With a task from the Christmas Trail, we would like to present the last “Task of the Week” this year and draw attention to the possibility of addressing probabilities in the context of MCM. Task: Packing Station in the Westend (task number: 779) You should pick up two packages for the boss. You do not […]
With a task from the Christmas Trail, we would like to present the last “Task of the Week” this year and draw attention to the possibility of addressing probabilities in the context of MCM.
You should pick up two packages for the boss. You do not know their size. You guess behind which of the yellow boxes they could be (in each box can only be one package). What is the likelihood that the packages will really be behind the ones you picked?
First of all, it has to be clarified how many boxes there are. Then one can calculate the probability of picking the first box and the second box correctly. In this case, combinatorial considerations are necessary as to whether the order plays a role. As answer format, multiple choice was chosen for this task, whereby the correct solution can be expressed in terms of two possible answers: once as a fraction and once as an estimate with percent, which underlines the equivalence of both forms. The task is recommended from grade 9 onwards.
With this task, the MCM team says goodbye to the Christmas break and wishes all users a Merry Christmas and a Happy New Year. We are curious to see how we can further develop the MCM project in the new year and look forward to an exciting time!
During summer, we visited Münster University. Even the WDR (a German TV station) reported on this. Since that, the work group headed by Stanislaw Schukaljow has developed several tasks and an own trail in Münster. Of course, we are very pleased to see that und hope for many visitors of the trail. On page 3 […]
During summer, we visited Münster University. Even the WDR (a German TV station) reported on this. Since that, the work group headed by Stanislaw Schukaljow has developed several tasks and an own trail in Münster. Of course, we are very pleased to see that und hope for many visitors of the trail. On page 3 of the university newspaper from December 2017, you can read the full article.
As a task creator for MathCityMap, it is important to look at the environment through “mathematical glasses”. Thus, buildings become cuboids, lawns become polygons or – as in the current task of the week – greenhouses become half cylinders. Task: Arched greenhouse (task number: 1950) Calculate the material requirement for plastic for the greenhouse. Give […]
As a task creator for MathCityMap, it is important to look at the environment through “mathematical glasses”. Thus, buildings become cuboids, lawns become polygons or – as in the current task of the week – greenhouses become half cylinders.
Calculate the material requirement for plastic for the greenhouse. Give the result in m².
When solving the task, students’ mathematical view is also taught. This involves the recognition of the object as a lying half cylinder. Once this has been achieved, radius, the circumference of the semicircle and height must be measured, so that the material consumption can be calculated. This corresponds to the surface of the half cylinder, which can be determined by means of formulas for the area of a circle and the surface of a cylinder.
Through cooperation with the MOOC Working Group of the University of Turin, we are looking forward to the first MCM tasks in Italy, which is part of today’s Task of the Week. Task: Height of the Building (task number: 2045) Determine the height of the building. Give the result in meters. The height can be […]
Through cooperation with the MOOC Working Group of the University of Turin, we are looking forward to the first MCM tasks in Italy, which is part of today’s Task of the Week.
Determine the height of the building. Give the result in meters.
The height can be approximated in various ways, e.g. by estimation or the intercept theorems. The task can be solved elegantly by looking for structures and patterns in the building facade. In this building, the horizontal strips, which can be found up to the roof, are noticed directly. For the total height, it is therefore only necessary to determine the height of a horizontal strip, as well as to count the number of strips. Minor deviations from the pattern can be approximated using estimates.
With this method, the task can already be solved by class 6 students. In the case of older pupils, the different solutions can be discussed and assessed with regard to simplicity and accuracy.
On 01.12.2017, Matthias Ludwig and Simone Jablonski presented MathCityMap as part of an internal teacher training at the Commercial Schools in Hanau. First, the theoretical basis for math trails, the MCM concept and selected research results were presented. Afterwards, the participants got to know the app with the aid of a trail created around the […]
On 01.12.2017, Matthias Ludwig and Simone Jablonski presented MathCityMap as part of an internal teacher training at the Commercial Schools in Hanau. First, the theoretical basis for math trails, the MCM concept and selected research results were presented. Afterwards, the participants got to know the app with the aid of a trail created around the schoolyard – consisting of a variety of geometrical, functional and combinatorial problems. Using the criteria for good MCM tasks, the participants then became active themselves after a change in perspective and sighted the schoolyard for possible tasks. In the process, a variety of ideas for MCM on the level of secondary school appeared. As an end product of the events, the participants could create their own tasks in the portal and combine them into a trail around the school. Of course, there was a lot of fun during the event, for example while answering the question of the height of the swing seat in a 45° angle:
MCM flying high
We thank the participants for their cooperation and feedback and look forward to numerous MCM tasks in Hanau.
Are you also interested in a MCM teacher training? Feel free to contact us!
Following an invitation from the Arab-German Young Academy of Sciences and Humanities (AGYA, funded by the BMBF), Matthias Ludwig was able to introduce MCM in Doha, Qatar. First, the MathCityMap project was presented at the International German School as well as at the Omar Bin AlKhattab Boys Secondary School. This was very successful and the […]
Following an invitation from the Arab-German Young Academy of Sciences and Humanities (AGYA, funded by the BMBF), Matthias Ludwig was able to introduce MCM in Doha, Qatar. First, the MathCityMap project was presented at the International German School as well as at the Omar Bin AlKhattab Boys Secondary School. This was very successful and the participants liked the MCM idea.
At the international German school
Matthias Ludwig at the Omar Bin AlKhattab Boys Secondary School
Afterwards, Matthias Ludwig had the opportunity to talk about the latest developments of MCM in the context of a podium discussion at the Texas A & M University at Qatar, where Prof. Dr. Martin Grötschl (President of the BBAW) and Mehdi BenChaabane (Qatar Foundation, Education Department) attended as well.
The vice president of the agya, Prof. Dr. Ahmad El-Guindy, was very impressed by MCM and created tasks for a Math Trail around the Khalifa International Stadium in the west of Doha with Prof. Ludwig the next day. We feel that MCM was not the last time well received in the Arab world.
Prof. Dr. Matthias Ludwig and Prof. Dr. Ahmad El-Guindy
In this year’s autumn, numerous tasks were created in Wilhelmsburg, district of Hamburg. The tasks are very convincing – especially in the context of the MCM concept – through their interdisciplinary and thematic diversity, which we would like to illustrate exemplary in our current Task of the Week. Task: Red area (task number: 1964) Determine […]
In this year’s autumn, numerous tasks were created in Wilhelmsburg, district of Hamburg. The tasks are very convincing – especially in the context of the MCM concept – through their interdisciplinary and thematic diversity, which we would like to illustrate exemplary in our current Task of the Week.
Determine the red area on which the ping-pong table stands. Give the result in m².
It quickly becomes clear that the entire area can not be approximated by a single geometrical object, or that this is only possible with significant losses in accuracy. It is therefore appropriate to divide the area searched into disjoint subspaces, which can be calculated using formulas. This is best done using a drawing. A particular challenge are the curved edges, where estimations and approximations are necessary. According to measurements and calculations, the total area is obtained by adding the area contents of all partial surfaces.
The area can be described using rectangles and triangles. In addition, the principle of the decomposition and additivity of surface content is necessary for solving the problem. The task can be used from class 7 onwards.
In the ongoing development and optimization of MathCityMap, the direct impressions and experiences of students and teachers with the project provide important feedback. Accordingly, the MCM team is very interested in a lively exchange and testing of tasks. On Wednesday, 08.11.2017, the MCM team welcomed Mrs. Nazanin Roushanaei, a teacher at the Hessen-Homburg school center […]
In the ongoing development and optimization of MathCityMap, the direct impressions and experiences of students and teachers with the project provide important feedback. Accordingly, the MCM team is very interested in a lively exchange and testing of tasks.
On Wednesday, 08.11.2017, the MCM team welcomed Mrs. Nazanin Roushanaei, a teacher at the Hessen-Homburg school center in Hanau, with her graduating class R10a at the Campus Westend. The students in the class will attend the Final Examinations for the secondary school certificate next spring and are currently reviewing relevant topics in math lessons, e.g. the subject of body calculations, which was compiled for the students in a diverse trail. In this context, Mrs. Roushanaei sees not only the chance to repeat exam relevant knowledge: “MCM offers the pupils the opportunity to get to know body computations in real places and in authentic situations.”
For example, the volume and weight of cuboids were discussed through benches in front of the lecture hall center. In addition to various geometric bodies, slopes and angles were calculated as well. To do this, the students had to model the selected objects with the help of familiar bodies and through flexible use of the acquired knowledge of formulas. Before the trip could start, necessary preparations were made. Due to the high number of Android devices in the class, the participants were able to agree on gamification elements, a tool that makes it possible to compete against each other and compare the results. At the moment, this tool is also planned for the iOS version. The app as well as the trail were downloaded from the class in advance, so that the actual run of the trail does not require internet connection. With the necessary materials (smartphone, pen, calculator and formulary) and the consent of the parents the trip could start.
Nazanin Roushanaei with the MCM App
On the day of the trip, the group was confronted with rainy weather, which however could not dampen the mood. The students were divided into groups of three. This group size has been proven as there are three main functions when running a trail: navigate, measure, and record. In particular, Mrs. Roushanaei noticed a group of three, which has made up of three boys with different migration backgrounds: “Each student from this group has been totally in his role in this trip. One of them always had an overview of the tasks and could link them directly with a mathematical formula. Another boy had a very good orientation in mind and worked as a very good navigator. The third boy was able to change the required formulas correctly. Together, the three boys were able to solve most of the tasks and thereby achieve the highest score in the competition. Since that excursion, I’ve noticed that these three guys are much more motivated in math class than they used to be. I have the impression that the use of MCM and this trail could arouse the interest of these guys in mathematics.” In particular, the used gamification elements motivated the students to solve as many tasks as possible.
Measuring in the group
The feedback given by the students was very positive as well. One student with below-average mathematics performance stated: “This was the most enjoyable trip I’ve ever done with school.” Others said that through solving the tasks, they finally relate to the subject and understand what these formulas are all about. “It was fun for them. They would have liked to stay longer to solve all the tasks” says Mrs. Roushanaei.
Calculations at the ping-pong table
In conclusion, Mrs. Roushanaei states: “MCM is great, not just for kids, but also for teachers. It offers the opportunity to experience mathematics outside and thereby make various calculations real. Although it is said that new textbooks have many authentic tasks; what is more authentic than having children measure real objects themselves? I can recommend any math teacher to use MCM for their own lessons and to make a project day or day trip for the class. I am convinced that, thanks to MCM, mathematics can be interesting for students even in tenth grade.”
Group photo of the class
The MCM team is pleased to receive the helpful and positive feedback from the class and wishes them all the best for their further exam preparation and participation. At least in the topic of geometric bodies, nothing can go wrong now!
As a few weeks ago, the Task of the Week leads us to the African continent, more precisely to the approximately 1000-meter-high Tafelberg in Cape Town. There you can find a monument of stone, which is also an ideal object for a MCM task. Task: Tafelberg’s Monument (task number: 1791) Calculate the mass of the […]
As a few weeks ago, the Task of the Week leads us to the African continent, more precisely to the approximately 1000-meter-high Tafelberg in Cape Town. There you can find a monument of stone, which is also an ideal object for a MCM task.
Calculate the mass of the stone monument. Give the result in kg. 1 cm³ of granite weighs 2,6 g.
First, the shape of the stone has to be considered more closely. When choosing a suitable model, a prism with a trapezoidal base can be used. For this, it is necessary to ignore minor deviations from the ideal body as well as to operate with the stone mentally. The required data are then determined and the required weight of the stone is obtained by means of the area content formula of a trapezoid, the volume formula of a prism and the given density.
The task shows that over the last few years, MCM has developed into an international platform for authentic “outdoor” mathematic tasks and has already been set up in many prominent places. We are looking forward to further tasks and are looking forward to the countries and regions in which new MCM tasks will emerge.
Joerg Zender, Iwan Gurjanow and Matthias Ludwig presented MCM in theory and practice on Friday, 17.11.2017 at the ISTRON conference at the Landesinstitut in Hamburg. The lecutre by Matthias Ludwig was very well attended with more than 120 listeners and led into the world of outdoor mathematics. He combined traditional methods such as measuring with […]
Joerg Zender, Iwan Gurjanow and Matthias Ludwig presented MCM in theory and practice on Friday, 17.11.2017 at the ISTRON conference at the Landesinstitut in Hamburg. The lecutre by Matthias Ludwig was very well attended with more than 120 listeners and led into the world of outdoor mathematics. He combined traditional methods such as measuring with the measuring table and the scientific and technological approach of MCM. In the fully booked workshop, Iwan Gurjanow and Joerg Zender presented MCM in practice. First, the participants got the chance to complete some tasks of the prepared trails and created their own tasks and a trail in the MCM portal afterwards. The success of the training was also made possible through the very good technical equipment and support provided by the Landesinstitut Hamburg.
Hamburg was fun again and we are looking forwards to coming back!
