Just for Fun   Each year in the Connecting Math to our Lives project we organize an exchange called "Just for Fun." Mathematics is often seen as serious, abstract and difficult. In the "Just for Fun" activities students can discover and share the playful side of math.   Original Just for Fun question from Sikunder Ali Baber from Pakistan: sikunder.baber@aku.edu   We pose the question such as " how many squares are there in the chessboard?" The common response is 64 or 65. But after careful observation we would come up around 204 squares. How did we come up to this? I am leaving this to my colleagues to discover. I will be contributing many more ideas in the future as well. If anyone is interested to communicate, please do write to me. A solution from Marondera High School, Zimbabwe: Students' Names: Charles Napuwera, Nesbert Shirihuru, Paul Dendere, Isaac Pasipanodya wldmhs@internet.co.zw   SQUARE AREA (in square units) NUMBER OF SQUARES ON THE CHESS BOARD 1X1=                    1                       64 2X2=                    4                       16 3X3=                    9                       4 4X4=                    16                      4 5X5=                    25                      1 6X6=                    36                      1 7X7=                    49                      1 8X8=                    64                      1 ________________________________ TOTAL NUMBER OF SQUARES 92   The solution for the question on the number of squares on a chess board is 92. We hope it's correct. A response from Sikunder Ali Baber: Dear Friends, Thank you very much of sending your response to the question posed in math just fun. I am really pleased to see your working and the presentation of the resolution of the chess board problem. Your solution seems to be appropriate and equally right. However, I would encourage you to look at this problem again for further insight. If suppose you would like to count the overlapping squares, then how many squares are there altogether. This aspect may give you different look in seeing this problem differently and would help you to sharpen your observational skills. Which I personally consider very important for the development of mathematical thinking. Even if you would like to extend this problem then you can ask, " How many rectangles are there in the chessboard?" I hope that you would still enjoy working on this problem. Many thanks Sikunder Ali Baber   Math Just for Fun problems from Rakodzi High School in Zimbabwe wldmhs@internet.co.zw   Dear Friends We are students from Rakodzi High School, Zimbabwe. We enjoy Mathematics and we find this project being fun. Here are a few Math problems just for fun. We hope you will respond and send us some solutions. We will be closing school on Thursday 7 December. We wish you a Merry Christmas. 1.There were 710 people on a train. At a station, No one alighted from the train. How many people were left in the train when it left the station? 2. What is the longest word in terms of miles? 3. Susan has two oranges and three children. What should she do if she has one favorite child whom she wants to give a full orange without embarrassing others? From: Victoria Muswere, Klery Chikwede, Vongai Mandizvidza and Gracious Pakarimwa RAKODZI HIGH SCHOOL, ZIMBABWE   Math Just for Fun problems from Marondera High School in Zimbabwe wldmhs@internet.co.zw Dear friends Our class is very much interested in playing with figures.Here are some of the problems for you. We hope you will find them interesting. MATHEMATICS PROBLEMS: JUST FOR FUN 1. Three men went to a restaurant and had a meal of $15. Each of the three men contributed $5 towards the meal. Later on the cashier noticed that he had overcharged the three men by $5. On refunding, the cashier thought it would be difficult for the three men to share the $5 equally, so he stole $2 from the refund and gave a $1 to each of the three men. This meant that the three men had paid $4 each. To find the total money he had held, the cashier calculated it as follows: 3 x $4 from the three men $12 Plus the $2 he had stolen + $ 2 Total amount he held $14 QUESTION: The cashier's balance failed to agree with the amount of $15 that he had received from the three men. (a)Where had the other dollar gone to make his balance equal to the amount he had received at first from the three men? (b)Adding the change they were given ($3) to the amount in the balance he calculated ($14) would give $17. Where had the other $2 originated from to make a total of $17 yet the three men had paid only $15 and received a change of $1 each? 2. In a pack of 4 hyenas chasing an antelope, one hyena is 4 times as fast as the second hyena. The second hyena is half times faster than the third hyena. The third hyena is three and half times as the fourth. How far will it take for all the hyenas to catch the antelope, which is twice as fast as the third hyena? From: Charles Napuwera and Nesbert Shirihuru MARONDERA HIGH SCHOOL, ZIMBABWE   We invite everyone to fill out this Math for Fun questionnaire!   Dear Friends,   We all know students who do not enjoy math and who might even fear it. You yourself might have felt like that at some stage or another. Working in the Connecting Math to our Lives Project, we have learnt that this is not the fault of the students, but often because math is not taught in a fun and lively way. In this message we are asking you to look back on your experiences with math, and help us gather ideas about what makes math fun and meaningful.   Recently we received a note from Krystle and Maha, two 9th grade students from Lebanon. They wrote:   *Hello, Math is not all that fun anymore, it is getting harder and harder every year. I wish there was a way to make math a more interesting subject. *For other students, the experience has been different. Sixteen year old Udara from Sri Lanka wrote to us:   *We need maths everyday, because without maths we can't do anything.Maths is not only a subject which we have to study at school. Maths is related to every activity in our life. With out maths, we can't even go to a shop and buy something,With  out maths we can even use money either. So maths really plays an important role in our lives.*   Could you help Krystle and Maha with some suggestions to make math fun? Do you share Udara's feelings? In the Connecting Math to our Lives Project we strongly believe that math should not be just a subject that gets taught in school, disconnected from real life. If math is learnt in a way that shows us how we can use it everyday in our lives, and how it links up with all the other things we learn in school like geography, and history, and art, more students will understand math and do well in the subject.   Please help us in our investigation to gather ideas about what makes math fun by filling out our survey below. Everyone can participate in this survey: teachers, students of any age or from any country. You can respond individually or send a group response. We will post your results on our website, so that everyone can learn from your ideas and perspectives.   Please send your completed survey to orillas-math@igc.org     _______________________ MATH FOR FUN SURVEY   1. Your name:  Lena Solis   2. Your age:  37   3. Your country:  California, USA   4. Please tell us about an experience you had with math that was really fun and exciting:     Where and when did this happen? I really did not get excited about math until I repeated Algebra I for a second year.  Once the "lightbulb" went on I was excited to see the light go on for others. The elementary experience I remember most was staying after school and my fourth grade teacher helped me with division.     What math skills were you learning at that moment?  I was learning how to "do" long division.  I felt a great sense of self-satisfaction once I really understood it.     What did the teacher do? (if there was a teacher.)  The teacher spent additional time after school tutoring me.  Mrs. Bias, really inspired me to be a fourth grade teacher.      5. What suggestions do you have for teachers to make math more fun for students and to help students learn math?  I think getting the students actively moving and creating during math is important.  I love art and I can easily integrate it into math.   6. Any other comments?  I enjoy sharing and if anybody would like to e-mail please feel free.   _______________________ MATH FOR FUN SURVEY   1. Your name - Udara Soysa   2. Your age -16+ (almost 17)   3. Your country- Sri Lanka   4. Please tell us about an experience you had with math that was really fun and exciting:   Where and when did this happen? 1 month ago in our computer class (not in school).   What math skills were you learning at that moment? Actually we were doing some Visual Basics programming using maths and "IF" & "LOOP" conditions.   What did the teacher do? (if there was a teacher.) Actually the lecturer asked me to give the class some exercises in the day before the incident happen because he said he would be late to come to class.   What did you (and any other students) do? When I was writing the exercise in the white board some students said that they don't understand how to write those programs. So I taught the whole class just as our lecturer do and after the class my friends said my teaching was very good and they understood what I taught. (later our lecturer also thanked me)   How did it make you feel? I felt very proud about my self.   5. What suggestions do you have for teachers to make math more fun for students and to help students learn math?     For Teachers:- Always try to give a individual attention to every student. Teaching should not be boring and should always try to get the attention of the students. Use charts, projectors and things which can attract students. Should always be encouraging and should not give students the idea that maths is a hard subject. Should understand the mentality of the students and try to be like a mother/father for the students.   For Students:- ·        Always do your home work.(most important thing) ·        If there is something that you don't understand, don't hesitate to ask the teacher's help after the class. ·        Always give your priority to subject matters because your education is you future. ·        Do not cut classes. ·        Try to wake up little early in the morning and go through the notes your teachers gave you yesterday.   6. Any other comments?   I would like to advice students to always keep a clean and well directed mind. It really help you to concentrate well in your studies and also in other activities in your life.           Ill directed mind can inflict- more harm         Than a life long hater or foe.           Well directed mind can help him -more than         Well wishers, parents, kith and kin.     Best Wishes and love to Everyone!!!!!!!!!!     Udara from Royal College Sri Lanka.     XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX     Solo por diversion   Todos los a#os, en el proyecto Conectando las Matematicas a Nuestra Vida, tenemos una actividad llamada "Solo por diversion" (o como dicen nuestros amigos en Argentina,"Divertimatematicas"). Y nos gustaria realizarla nuevamente con el grupo de este a#o. Muchas veces vemos a las matematicas como algo serio, abstracto y dificil. En las actividades de "Solo por diversion" "Divertimatematicas" los alumnos descubren el lado ludico de las matematicas.   Mensaje original de Sikunder Ali Baber desde Pakistan para la seccion de Solo para divertirnos: sikunder.baber@aku.edu Presentamos a ustedes la siguiente pregunta..."cuantos cuadrados tiene el tablero de ajedrez? Una respuesta comun seria 64 o 65 cuadrados. Pero despues de una observacion cuidadosa la respuesta podria rondar hasta los 204 cuadrados. Como llegamos a esta respuesta? Les dejo la interrogante para que traten de descubrir... Enviare mas contribuciones con ideas en el futuro. Si estan interesados en comunicarse conmigo, pueden escribirme a mi direccion electronica: Desde la Escuela Superior Marondera, en Zimbabwe los estudiantes Charles Napuwera, Nesbert Shirihuru, Paul Dendere e Isaac Pasipanodya nos envian la siguiente solucion a la pregunta de Sikunder: wldmhs@internet.co.zw Area cuadrada (en unidades cuadradas) Numero de cuadrados en el tablero: 1 x 1           1                               64 2 x 2           4                               16 3 x 3            9                               4 4 x 4           16                              4 5 x 5           25                              1 6 x 6           36                              1 7 x 7           49                              1 8 x 8           64                              1 _________________________ TOTAL DE CUADRADOS 92 La solucion al problema es que el tablero de ajedrez tiene 92 cuadrados. La respuesta de Sikunder es la siguiente: Amigos, gracias por enviar su respuesta a la pregunta en la actividad de las matematicas solo por diversion. Me ha gustado ver que han trabajado para presentar la solucion sobre los cuadrados de un tablero de ajedrez. Su solucion parece apropiada y correcta. No obstante, les exhorto a volver al problema para una vision mas profunda. Si cuentan los cuadrados que se trasponen o entrecruzan,  entonces cuantos cuadrados hay? Este aspecto les puede ayudar a ver el problema desde otra perspectiva y afinar sus destrezas para la observacion, las cuales considero muy importantes para el pensamiento matematico. Si desean ampliar este problema, se pueden preguntar cuantos rectangulos hay en un tablero de ajedrez? Espero que continuen disfrutando mientras buscan la solucion a las preguntas. Muchas gracias Sikunder Ali Baber   Problemas solo para divertirnos desde la escuela superior Rakodzi en Zimbabwe:   Saludos amigos: Somos estudiantes de la escuela superior Rakodzi en Zimbabwe. Nos gusta la matematica y encontramos este proyecto muy divertido. Aqui les enviamos algunos problemas matematicos solo para divertirnos. Esperamos nos respondan con algunas soluciones. Como terminamos nuestras clases el 7 de diciembre, les deseamos una Feliz Navidad. 1.      Hay 710 personas en un tren. En la estacion, nadie bajo del tren. Cuantas personas se quedaron en el tren cuando este salio de la estacion? 2.      Cual es la palabra mas larga, si la medimos en millas. 3.      Susan tiene 2 chinas (naranjas) y tres ninos. Que deberia hacer si quiere dar una china (naranja) completa a uno de los ninos sin abochornar a los otros dos? Mensaje enviado por Victoria Muswere, Klery Chikwede, Vongai Mandizvidza and Gracious Pakarimwa desde la Escuela Superior Rakodzi en Zimbabwe     Problemas matematicos solo para divertirnos desde la escuela superior Marondera en Zimbabwe: Estimados amigos: Nuestra clase esta muy interesada en jugar con las figuras. Aqui les enviamos algunos problemas que esperamos encuentren interesantes: 1. Tres hombres han comido en un restaurante por $15. Cada hombre dio $5 por su comida. Luego el cajero nota que ha dado una vuelta de $5 a los tres hombres. El cajero piensa que los tres hombres no van a poder dividir en partes iguales los $5, por lo que toma para el $2 y da un $1 a cada uno de los hombres. Esto significa que cada hombre solo pago $4 por la comida. Para calcular el total de dinero, el cajero utilizo el siguiente procedimiento: 3 x $4 de los tres hombres es igual a $12 Mas los $2 que tomo pra el Nos da un total de $14 Pregunta: El balance no cuadra con los $15 que el cajero recibio de los tres hombres. (a) donde esta el otro dolar (b) Sumando el cambio que ellos recibieron $3, el balance de $14 suma entonces $17. Donde estan los otros $2 porque los hombres pagaron $15 y recibieron un cambio de $1 cada uno. 2. En una manada de hienas que cazaban un antilope una hiena es 4 veces mas rapida que la segunda hiena. Lac segunda hiena es media vez mas rapida que la tercera hiena. La tercera hiena es tres veces y media mas rapida que la cuarta. Cuan lejos puede llegar el antilope que es dos veces mas rapido que la tercera hiena. Enviado por Charles Napuwera y Nesbert Shirihuru Escuela Superior Marondera en Zimbabwe   ¡Les invitamos a tod@s a participar en esta encuesta!   Queridos amigos,   Todos conocemos estudiantes que no disfrutan las matemáticas y que incluso tienen temor de ellas. Ustedes también puede que se hayan sentido de la misma manera en alguna etapa de sus vidas. Trabajando con el proyecto Conectando las matemáticas a Nuestras Vidas hemos aprendido que este tipo de temor a las matemáticas no es culpa de los alumnos, sino que frecuentemente esto ocurre a causa de que las matemáticas no se enseñan de una manera divertida y animada. En este mensaje les estamos sugiriendo que miren hacia atrás y piensen en sus experiencias con las matemáticas, para que nos ayuden a construir ideas sobre cómo hacer las matemáticas más divertidas y significativas.   Recientemente recibimos una nota por parte de Krystle y Maha, dos estudiantes de 9no grado en el Líbano. Ellas escribieron:   *Hola! Las matemáticas ya no son tan divertidas como solían ser. Con cada año que pasa se hacen cada vez más difíciles. Nos gustaría que hubiera alguna manera de hacer que las matemáticas fueran una materia más interesante.*   Para otros estudiantes, la experiencia ha sido muy distinta. Udara, de 16 años y de Sri Lanka nos escribió:   *Necesitamos las matemáticas diariamente porque sin las matemáticas no podríamos hacer nada. Las matemáticas no sólo son una materia que estudiamos en la escuela, sino que se relacionan con toda actividad en nuestro diario vivir. Sin las matemáticas no podríamos ni tan siquiera ir a una tienda a comprar algo. Tampoco sabríamos utilizar el dinero. Realmente las matemáticas juegan un papel muy importante en nuestras vidas.*   Podrían ayudar a Krystle y a Maha con sugerencias sobre cómo hacer las matemáticas más divertidas? Comparten ustedes el sentir de Udara? En el Proyecto Conectando las Matemáticas a Nuestras Vidas creemos firmemente que las matemáticas no deben ser simplemente una materia enseñada en la escuela, desconectándolas del diario vivir. Si las matemáticas se aprenden de una manera en que muestren cómo podemos utilizarlas en nuestra vida diaria y cómo se relacionan con el resto de las cosas que aprendemos en la escuela como geografía, historia y arte; más estudiantes entenderán las matemáticas, harán una mejor labor en la materia y continuarán sus estudios de matemáticas.   Por favor ayúdenos en nuestra investigación para reunir ideas sobre qué hace que las matemáticas sean divertidas, llenando la encuesta a continuación. Todos pueden participar de la encuesta: maestros, estudiantes de cualquier edad y cualquier país. Pueden responder individualmente o grupalmente. Publicaremos sus resultados en nuestra página en la red para que todos puedan aprender de sus ideas y perspectivas.   Por favor envíe su forma llena a orillas-math@igc.org     Encuesta Matemáticas para diversión   1. Su nombre   2. Su edad   3. País en que vive   4. Por favor cuéntenos sobre alguna experiencia que haya tenido con las matemáticas que haya sido divertida y excitante:           Cuándo y dónde aconteció esto?           Qué destrezas matemáticas se estaban estudiando en ese momento?           Qué hizo el/la profesor/a (si hubo profesor/a envuelto/a)?           Qué hizo usted (y otros estudiantes)?           Cómo lo hizo sentir?   5. Qué sugerencias tiene para los maestros para que hagan las matemáticas más divertidas para los estudiantes y que faciliten el aprendizaje de las matemáticas?   6. Algún otro comentario?