Mathematica regina omnium scientarum et

09.07.2019., utorak


From 1 to 5 July, Croatia was the host for the international meeting in Osnovna škola Josipa Kozarca in Slatina. On the first day our guests were greeted by our teachers and our students. After the welcoming show and a short tour around the school, our guests were taken on a short excursion to a nearby city of Đurđevac where they were able to visit the Croatian Sahara. On the second day, our path has taken us to Osijek to the Faculty of Mathematics where we were warmly welcomed by the professors and we were able to listen to a lecture in English related to our project. Then we went on a tour around the city (cathedral, the main square, Tvrđa, museum of Slavonia and many more). On the third day our guests were taken on an unique experience to Adrenaline park Duboka, Orahovica lake and the old Ružica grad. On the fourth day we visited the heart of our county Virovitičko- podravska where we visited the town of Suhopolje and Virovitica. On the last day, before deporting for the airport, we went to visit the old castle of Trakošćan. Below you can see some of the photos from this unforgetable meeting.

24.06.2019., ponedjeljak

ABOUT MATHEMATICS ... discreetly Activity for June 2019.

Activitiy description:
7th graders took part in the Cryptology Workshop, where they introduced with the fact what cryptology is and how cryptography is one of its branches and how they evolved through history.

Furthermore, they had the opportunity to work with skytal - stick by which the Spartans encrypted their messages from the 5th century BC. Cr. Skital was a wooden stick around which a parchment ribbon was wrapped around, and the message was vertical written. After typing the message, the ribbon would be folded away and there would be mixed signs that only the one with a stick of the same thickness could read. The students got sticks of different thickness and paper that wrapped around the stick and wrote their messages.

They noticed that this simple encryption method was very effective because they could not decipher other messages without a stick of the same thickness.

Polibi square
After that, they decrypted the messages by using the Polibi square. Polybias was a Greek (and Roman) historian who studied and wrote during the 2nd century BC. Cr. He took over and perfected the idea of Greek mathematicians by using a simple mathematical method of using the numbers and the coordinate system to send encrypted (secret) messages. The polybium square is essentially a square of 25 fields (5 rows of 5 columns). Each field has one letter, besides the field that contains the letters I and J. Each row and column is numbered 1 to 5 so each letter is assigned a pair of numbers. By using the Polibi square, the students have decrypted the names of partner countries.

After that, they got a little more contemporary version of the Polibi square, where instead of the letters they got smilies and this version of the Polibi square is adapted for mobile phones. These activities should be deciphered by "I Love Mathematics".

The last activity is related to Gaj Julije Cezar. He is the creator of Caesar's code whose aim is to replace a certain letter with the letter that is three places further from it in the alphabet (A ’ D, B ’ E, etc.).

In order to make it easier for students to use Caesar's code with an arbitrary shift, instead of summing up, students can use a circle ("wheel") made of cardboard with all alphabetic letters printed in the row. Let the circle ("wheel") consist of two circular portions. It is necessary to fix the outer part so that the inner part can rotate in the circle. So we get all 25 possible combinations of open and encrypted alphabet. The students cut their circles and joined them so that the inner circle could rotate around the outside, which is necessary. There was a word written on the board that did not make any sense and the key was given to students (C = F). The students set up their "Caesar wheels" and deciphered the default term.

Activity aim:
The popularization of mathematics with an emphasis on the development of creativity, curiosity and imagination. The security of the cryptosystem lies precisely in our inability to quickly and efficiently solve the appropriate problem in the area of algebra, number theory or combinatorics. Interesting encryption methods and in particular the detection of methods for breaking the encryption system will enable students to experience the power and beauty of math. Also, to connect the teaching of Math and History.

Contemporary methods of work:
Learning and teaching conducted by discovery and conversation
Learning outcomes:
Getting to know cryptology and seeing how cryptography is a part of cryptology and how a major role in mathematics it has with all its domains. The popularization of mathematics and the connection of mathematics teaching to history teaching.
Activity results:
The students have adopted the basics of cryptography: basic algorithm (Alice -Bob -Eve), encryption (encryption), decryption and key. In history examples, they coded or decoded the default codes and observed the development of cryptography as well as its growing importance (from military, intelligence and diplomatic services to telecommunications and banking). Simply said, cryptology has become our daily life.
The workshop was created and accomplished by History teacher Martina Grundler Hrala in in cooperation with Math teacher Anita Jukić and English teacher Azra Benković.

The activity is accompanied by making a short film in English which will be released on a
transnational meeting in Croatia in July 2019.

In purpose of making this kind of a film, the activity is translated in English and leading actors are students who present their knowledge through the activity (student Lorena Filić). For documenting the activity we are going to use multimedia equipment, photo camera, camera, internet, Youtube channel and Adobe Premiere Pro program (student Tvrtko Kolarić).

23.06.2019., nedjelja

BETWEEN US … ORGANISMS Activity for April/May 2019.

Talking to students, explain the purpose of the activity. Think, based on our own experience, how many times we have been in a situation to intervene in the relationship between the prey and the predator trying to disable the predator in his intentions. Of course, we would save the prey, victim and conclude that we did a good deed. But is that so? Ask the question: What would happen if, for example, people would often release frogs from the copperhead's jaws or sparrow from the hawk's claws so that predators always kill each other? The students will conclude that this would lead to the appearance of a large number of frogs and sparrows and to the destruction of the copperheads and hawks. The consequence of such order of organisms in nature would disturb the number of other living beings that feed frogs and sparrows and ultimately lead to their extinction. In the end, food would disappear, and frogs and sparrows would disappear. And that would be the end of it. Explain the students how this kind of event is called an ecological catastrophe.

In this way, the students should become aware that this relationship between organisms implies interdependence in the diet creates the only possibility of preserving life on our planet. That is why this relationship is the most important. 7th graders will learn this school year about biolinbiology teaching systematics by studying their anatomy, physiology, ecology and evolution. Using the acquired knowledge, within the project "Mathematics-the queen of science", students will explore the nutritional relations between the parks of the Papuk Nature Park with a special emphasis on the Ivanjski rovaš type. It's group activity, workshop entitled: "I EAT, YOU EAT, HE EATS - RELATIONSHIP THAT KEEPS LIFE ON EARTH" (subtitle: "The nutritional realtion between Ivanjski rovaš and other organisms of the Park Papuk Nature Park"). After the presentation of a rare, strictly legally protected and the smallest lizard in Croatia, noticed 2008 only in the Papuk Nature Park and at several locations in Ilok, students will be divided into three groups.

Group 1: The production of food chains that include PP Papuk organisms grouped according to the diet in the producers and consumers of I, II, III and IV order and featuring Ivanjski rovaš as consumer II order.

Group 2: Production of nutrition grid (intertwined feeding chains - one member appears in multiple chains) based on analysis of the first group's work.

Group 3: Production of nutritional pyramids (number among members of individual nutrition groups) based on established relationships between organisms in food chains and nutritional grid after analysing works of 1st and 2nd groups.

Activity aim
To stimulate students' interest in science by researching nutritional habits of organisms, to develop students logical thinking and inference by placing individual organisms into appropriate food groups, to encourage environmental awareness among students to act
responsible and by respecting natural laws without harmful interference, provide the maintance of natural balance in the area where they live.
Motivation for activity comes from the fact that someone always eats something in nature and that is completely normal. By acquiring this natural legacy, it enables the circulation of matter and the flow of energy through the living being, which is the foundation of the entire life in the Earth. So, nutrition relations among organisms most clearly represent the dynamics of life that excludes any monotony.

Contemporary methods of work: collaborative learning, research work using ICT, dialogue method, writing methods, reading methods with understanding of teaching assignments, skillful drawing methods and color expression.
Learning Outcomes: Students will differentiate eating habits of particular species and their role in the food chain, assamble and explain nutrition chains, link feeding chains to nutritional grid and shape nutritional pyramid, monitor the abundance of organisms of specific habitat.
Activity Outcomes: Based on the established nutritional relations, the students conclude on the importance of conservation of all species, so that each of them contributes to a stable natural balance and the maintenance of the life we know it. Consequently, the students will conclude that they are involved in this process in their daily lives by taking the place of the highest order consumer - collectors, plowmen and hunters who have no natural enemies. Therefore, man carries the greatest responsibility.

The activity is created and accomplished by students and Biology teacher Brankica Safin.

Within another workshop called "Between Us ... organisms", students are examining examples of relations between living organisms.
They are conducting a research on the population of domestic animals that live in the same area as they do and based on collected data ,
they are doing statistical analysis and that way they link math to real life.

The students visited,on their own, several owners of pig farms, sheep, chickens, cattle. The owners held interviews based on which they collected the necessary information and photographed the farm and the animals. The owners of the farms are Josip Šomođi, Zdravko Vukovski, Željko Bobanić, Vjekoslav Hes, Goran Vuković, Dunković Dijana, and interviews were conducted by a student of the 6th grade, Josipa Dorić.

27.05.2019., ponedjeljak

Meeting in Portugal

From 13 to 17 May our teachers and students went to Portugal to school Santos Simőes in Guimarăes. In the link below you can read about their experience and see many amazing photos of the visit.
Fourth mobility in Portugal

14.04.2019., nedjelja

I LIVE IN... Activity for February/ March 2019

Activity description:
There was a workshop for 7th graders where they, in groups, collected, studied and graphically presented the statistical data of population total number movement, population national structure and natural modification of Republic of Croatia's inhabitants in period 1981-2011 according to the data from population census.

The first group presented statistical data of Republic of Croatia's population total number movement in mentioned period and presented it by line diagram.

The second group presented statistical data of national structure of Republic of Croatia's inhabitants in mentioned period and presented it by pie chart.

The third group presented statistical data of natural modification of Republic of Croatia's inhabitants in mentioned period and presented it by bar diagram.

for this activity comes from the fact:
-in 90's Croatia went through war destruction in a strle for independence and coming out from SFRJ and consequences were numerous society changes, one of them was a national structure modification of RH's population. Because of turbulent social geographic and socioeconomic movements, the total number of RH's inhabitants is constantly reducing and natural modification is negative.
-presenting statistical data is part of mathematics
-to connect activities of Geography and Mathematics
-to encourage researching and connecting related sciences and to apply the theory to concrete tasks in real life

There was a workshop with 7th graders where they , in groups, explored the discoveries of America, Africa, Australia and Oceania.

The first group explored the discovery of America. The journey of Christopher Columbus and Amerigo Vespucci.

The second group explored the discovery of Africa. Circumnavigation of Africa by Portuguese sailors: Diogo Cao, Bartholomeu Dias and Vasco da Gama.

The third group explored the discovery of Australia and Oceania. The journey of James Cook.

All groups used NEW globe and geographic map of the world.
Inspiration for this activity comes from the fact:
-all „big geographic discoveries” changed the cognition of our planet's size and appearance.

-to connect the activities of Geography and Mathematics
-to encourage curiosity, research and positive attitude about natural values.
-to connect related sciences

Film projection „THE MISSION, 1986”

7th graders were involved in a workshop that connects film art ( media culture class) and Geography class. It's about watching and directed interpretation of The mission plot.
The student's task was to interpret story setting noticing location features that story setting unrolls. As the theme is placed on 15 location, from which the biggest parts are South American areas, students were paying attention to the areas.
Tasks that were directed to connect film plot and Geography class, consist of students' dealing with geographical map and globe, noticing natural geographical area features and recognition of typical flora and fauna.

After they have watched the film and paid attention to selected scenes, students have to solve the task. They have blind map od South America and film synopsis with marked locations od the action. Firstly, students are looking for South American countries, they mark them with colours on the blind map and then precisely determine geographical location in those countries. Afterwards, using film scenes, they determine which natural geographical features are in these countries and using their own symbols inscribe it on the blind map. This way, students can inscribe rainforest vegetation, high mountains, waterfalls, monkeys as prototypes animals, etc.
Task is finished when students do their own geographical map of The Mission film from 1986. Students present their work and mutually compare their geographical maps.

MOTIVATION for this activity comes from:
- importance of connecting teaching and non teaching contents and interdisciplinary approaches to the class
-fact of importance of noticing life features of other nations and cultures with purpose to cherish cultural and intercultural relations, but also deepened learning strategies in Geography class.

-to connect media culture class, in this case, film art with Geography class
-to encourage research, creative way of students' expressing
-to encourage and raise awareness of intercultural dialogue

The activity is accompanied by making a short film in English which will be released on a transnational meeting in Portugal in May 2019. In purpose of making this kind of a film, the activity is translated in English and leading actors are students who present their knowledge through the activity.
For documenting the activity we are going to use
multimedia equipment, photo camera, camera, internet,
Youtube channel and Adobe Premiere Pro program (Tvrtko Kolarić).

The activity is created and accomplished by Math teachers Anita Jukić and Denis Vujanović, Geography teacher Mira Safin Knežević, Croatian teacher Danijel Vilček in cooperation with English teacher Azra Benković.

25.02.2019., ponedjeljak

How much CHEMISTRY is in CHEMISTRY? Activity for January 2019.

Activity description
We conducted a planning process of eco soaps production among 7th graders included in extracurricular activity Fuleren- young chemists. Soap is anionic surfactant used for washing and cleaning. It is in solid aggregate state or in a shape of viscous liquid. The difference of chemical structure is shown in sodium or potassium salts of fatty acids. We get soap with acids reaction with strong alkalis in process of saponification. Nowadays, soaps are more used for personal hygiene, while in the past these products were a main resource for cleaning because of soap's ability to remove greasiness. Long polar molecule of the soap with the hydrophilic part absorbs water while the hydrophobic part escapes water.

In the aqueous solution the soap molecule is directed so the hydrophobic part is directed toward the fat molecule.When the fat drops ,completely encapsulates the molecules of the soap,it creates balloon clumps of fat called micelles, on the outer part where hydrophilic ends of the soap are exposed. As these endpoints are plunged to the water, such a cluster is floating and during the washing it will easily leak down the stream of water.Soaps are also surface-active substances and that reduces the surface tension of water.

During our workshop we were conducting a cold soap manufacturing process.We've tried to make good quality soaps and we were trying to create an ideal ratio of alkaline, water and fatty acids.The reason for the addition of the base lies in the aspiration of the process of saponification. Saponification is the process of fat degradation, analogously to the process of soap formation which includes time dispersion of soap. The cold production process was carried out to eliminate the possible unwanted effects of the corrosive sodium base. The production process was carried out through 10 steps. We have started with the inevitable preparation of metal molds for soaps and dishes and laboratory equipment. Afterwards, we weighed the ingredients into glass bottles and gauge glass and weighing in, according to the saponification factor, was very important. Mixing of water and hydroxide should be conducted very carefully. Carefully add the base to the water! Never water in the basin. Leave the solution to cool with occasional stirring. Keep in the airy room. As the base cools down, you should warm the oil. The oil and lye must be of the same temperature. While stirring slowly add the oil. Add essential oils and dyes. Pour the soap in the molds and pay attention it's evenly distributed. It's time for cleaning the space and laboratory equipment. Thoroughly wash all the dishes! After 24 hours remove the soap from the molds and leave it for 4 weeks. Try soaps after 4 weeks.

Inspiration for this activity:
-more common homemade and natural (eco) soaps manufacture
-very simple process used in ancient times
- developing inovation and creativity in children because of possible use of different ingredients such as essential and edible oils and different nutritional colours
-children's interest to make their own usable soap
-use in everyday life
-chemistry and mathematics link

Activity aim
-to connect by carrying out math and chemistry experiments using a daily batch of chemical calculations, by applying analogously andmanufacturing preparations we use daily
-popularize eco products in everyday life
-encourage pupils to protect nature and use eco and natural products

The activity is accompanied by making a short film in English which will be released on a transnational meeting in Portugal in May 2019. In purpose of making this kind of a film, the activity is translated in English and leading actors are students who present their knowledge through the activity. For documenting the activity we are going to use multimedia equipment, photo camera, camera, internet, Youtube channel and Adobe Premiere Pro program.

The activity is created and accomplished by Math teacher Anita Jukić and Chemistry teacher Mateja Filković in cooperation with English teacher Azra Benković.

28.12.2018., petak

Activity: What can be seen when the NIC does not see? ONLY IN THE DARKNESS YOU CAN SEE THE STARS, December, 2018


Activity description:
There was a workshop among 7th graders where they were studying shining stars in individual constellation and calculating apparent star size. Apparent star size is a quantitative size of a glowing celestial object, i.e. the measure of brightness which it creates on Earth surface. Apparent star shine describes how much the star shines in the sky, not considering the reasons of its strong or weak glow,i.e. distance or real quantity of radiated light. Apparent (observed) glow expresses in, so called apparent star sizes magnitudes-m. There are more methods of determining apparent star size, and we picked Argalander's method. This method uses a sequence of neighboring stars that depend of an instant glow. We've studied star in constellation : Great Bear, Orion, Cepheus and we've tried to determine apparent size of a comet Wirtanen, so called Comet, which is, these days, visible to the naked eye and it's going to be visible on Christmas Day in the evening.

Inspiration for this activity comes from the fact that astronomy:
-is one of the oldest sciences made from primary human activities and practical needs
-has got a long history in Croatia since 12th century and series of discoveries and Getald's discovery
of binoculars and Bošković's geometrically determining of comet's path are just some of them
-favorite science among children because of practical use and amateurs, still has a special part in
discovering and watching celestial phenomena
-related to Mathematic

Activity Aim:
-to connect astronomy and mathematics with Christmas theme
-popularization of astronomy and similar sciences

Additionally the activity is accompanied by making a short film in English which will be released on transnational meeting in Portugal in May 2019. In purpose of making this kind of a film, the activity is translated in English and leading actors are students who present their knowledge through the activity. For documenting the activity we are going to use multimedia equipment, photo
camera, camera, internet, Youtube channel and Adobe Premiere Pro program.
The activity is created and accomplished by Math teacher Anita Jukić and Physics teacher Martina
Bukvić in cooperation with English teacher Azra Benković.

Science and culture - Glagolitic script in Mathematics, November, 2018

Did you know that each Glagolitic letter is a mathematical number?

We did two activities:

Description of the 1st activity:
There was a Glagolitic inscriptions workshop among 7th graders called Glagolitic script in Mathematics. Through motivation talk about Glagolitic script, students were remembering previously acquired knowledge of an old, Croatian letter. In central part, students were given worksheets filled with Glagolitic letters and they should unriddle which Glagolitic letter represents each Latin letter. To connect Mathematics and Glagolitic script, students were cutting cardboard Glagolitic letters and then made Glagolitic inscription, name of the project Mathematica regina omnium scientarum et. Inscription, made at the end of the workshop, was exposed on school billboard dedicated to the project.

Workshop manager: Ivana Strupar, Croatian teacher

Activity: Glagolitic script and Mathematics, November, 2018

Description of the 2nd activity:
7th graders have already been familiar with Glagolitc script and letters during so far school education, in elementary school education. During the workshop Glagolitic script and Mathematics, students were discovering, for the first time, that each Glagolitic letter also presents one number so they can also write numbers and solve different mathematical operations. In preamble of the workshop, students reminded themselves what Glagolitic script is, its characteristics and importance for Croatian culture and history. Students were filling in worksheets with information about the Baška Tablet, the most important Croatian Glagolitc monument. Students had to write numeric data of the Baška Tablet in numbers of Glagolic script. In central part of the workshop students were, in pairs, solving Mathematics exercises in Glagolitic script. Works, made during the workshop, were exposed on school billboard dedicated to the project.

For the needs of the activity we have made a memo:

Workshop manager: Hana Tepeš, Croatian teacher

Croatian Glagolitic script is the oldest letter of Croatian people and big part of its national identity and culture. The aim of this project activity is to connect Croatian inheritance with, seemingly unrelated , Mathematics. Students were discovering correlation of letters and numbers, language and Mathematics, inheritance and science.
Also, the aim of this workshop is promotion of Croatian culture inheritance. This way, we want to encourage students to think of the preservation and existence of Croatian Glagolitic script and celebrate, understand and protect its unique value.
Additionally the activity is accompanied by making a short film in English which will be released on a transnational meeting in Portugal in May 2019. In purpose of making this kind of a film, the activity is translated in English and leading actors are students who present their knowledge through the activity. For documenting the activity we are going to use multimedia equipment, photocamera, camera, internet, Youtube channel and Adobe Premiere Pro program.

The activity is created and accomplished by Croatian teachers Hana Tepeš and Ivana Strupar and
Math teacher Anita Jukić in cooperation with English teacher Azra Benković.

28.11.2018., srijeda

MATHEMATICS - WHAT IS IT? Activity for September/October 2018

Activity description
Students in 7th grade learn about proportional variables which depend one of another in two different ways.
Rule of proportional variables says, how many times one variable increases, that many times the other variable increases ( and vice versa).
Rule of vice versa proportional variables says, how many times one variable increases, that many times the other variable decreases (and vice versa).

During the activity, students will be divided into two teams. One team will spend the activity in the school yard applying proportionality on calculation of difficult measurable heights of some object, e.g. trees, street lamps and similar, also they’ll measure length of a shadow.

The other team will, based on proportionality, explore are the dolls they played with, proportionally built, considering people in real life.Through these activities, students need to become aware that everything learnt on Math lessons is applicable to various life spheres, from measuring to imposed measures of ideal look.

25.09.2018., utorak

Meeting in Romania

From 6th to 10th August, our teachers went to Romania for an international project meeting.
On the first day there was a meeting for result analysis and a discussion about the disemination of results in a form of workshops. Also there was a fun summer school activity called 'Fun Math' that all the project partners were able to participate in. On the second day everybody shared experiences about motivation methods, discussion about the focus scale and there was further talk about the implementation of the project and then there was another summer school activity that everybody could participate in called 'Math and Art'. Later in the afternoon there was a showing of a movie related to the rich Romanian history.
On the third day there was still talk about the motivational experiences and also all the partner countries were able to try out the popular japanese paper folding method called origami. After, there was a meeting about the upcoming meeting in Portugal and the Chemistry festival that will be organised there and all the necessary reqirements for the next school year.
On the fourth day there was a discussion about weak points and possible outcomes on budget and also potential threats that may come in the activities during project implementation and prevention methods.

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