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 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.

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 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.

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 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.

On 14.11.17, Iwan Gurjanow and Simone Jablonski presented MathCityMap as part of an internal teacher training at the Werner-von-Siemens school in Wetzlar. First, the theoretical basis for Math Trails as well as the MCM concept were presented to the participants. With the help of the criteria for good MCM tasks, the participants were then themselves active and searched for possible tasks at the schoolyard. After a change of perspective, the participants learned about the app by means of a trail in the schoolyard, consisting of different geometrical problems. As final product, the participants created their own tasks in the portal and merged them into a trail for the school.

We would like to thank the participants for their cooperation and feedback and look forward to numerous MCM tasks in and around Wetzlar.

Are you interested in teacher training on MCM? Feel free to contact us!

As a part of a teacher training at the Johanneum Gymnasium Herborn, a modeling task was created, which we would like to present to you today as the “Task of the Week”.


Task: Brick in the Wall (task number: 2040)

The wall in the schoolyard should be sprayed. It is planned to save color for the hole in the wall. Calculate the area to be sprayed in m². Enter the result with two digits.


The challenge in this task is to approach the existing hole in the rectangular wall as precisely as possible. Different models can be chosen for this purpose. On the one hand, one could assume the hole as a circle and determine an average diameter. More precisely, however, the result is obtained by approaching the hole as an ellipse and measuring the axes.

The task requires a certain amount of creativity and shows that the clear mathematics in the environment outside the classroom reaches its limits. The pupils acquire modeling competences, especially in the skillful choice of a mathematical model. The various solutions and results of the pupils thus form an ideal basis for discussing appropriate models. The problem can be applied with the treatment of circle and ellipse from class 9 onwards.

Today, we would like to introduce you a task from Speyer, which was created there by Katalin Retterath. It is about the famous Way of St. James, which leads through the city to Santiago de Compostela.


Task: Jacobean Pilgrim (task number: 1614)

Measure/estimate the step of the Jacobean Pilgrim. How many steps would he have to take if he were to travel the 2,500 kilometers to Santiago de Compostela?


How did you get the idea to create MathCityMap?

I am a consultant for teaching development in mathematics at the Pedagogical State Institute in Rhineland-Palatinate. For a number of years, we have been developing mathematical rallies, which are well received by both our pupils and the training events. First we experimented with LearningApps, then with Actionbound – both were OK, but not really satisfactory. We have become acquainted with MathCityMap and we would like to introduce the MathCityMap project here.

What are the mathematical competences and contents associated with the task?

Students must estimate and/or measure, work with large numbers. The task is solved by a group – thus, communicating plays a great role and if the students explain their their solution to one another (which would be desirable), then also argue.

Has the task already been tested by students or did you receive feedback in other forms?

The task itself has been tested by students (many different classes), but still with Actionbound. The students were able to solve the problem without major (content) difficulties – with the units and number of zeros, however, it was not so good. I have only entered two-three tasks at MathCityMap to test the software. A test of the tool will be considered in spring.  

The MCM team thanks for the interview and is looking forward to further tasks in Speyer!

On 12.10.2017, the MathTrails project seminar from the Theodosius-Florentini-Schule Gemünden visited the MathCityMap team in Frankfurt. Marie-Noelle Klug, a participating student in the project, has thankfully provided us a great report as well as photos, which give an insight into how the students have experienced the day:

The P-Seminar “MathTrails” led the students of the Q11 of the Theodosius-Florentini-Schule Gemünden to Frankfurt to get to know the origin of the project MathCityMap and to get the necessary information about the seminar.

We arrived at the Goethe University in Frankfurt around 10:30 am, where we were welcomed by Iwan Gurjanow and Joerg Zender. Afterwards we were introduced to the concept of MathCityMap in detail and we got useful tips for dealing with the materials we needed to test a trail. Then we started in groups of three with our smartphones, on which we had previously installed the app MathCityMap, and made a small trail with different tasks. For example, we had to calculate the shoe size of the T Rex statue. We had a stick, measuring tape and a pocket calculator. Now one had to become creative and come to own solutions, whereby the app also provides up to three hints.

© Marie-Noelle Klug

After all the groups finished the trail, we got together again and held a brief feedback round. Afterwards, we received the criteria and tips for the creation of our own tasks for a trail, what we could then test again in our small groups.

For example, the task was to “calculate the inner surface of the O”

© Marie-Noelle Klug

Several tasks were created in each group, which allowed us to create the first own trail of our group on the web portal.

In conclusion, the excursion was a great success for the students and many questions were answered. The class is now very well prepared for the project and hopes for a successful end result.

 

With two trails in Salzburg, we can now welcome Austria as the 9th country with a MCM Trail. The current task of the week presents a task in the field of the surface of a cylinder. It is located in the trail at the natural sciences faculty of the Paris-Lodron University in Salzburg.


Task: Lamp (task number: 1908)

How large is the black painted surface of a lamp without the base plate? Give the result in m². Round to two decimal places.


The pupils first recognize the lamp as cylindrical and then determine the black surfaces. For this, it is necessary to divide the lamp into two cylinders. For the upper small cylinder, the shell surface as well as the cover are calculated, for the lower cylinder only the shell surface. Height and radius need to be measured. Subsequently, the individual surfaces are added and the total painted surface area is obtained.

The task can be assigned to the subject area of ​​geometry and, in particular, geometrical bodies (cylinders) and can be used from class 9 onwards.

The MathCityMap idea lives from its active users and task creators in different places. Today, we would like to present a new trail at the University of Heidelberg that Mr. Niccolò Rigi-Luperti created there. In a short interview, for which he was thankfully available, we would like to let him speak for himself and give us an insight into the background to the trail creation.     

How did you hear about MathCityMap?

Through my job as a scientific assistant in the project “MINTmachen!”. There, we bring students closer to MINT subjects through e.g. holiday courses, workshops at the Girls-Day or possible BOGY-stays at the university (www.mintmachen.de). My boss (Dr. Michael Winckler) had learned from MathCityMap and asked me to get to know the app to see if and how we could integrate it into our work.   

How did you get the idea to create your own trail? Have you created this for a particular event or target group?

It seemed to me the best way to get a feeling for the app and the job. According the target group, I was thinking of math-physics-computer science first semesters, which should solve small group tasks in the introductory days for mutual learning. In my opinion, this is a very good way to do this, especially because they are doing maths together and seeing different campus locations.

What mathematical content and skills are required in your trail?

In the order of the four tasks: simple probability calculation, precise counting of objects, trigonometry and potential & kinetic energy, combinatorics.   

Which of the tasks is your “favorite task” and why?

The third task, “wheelchair“. I think it is nice to see the slope as a large acceleration ramp. It is the only physical task, and it can be solved in different ways, but they are of varying complexity. The easiest way to do this is to use energy conservation. Doing so, you solve the problem quite efficiently, it is only necessary to do a few line transformations as well as a single length measurement.

A popular MathCityMap task is concerned with the volume of fountains and how many liters of water are contained. The question can be used for a wide range of geometric themes, depending on the shape of the selected fountain (rectangular, circular, …). The Task of the Week is a particular challenge because the fountain has to be modeled with help of different geometric bodies.


Task: Water in the Fountain (task number: 1420)

How many liters of water are in the illustrated fountain?


The illustrated fountain can be modeled using a cuboid and a cylinder (divided into two parts). If this has been recognized, the necessary quantities must be collected and the individual volumes calculated. Finally, the conversion in liters is required. The task with cylinders can be used from class 9 onwards; simpler fountain shapes are already possible from class 6 onwards.

Depending on the structure of the well, the collection of the data can be a challenge and the students have to become creative. For example, the circumference of a circle can be helpful for the determination of the diameter. Not at least through such considerations, a flexible handling of mathematical formulas and correlations is promoted.