched, and fence for his favorite devil a protected area around the chair. So he tried to explain to him how to draw a circle and what is a radius.<br />When I leave the children to determine on their own for what they want to meet with the devil, I get information about the material(s) which is (are) difficult for them. Every child experiences satisfaction when he is in the role of the devil of the numbers. Sometimes the Robert children themselves start looking for ways to explain things - they move from one role to another and these are very nice moments of my work.<br />I'll tell you some of our devilish ideas about figure numbers. The Devil Girls had ideas to draw triangular numbers on their nails, plant flower beds - in each bed the number of flowers would be a different triangular / quadrangle number, decorate cupboards or dishes with points representing different figures, and so on.<br />The child athlete replaced the coconuts with medals. He said that once he gathers more medals he would invite his classmates at his home. He will arrange the medals like the devil of the numbers from the book arranges the coconuts. He will first explain why they are arranged this way and then will tell about his achievements.<br />Another child offered to open a store. People could buy things with banknotes which values are triangular numbers.<br />I intend to execute this idea by organizing a Charity Sale with items made by the children. Every buyer will exchange a real currency with ours and then will go shopping. He will also solve a problem related to representing a number as a sum of triangular numbers.<br />We played the role of devil IT specialists with my older students. We have created dynamic software with Geogebra to help other students learn different facts about figure numbers. Some of the created files are:<br />• A puzzles with which small students exercise the finding of face of a rectangle and formulate hypotheses to find the N-th triangle number.<br /><a href="https://l.facebook.com/l.php?u=https%3A%2F%2Fggbm.at%2FNFfV7RA6&h=ATNXsUfMzNoZ5zoXkfEyrCVBwiI5uHCBwUuMPhCB9rWYGStC8kWxCljm0j663SsNcm20jxr2aG5J5QHb2I9MSpxanV4KbS8jnq30qWtJqYRt1PryN7V8lzu9tc3nxuNB3mD6vAo">https://ggbm.at/NFfV7RA6</a><br /><a href="https://l.facebook.com/l.php?u=https%3A%2F%2Fggbm.at%2FSNS2qQ2d&h=ATNXsUfMzNoZ5zoXkfEyrCVBwiI5uHCBwUuMPhCB9rWYGStC8kWxCljm0j663SsNcm20jxr2aG5J5QHb2I9MSpxanV4KbS8jnq30qWtJqYRt1PryN7V8lzu9tc3nxuNB3mD6vAo">https://ggbm.at/SNS2qQ2d</a><br />• A puzzle in which students find dependencies related to the array of triangular numbers and construct square numbers.<br /><a href="https://l.facebook.com/l.php?u=https%3A%2F%2Fggbm.at%2FjvjPFMWA&h=ATNXsUfMzNoZ5zoXkfEyrCVBwiI5uHCBwUuMPhCB9rWYGStC8kWxCljm0j663SsNcm20jxr2aG5J5QHb2I9MSpxanV4KbS8jnq30qWtJqYRt1PryN7V8lzu9tc3nxuNB3mD6vAo">https://ggbm.at/jvjPFMWA</a><br />Congratulations on choosing these books and thank you for the opportunity to share experience related to their use.Nely Stoyanova2017-04-30T16:50:38ZRE: Share your classroom ideas hereRobert Baldurssonhttp://www.scientix.eu/c/message_boards/find_message?p_l_id=&messageId=6051042017-04-30T15:57:35Z2017-04-30T15:57:35ZThank you for sharing Tullia <img alt="emoticon" src="http://www.scientix.eu/scientix-theme/images/emoticons/happy.gif" >Robert Baldursson2017-04-30T15:57:35ZRE: Share your classroom ideas hereTullia Urschitzhttp://www.scientix.eu/c/message_boards/find_message?p_l_id=&messageId=6041372017-04-27T21:55:06Z2017-04-27T21:47:02ZHello, I'm Tullia, from Italy. <br />I teach maths and science in a middle school (from 6th to 8th grade)<br />I really love "The number devil book", and every year I suggest to my students to read it, as a way to make them "playing with numbers" and feel a little bit more engaged with the world of mathematics without fear.<br />This year I took the chance to work more on the book, with my 11 years old students and they were really very engaged.<br />It took one months to students reading the book. We read some chapters together at school, to prepare the "magic environment" of the book. While reading the first chapter we started getting engaged: we cut the biggest chewin-gum we found in very little parts, imagining to a cut it till the nanoscale...<br />Then we played with series of numbers, and we played with calculators, to find how many times we had to cut a sandwich "to reach the moon" (the sandwich was 6 cm high: each time its size was becoming half, but its height was becoming double… they had to discover how many times they needed to cut in order to reach the distance Earth-Moon).<br /> <br />Playing in this way, it happened that students enriched their love for our time with the book, so I proposed them to invent a game based on the book itself. We had a brainstorming and we decided to design a complete game, and its rules. We called it “<strong>The number devil game</strong>” (Il gioco del Mago dei Numeri) and we agreed that every student had to prepare 5 exercises to put in the game, in order to repeat all the mathematical contents they studied from the beginning of the school year!<br /> <br />If someone wants to try…<br /> <br /><strong>Materials:</strong><br />60 cards “The wizard questions”<br />12 cards “inspiration”<br />6 stars (divided in 6 pieces)<br />2 dices<br />6 pawns<br />1 hourglass<br /> <br /><strong>Players</strong><br />From 2 to 6 (also divided in teams)<br /> <br /><strong>Age</strong><br />from 11 years old<br /> <br /><strong>How to play</strong><br />Put in the middle of the board the two decks of inspiration and wizard cards.<br />Put the pawns on the start box. Every player throw the dices: the first one is that who have the highest score.<br /> <br />Every time you reach a game box (except when you reach a nightmare or an inspiration box) you have to take a “wizard card”. “Roberto”, the player, has the time of one turn of the hourglass to answer the wizard question. If the answer is correct, he wins a piece of star. (Nothing in case he fails, or the time is over).<br /> <br />Something bad happens if the player arrives in one of the 4 “nightmare boxes”:<br /><ul style="list-style: disc outside;"><li>“<em>Lo scivolo infinito</em>” (the infinite chute): throw the dice and go back of the number of boxes showed on the dice</li><li>“<em>Il professor Mandibola</em>” (Professor Jaw): stop for a round</li><li>“<em>Il pesce incantato</em>” (the enchanted fish): go one box back</li><li>“<em>La bicicletta</em>” (the bicycle): go back to the start box</li></ul>There are other 4 special boxes: the inspiration boxes, that allow you to collect a "inspiration card", useful to to cancel nightmare effects.<br /> <br /><strong>Aim of the game</strong><br />Aim of the game is completing a round of the board AND completing the star puzzle.<br /><br />images here: <p style="text-align: center"><span style="color: #000000"><span style="font-family: Inconsolata"><span style="font-size: 18px"><a href="https://goo.gl/Wfk5ca">https://goo.gl/Wfk5ca</a> </span></span></span></p><br />TulliaTullia Urschitz2017-04-27T21:47:02ZRE: Share your classroom ideas hereRobert Baldurssonhttp://www.scientix.eu/c/message_boards/find_message?p_l_id=&messageId=6032182017-04-27T10:04:50Z2017-04-27T10:04:50ZThanks for sharing Tadeja this interesting lesson plan about the Fibonacci sequence! Have you already tried it out and how did it work?<br />Do you find the book useful to motivate students about mathematics?<br />Do you perhaps have a Number Devil in your class? <img alt="emoticon" src="http://www.scientix.eu/scientix-theme/images/emoticons/happy.gif" >Robert Baldursson2017-04-27T10:04:50ZRE: Share your classroom ideas hereTadeja Kobalhttp://www.scientix.eu/c/message_boards/find_message?p_l_id=&messageId=6026142017-04-25T17:13:01Z2017-04-25T17:13:01ZHello,<br /><br />I'm Tadeja. I teach math in a secondary school -young from 15 to 19 years. Here is my idea about using The number devil:<br /><br />When you teach a mathematical proof technique of mathematical induction, you can use the 6th chapter of THE NUMBER DEVIL. You can tell the students to find a property of Fibonacci sequence in the book which they can prove with induction.<br />I expect students to find the property: f(1)+f(2)+…+f(n)+1=f(n+2) from the book. Their task is:<br /><ol style="list-style: decimal outside;"><li>to write this characteristic (by themselves) and</li><li>to prove it with induction.</li></ol>The proof is easy enough fort he 18 years students of secondary school. Later, when students have already done the task, teacher can assure if they have really understood the induction by asking them:<br />In the prove we use the iductive step:<br />f(1)+f(2)+…+f(n)+f(n+1)+1 =( f(1)+f(2)+…+f(n) ) +f(n+1)+1 = f(n+2) – 1 + f(n+1) + 1 = …<br />One can see that -1+1 =0, but this part could also work if we would use any other number instead of 1, let say 5. Why this is not right?<br />By asking students that question we check if they have understood the meaning of the base case and the whole proof technique.Tadeja Kobal2017-04-25T17:13:01ZShare your classroom ideas hereRobert Baldurssonhttp://www.scientix.eu/c/message_boards/find_message?p_l_id=&messageId=6011612017-04-23T06:59:25Z2017-04-23T06:59:25ZUse this thread to share your classroom ideas inspired by The Number Devil: A Mathematical Adventure by <span style="font-size: 16px">Hans Magnus Enzensberger. Looking forward to hearing your ideas!<br /><img src="http://www.scientix.eu/documents/10137/595389/Number+Devil.jpg/3aaeadac-c2e9-443a-9722-6ccb0c63e5d5?t=1491206213000" style="height: 308px; width: 200px;" /></span>Robert Baldursson2017-04-23T06:59:25Z