„Maths around us” “Maths in games” and its results
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Introduction............................................................................................................................................. 3 Project aims ............................................................................................................................................. 3 The fifth stage “Maths in games” ............................................................................................................ 4 Activity 1 Ancient games and their history ............................................................................................. 5 Activity 2 Creating dominoes .................................................................................................................. 5 Activity 3 Let’s play Sudoku ..................................................................................................................... 8 Activity 4 Theatrical chess exhibition ...................................................................................................... 9 Activity 5 Gambling games .................................................................................................................... 11 Activity 6 Billiards in Maths aspects ..................................................................................................... 13 Activity 7 National games connected with Maths:............................................................................... 14 Summary ............................................................................................................................................... 16 Evaluation .............................................................................................................................................. 16
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Introduction The key linking all five partners of our project „Maths around us” was Mathematics. Our main aim was to improve Maths skills of students by perceiving Maths issues in their closest surrounding world. Students were encouraged to do their best to solve Maths tasks and to find similarities and differences between the environments of five participated schools by using a wide range of different ICT applications with English language as language of communication between partners. The project was divided into five parts:
“Maths in kitchen” with Italian school responsible “Maths in vehicles” with Bulgarian school responsible “Maths in buildings” with Turkish school responsible “Maths in nature” with Polish school responsible “Maths in games” with Spanish school responsible
Project aims The project priority was to develop maths, ICT, English and social skills by solving a wide range of tasks. Students awareness of maths existing everywhere increased and all time maths accompanies humans’ life. Teachers tried to design such tasks where finding solution or understanding the topic needed to use ICT applications free and available on the Internet and needed to work in group or pair work. Working on tasks needed to use English language.
All games, presentations, interviews, maths tasks, lessons students prepared in English. During motilities they also communicated and solved all tasks using this language. Before and after the project they solved English diagnostic test. Most of them achieved A2 level as it was expected. One of the project purpose was to develop ICT skills which are very important in contemporary world. Students were familiarized with a wide range of applications. They are free and can be easily found on the Internet. The list of apps used in the project: tagxego, smilebox, match memory game, hotpotatoes, issue, tools educator, you tube, comiclife, iMovie, moviemaker, doc.google, shapecollag, quizlet, dropbox, same quizy, symbaloo, proprofs, answergarden, socrative, kahoot, monkeyjam, blog, google maps, easly.ly, fodey, pikochart, webpage, edycaplay, blubbr, prezi, tondoo, padlet. Social and cooperation skills Doing project activities our students developed social skills. They mainly worked in pairs or in a groups enriching cooperation skills. During mobilities our students cooperated in international groups using English as language of mutual cooperation. All results of our mutual work were uploaded to eTwinning platform, our blog and our facebook.
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The fifth stage “Maths in games” Maths in games activities were divided into monthly tasks which we uploaded on eTwinning space. Students worked on maths topics such as: probability calculus, Sudoku, Maths dominos, chess, national maths game. Students prepared some interesting presentation about different games along the history: many Egyptians games, Assyrian, Mesopotamian, Vikings, etc. Games rules are sometimes not known with certainty, but thorough manuscripts and other findings can achieve a possible approach. They could choose application for their presentations.
All students were familiar with rules of dominoes. Their task was to create new dominoes with different rules: animals, words, living things…with maths or language aspects. They became acquainted with history and Sudoku tasks. Students created exhibition theatrical "Chess play” and presented it by means of chosen applications. Students found different gambling games on the Internet, familiarize with the topic of probability in different gambling games.
Knowledge of different billiards rules. Study of the influence of the angles in the game.
Knowledge of different games related with Math and numbers (the best would be a presentation of national game). Evaluation
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Activity 1 Ancient games and their history Examples: Using various computer applications students presented the history and rules of ancient games: https://www.youtube.com/watch?v=SD0ycv70QnQ&feature=youtu.be https://www.youtube.com/watch?v=KNuly6Iee0Q&feature=youtu.be https://www.youtube.com/watch?v=bxShIUCjEf0 https://www.youtube.com/watch?v=9i83REXxfqQ&feature=youtu.be https://issuu.com/ewanenkin/docs/b1126f5c8.pptx https://youtu.be/VEcT7nFQHwo https://issuu.com/ewanenkin/docs/tutcy.docx_d45be16fdc727e https://issuu.com/ewanenkin/docs/it
Ancient game: AWALE an African ancestral game. This game teaches us how to watch our seeds, and at the same time, care your opponent's harvest.
Activity 2 Creating dominoes Students creates dominoes about maths or English as the main topic.
Examples: https://youtu.be/qqwMhFWk3SY
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https://issuu.com/ewanenkin/docs/domino
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Activity 3 Let’s play Sudoku Students were familiar with history of Sudoku and solved Sudoku tasks at different levels. At some project schools they took part in Sudoku competitions: Examples: https://issuu.com/ewanenkin/docs/pol.pptx
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https://www.youtube.com/watch?v=faIxwLkzTE0&list=UUJablhPP_EccMlqzGkIjv5g&index=30 https://issuu.com/ewanenkin/docs/sudoku https://issuu.com/ewanenkin/docs/suu.docx https://issuu.com/ewanenkin/docs/su
Activity 4 Theatrical chess exhibition Students learned how to play chess and made movies, presentation or comics about it. They also played chess and participated in chess competitions.
Examples: https://youtu.be/7z-lzeHLoeM https://issuu.com/ewanenkin/docs/bulgata.pptx https://youtu.be/VoGRHQtdFxI https://youtu.be/AbSM_esiEsk https://www.youtube.com/watch?v=FYiEAMhU4mE&feature=youtu.be https://www.youtube.com/watch?v=G1S3VA58XSA&index=25&list=UUJablhPP_EccMlqzGkIjv5g
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Activity 5 Gambling games Examples: Software used to play these types of games: https://www.kurnik.pl/ you have to log in and can play online with others. There are many boarding games to choose and gambling games. gambling games: we used padlet to show you our presentation:
https://padlet.com/nenkin/8gaqyi7itmls https://issuu.com/ewanenkin/docs/bingo.pptx Here are some links for various games software. http://www.chesslab.com/ https://www.playok.com/ https://www.coolmath-games.com/1-classic-games We introduce you an ancestral math game, who calls, the Tower of Hanoi, also called the Tower of Brahma. It consists of three rods and a number of disks of different sizes, which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape. The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules: Only one disk can be moved at a time. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod. No disk may be placed on top of a smaller disk. With 3 disks, the puzzle can be solved in 7 moves. The minimal number of moves required to solve a Tower of Hanoi puzzle is 2n − 1, where n is the number of disks. In this website you can play and challenge you and your peers: http://www.ajedrezeureka.com/torres-de-hanoi/ https://youtu.be/k91tNtR69TI https://youtu.be/Qgg4vimWGp8 Probability in the game Everyone's dream: “win in gambling” to those who do not happen at least once in their life to try their luck and become a millionaire playing a card, the lottery or the superenalotto? But how practical are the chances of victory? More generally, in the superenalotto, how many chances are that one of the winning combinations will come out? what is the probability of doing a 5 +, or the probability of doing the magic 6?
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We see it reading and giving a mathematical justification of the result with the calculation of probabilities. I start from the end of the article to never play the lottery, lotto or any game of chance! We can all afford to play one euro by whim, but with the awareness of having thrown it to the wind. Let's see why: very few people have a precise idea of how many are the precise probabilities that come out just the six numbers chosen, to calculate the probabilities that a sequence of six numbers come out from 90 available we must refer to that which in combinative calculation goes under the combination of name simple. In practice it is a matter of calculating the possible number of sequences K = 6 numbers, choose between n = 90 numbers, among which is the winning sestina. The number of possible six-fold that can get out (that is the number of possible 6 with the exception of the winning one) is calculated with the formula đ?‘ ( đ?‘› đ?‘˜) đ?‘›! (đ?‘› −đ?‘˜)!đ??ž! where( đ?‘› đ?‘˜) is called the binomial coefficient, n is the number of possible numbers (in our case 90) and k the number of elements that make up each sequence (in our case 6). Now attention and concentration: đ?‘ = (90 6 ) = 90! 84!6! = has 622.614.630 sequences. This means that with 90 numbers we can compose 622.614.630 sestinas, not bad right? Therefore the probability of doing six at the superenalotto playing only one sestina, is 1 out of 622.614.630. We do not report the calculation of a 3, a 4, a 5 or a 5+, but we already see the results: Probability of doing 3 at the superenalotto 1 out of 326 Probability of doing 4 at the superenalotto 1 out of 11906 Probability of doing 5 at the superenalotto 1 out of 1235346 Probability of doing 5+ at the superenalotto 1 out of 103769105 With similar calculations you can see that any game is just an illusion of a victory, but remember to win, you will never be you!
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Activity 6 Billiards in Maths aspects Examples: Polish project students discussed how to play bilard, what is the way of the billiard ball? They couldn't play but watch the movie about playing this game from maths point of view.
https://www.youtube.com/watch?v=vz7OdTtnQWI&feature=youtu.be https://issuu.com/ewanenkin/docs/bilard.pptx https://issuu.com/ewanenkin/docs/bulgaria_billard.pptx https://youtu.be/FzP2zJKb2hY https://issuu.com/ewanenkin/docs/spanish_billard.pptx The game of billiards between physics and geometry Charm and mystery have always characterized the attention of fans both of the game of billiards and geometry. They look at it with surprised and ecstatic faces as if it were a magic game. Around this mystery, there are geometric rules that lay the foundation to understand more or less complex phenomena that occur within the green table. Mr. Fabio Margutti, fond of such phenomena, has decided to study them by applying the method handed down to us by Galileo Galilei: observe the phenomena through experimentation, collect the information and extrapolate the basic rules. Therefore he has started to carry out tests on tests using as a unit of measurement particular points of reference called diamonds that, by international convention, are marked at specific distances on the wooden part of the banks of each pool and allow to intercept and identify the trajectories. Basically, moving a marble along any primary diagonal, on impact with the first bank, we get a well-defined secondary path related to the response of the marble with the subsequent banks. Every point of this path represents a potential arrival of the standing trajectory. Among the many hypotheses to be done we must try to understand what relates the primary trajectories with respect to the same arrival. Analysing graphically the possible trajectories we realize that they converge in a more or less accentuated way towards a point outside the billiards called centre of convergence. The principle of the centre of convergence can be translated conceptually to all the arrivals in the pool table, thus obtaining an external mapping to the pool of convergence centre. Since the outer space is multiple, we need to search for as many points as possible outside the billiards by establishing the correlations of arrival and the consequent necessity of ordering and grouping them according to the most practical modalities of the game of billiards. The next step is to try to compare the real trajectories with those ideal geometric. If they do not match, their deviations could inform us about the physical phenomena that alter geometric trajectories. Studies show the behaviour of a marble that hits the side of a generic billiard made up of a particular type of elastic rubber with triangular profile covered with fabric.
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Activity 7 National games connected with Maths: Polish example: Quiz about the creator of Farmer board game from Poland - Karol Borsuk:
https://samequizy.pl/how-well-you-know-karol-borsuk/ how to play Farmer:
https://issuu.com/ewanenkin/docs/farmer_by_karol_borsuk.pptx_d4f1d8643cb348 our farmer competition:
https://www.youtube.com/watch?v=a8JqxIfvOY&list=UUJablhPP_EccMlqzGkIjv5g&index=24
Bulgarian example: https://issuu.com/ewanenkin/docs/bulgaria_game.pptx
Turkish example: https://youtu.be/bXMIGeDeS_I
Spanish example: https://issuu.com/ewanenkin/docs/spaish_game.docx
Italian example: La "scopa" (in English broom) - a typical Italian card game "Scopa" is the most popular card game played with a deck of 40 cards that include: ace, 2, 3, 4, 5, 6, 7, jack, horse (or woman) and King. They are assigned values from 1 to 10 in the order listed. The name of the game refers to the fact that the winner usually takes all or at last the majority of the cards on the table, so he "sweeps them away". Over the years, variants based on the same game scheme were born. Let's list some of them: Bazzica scopa, Cirulla, Rubamazzo, Scopa a perdere, Asso piglia tutto, Scopone scientifico etc.
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Milano 1937 ITS STORY The birth of "scopa" and "scopone", in spite of the many efforts of fans and scholars is still shrouded in mystery. The only certain thing about the game is that "scopa" can be considered "the mother" of "scopone" as we know it today. Since the birth of "scopone" can be traced back in the middle of the 18th century it is probable that the game of "scopa" was born at least a century before. The only book on this subject that teÄşls different things is: La scopa- Aschero Cireneo - ed. Zibetti- 1995 which states..... ..."born among the sailors in the taverns of the port of Naples around 1490". Unfortunately we haven't any document reference since at that time the playing cards had just begun to spread among the population of lower social rank replacing dice and dominos in gambling. The 40 cards Napoli, Tip. Cataneo, 1840 The game of "scopa" and the Maths It will seem strange but the game of "scopa" turns out to be the most complete to develop and enhance the computing skills from nursery school to high school, so that it is one of the 11 games to upgrade the calculation skills in primary and high school. In particular, in primary school it allows to reinforce the ability to add and subtract within ten, enhance skills of critical thinking (avoid playing cards that can allow the opponent to "sweep the cards away"; formulate hypotheses on the cards in the opponent's hands and establish a course of action, try to get hold of the cards marked 7, particularly the "golden" ones, prefer to take "golden" cards rather than another "seed". In high school it is an excellent application for probabilities. Let's make some examples. I have a deck of 40 cards distributed among 4 players (10 each). Calculate the probability that a player has in this hands 2 cards(no more) marked 7, knowing that he has at least one. Applying the probability calculation the result will be: NO OTHER "7": 0,4442 ANOTHER "7": 0,4284 2 MORE "7": 0,1182 THE OTHER 3 CARDS "7": 0,0092 TOTAL: 1,0000. Are there any methods and systems to win the game of "scopa"? The answer is half no - half yes. There are some mathematical systems now tested for a long time which allow to win almost always this game; they are tried and tested systems whose results are almost always reliable. "The 24", "the 36", and "48" are the most famous, but there are others very good. The set of these systems makes the player very strong. But remember...... Maths can never replace luck. So we end our little journal into the world of the game of "scopa"
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Summary We created tasks which helped students to know the rules of many games from Maths point of view. We wanted to match games, Maths, ICT and English in this part of the project. All tasks we worked on were presented by means of interesting and free IC application.
Evaluation https://issuu.com/ewanenkin/docs/analisys_of_survey__maths_in_games_
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