Task of the Week – MathCityMap

Task of the Week: Height of the Powder Tower in Merano

In the beautiful South Tyrolean city of Merano, teacher Michael Perkmann recently created the task “Height of the Powder Tower in Merano”, which we would like to present to you today as the task of the week. The goal of the task is to determine the height of the old powder tower. Michael Perkmann reports […]

In the beautiful South Tyrolean city of Merano, teacher Michael Perkmann recently created the task “Height of the Powder Tower in Merano”, which we would like to present to you today as the task of the week. The goal of the task is to determine the height of the old powder tower. Michael Perkmann reports about his task and the use of MathCityMap in the classroom in the following.

How did you come across the MathCityMap project? How do you use MCM?

I first heard about MathCityMap about 3 to 4 years ago at a teacher training course in South Tyrol. At that time we did the first Mathtrails in groups and tried to create our own tasks.

Since there are hardly any tasks and trails in South Tyrol and especially in Merano at the moment, I have always planned to create my own math parkour with my students one day.

I created this task for the Powder Tower together with my students from the Business School in Merano as part of an interdisciplinary project to get to know the MathCityMap platform better.
The goal is that the students themselves will soon create several tasks in the vicinity of Merano.

Together we will try to enter the tasks into the portal and then create a trail.

What can the learners gain by working on the tasks?

I think that working on tasks requires many competences of the students, especially modeling, creating text tasks, applying mathematical representations, creativity in solving mathematical problems.

This is often neglected in frontal teaching. MathCityMap is therefore a great addition to the lessons and the work outside the class motivates and makes fun for the students.

Present your task at MathCityMap!

We regularly present interesting tasks and trails from all over the world in our rubrics “Task of the Week” and “Trail of the Month”. Would you also like to present your task or trail to other users? We are very happy about that! Therefore, you just have to send an email to barlovits[at]math.uni-frankfurt.de. Answer the […]

We regularly present interesting tasks and trails from all over the world in our rubrics “Task of the Week” and “Trail of the Month”. Would you also like to present your task or trail to other users? We are very happy about that!

Therefore, you just have to send an email to barlovits[at]math.uni-frankfurt.de. Answer the following questions in your mail:

How did youget in contact withthe MathCityMap project? How do you use MCM and why?
Describe your trail / your task. What is special about this trail / task?
What are your didactic goals in using MathCityMap and your trail / your task?
Further remarks about MCM?

We are looking forward to your answers!
Your MathCityMap team

Task of the Week: A Giant from University

In Freiburg, student teacher Meryem Moll has created the task “The giant in front of the Albert-Ludwig University” which we present today. The aim of the task is to estimate the size of a statue: How tall would the statue pictured be if it stood up? In the following interview, Meryem Moll talks about her […]

In Freiburg, student teacher Meryem Moll has created the task “The giant in front of the Albert-Ludwig University” which we present today. The aim of the task is to estimate the size of a statue: How tall would the statue pictured be if it stood up? In the following interview, Meryem Moll talks about her studies, MathCityMap and the task.

How did you come across the MathCityMap project? How do you use MCM?

I came across the MCM app while searching for a topic for my bachelor’s thesis in mathematics at the University of Education in Freiburg in the bachelor’s degree for primary education.

I am very interested in the meaningful use of digital media in elementary school as well as gamification of lessons, which is why my supervising lecturer made me aware of the MCM project. My bachelor thesis was about how the process-related competencies “problem solving” and “modeling” can be promoted already in elementary school with the help of the MCM app.

I think working with the app is great, especially because it is also very naturally structured and easy to use, which is why I also think it can be used profitably for elementary school students. For my future teaching as a math teacher, it’s important to me that the children see a personal benefit and meaning behind the math tasks at school or in math in general, and that they apply them to their own learning. This is something that apps like the MCM app can contribute to enormously, as students nowadays grow up with digital media and these can be used in such a meaningful way.

What can the children learn by solving the task?

In the task “The giant in front of the Albert-Ludwig University”, I was concerned with the learners being able to decide which parts of the statue’s body are relevant for measuring the height of the body, as well as the correct use of or handling of measuring devices (meter stick/tape measure).

In addition, the children should use their previous ideas of size with the task by first estimating the size of the giant and then also comparing it with their own height through a personal reference. In general, however, I was primarily concerned that the children should be able to experience application-based math lessons with the help of the trail and learn to transfer the “theory” from the classroom to reality, thereby deepening their understanding of it.

Task of the Week: Volume of the Bulwark

Katalin Retterath is a mathematics teacher and consultant for teaching development in the German fedaral state Rhineland-Palatinate. In the following interview, she introduces us to a task that was created during an teacher training on outdoor mathematics teaching. The task: Bulwark – Volume: Task: “Go to the interior of the bulwark. Calculate the volume of […]

Katalin Retterath is a mathematics teacher and consultant for teaching development in the German fedaral state Rhineland-Palatinate. In the following interview, she introduces us to a task that was created during an teacher training on outdoor mathematics teaching.

The task: Bulwark – Volume:

Task: “Go to the interior of the bulwark. Calculate the volume of the interior in m³ up to the capstones. Assume that the floor is level.”

The goal here is to calculate the volume of a cylinder, which the bulwark encloses with a circular base.

You describe in the category “About the object” that the task was created during an teacher training. How do you use MCM and why?

I am a consultant for instructional development at the pedagogical state institute in Rhineland-Palatinate, Germany. I don’t remember how I got to know MCM, probably at a conference. I have known MCM from the beginning and use it in my classes 1-2 times a year during virus-free times.

At the pedagogical state institute we offer advanced trainings also for the use of media in mathematics lessons, here MCM is a topic again and again. One of the most successful advanced trainings is “Outdoor Mathematics” – a two-day event, which we have offered so far alternately in Speyer, Bad Kreuznach and Andernach. The task “Bulwark – Volume” was created by a group of participants in Andernach – I just created it in the MCM system.

How do you plan to use MathCItyMap in the future? What ideas do you have for using MCM in math classes?

It’s a very great tool! I look forward to using it again. We consultants have also used MathCityMap in another way, including outdoor math: we created a series of surveying tasks around Speyer Cathedral (code: 031829) and entered them into MCM.

With the help of MCM we have been able to create very appealing booklets for the participants of the advanced training [also MathCityMap offers the possibility to download a trail guide as a companion booklet to the trail; editor]. These booklets help document the work so that the field trip can be better integrated into the classroom: In addition to entering results in the app, the notebooks are used anyway / in parallel. I would try it out like this in a 10th grade or high school class – if times allow and I have a suitable class.

Task of the Week: GeomeTREE

Our new Task of the Week is presented by Marius Moldovan. The upper secondary student from Bad Neustadt has created three math trails in Bad Neustadt together with 13 other learners as part of his school lessons. We talk about his task “GeomeTREE” task in the following interview: How do you use MCM? I […]

Our new Task of the Week is presented by Marius Moldovan. The upper secondary student from Bad Neustadt has created three math trails in Bad Neustadt together with 13 other learners as part of his school lessons. We talk about his task “GeomeTREE” task in the following interview:

How do you use MCM?

I am a student at the Rhön Gymnasium in Bad Neustadt. As part of a project in school, we (14 students) created three trails in Bad Neustadt. We have been working on the trails for several months and would like to publish them now.

Note: In the meantime two of the trails have been published:

Describe your task. How can it be solved?

My task is about determining the height of a tree. For this you should use the ray theorem or the Förster triangle. It is a good idea to form a ray set figure with the tree using a geo triangle. To do this, hold one corner of the triangle in front of your eye. One of the short sides of the triangle must be parallel to the ground, while the long side must point to the face. Then you have to decrease or increase your distance to the tree until the extension of the long side of the triangle ends exactly at the highest point of the tree. Now all you have to do is measure the distance from your point of view to the tree and add your height up to your eyes. Since the two short sides of the geo triangle are the same length, the distance to the tree is also the height of the tree from eye level.

What can you learn by working on this task?

The goal of the task is to expand students’ geometric understanding. The ray theorem should be conveyed in the task in a comprehensible way, which additionally demonstrates its possible applications outside the classroom.

Task of the Week: The snail’s journey

Dennis Kern, student at Goethe University Frankfurt, introduces our new assignment of the week: As part of an Intensive Study Programme for students from Europe, a group led by Dennis Kern created the task “The snail’s journey”. In the following, he gives us an insight into the European exchange program with MathCityMap. How did […]

Dennis Kern, student at Goethe University Frankfurt, introduces our new assignment of the week: As part of an Intensive Study Programme for students from Europe, a group led by Dennis Kern created the task “The snail’s journey”. In the following, he gives us an insight into the European exchange program with MathCityMap.

How did you come across the MathCityMap project? How do you use MCM and why?

As a mathematics student at Goethe University in Frankfurt, I saw in the winter semester 2018/2019 that the course “MoMaTrE – Mobile Math Trails in Europe” was offered for the didactics part of my studies. There, students from different countries in Europe came to Frankfurt to discover and evaluate the MathCityMap project and the app together, as well as to create their own trails in groups and test them with school classes.

In addition, I used the app in another course at the university and have since even decided to write my academic term paper as part of my teaching degree on processing strategies when solving problems.

Describe your task. How can it be solved?

“The snail’s journey” we created together at the Historical Museum at Frankfurt’s Römerberg. We tried to investigate the experiences of an animal, which in a certain way can only move in two dimensions (because it must always be in contact with a surface), in our three-dimensional world. The animal in question is a snail. How does it cross a staircase? Of course, it cannot jump from step to step, but must crawl along the surface.

The task is to calculate how long this takes for this staircase. To do this, you have to measure the height and width of a step and multiply it by the number of steps (the steps are all about the same size). This gives you the distance the snail has to travel. If you then read from the task how fast a (garden) snail crawls, you can determine the required time by dividing. Finally, the result must be divided by 60, because it should be in the unit minutes.

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As part of the Intensive Study Programme, two math trails were created on the Römer in Frankfurt.

The task is part of the trail “ISP Frankfurt Lower Secondary” (Code: 131369) for grades 5/6. Also the trail “Upper Secondary ISP Frankfurt” (Code: 071368) for grades 7/8 was created.

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What are the didactic goals of the task?

As already mentioned, students are made aware of dimensional differences, because the snail is relatively small compared to the stairs and cannot fly or jump, and therefore as a snail you do not have the luxury of using the dimensional advantage here. In addition, we wanted to choose an object that is not immediately completely measured with one measurement.

There is also differentiation here, because lower-performing students are likely to make the same measurement ten times, while higher-performing ones realize that nine measurements can be saved. Then, with the conversion from centimeters to seconds, i.e. from distance to time, the handling of units from different categories is practiced, but also in one and the same unit, because you still have to convert the result from seconds to minutes.

Any other comments about MCM?

I think it’s great to finally have a really good answer to the complaint “What do we need all this for?” from learners in math classes. Editing math trails with this app picks them up where they are all the time anyway – on their smartphones – and motivates them in a way that classic math lessons probably can’t do.

Task of the Week: An off-limits flowerbed

Emanuele Amico, teacher student of the University of Catania in Italy, created our new Task of the Week. In the interview, he describes the task “Una aiuola off-limits“ [“An off-limits flowerbed”] and gives us an insight how the University of Catania [partner in the MaSCE³ project] uses MathCityMap in teacher education courses. How did […]

Emanuele Amico, teacher student of the University of Catania in Italy, created our new Task of the Week. In the interview, he describes the task “Una aiuola off-limits“ [“An off-limits flowerbed”] and gives us an insight how the University of Catania [partner in the MaSCE³ project] uses MathCityMap in teacher education courses.

How did you get to know the MathCityMap system? How do you use MathCityMap?

I have started using MathCityMap only a few months ago. I am attending a Master’s Degree course in Mathematics at the University of Catania. During the lessons of the “Mathematics Education” course the teacher presented the MathCityMap project, highlighting the theoretical framework and the methodological aspects on which it is based, the needs to which it responds, the ways in which the objectives of the project are pursued. I had the opportunity to experience MathCityMap from both sides: as a student, through participation in a math trail prepared by the teacher and proposed to the class group, but also as a creator of my own task that met the requirements for publication [see “Criteria for a good task” on our tutorial page]. In this context, taking inspiration from a traffic island in the immediate vicinity of the Department of Mathematics and Computer Science, the idea of my first (and so far only) task “An off-limits flowerbed” was born.

Describe your task. Where is it located? What is the mathematical question? How can you solve it?

The task requests the calculation of the area of a surface identified by the marker strips delimiting a traffic island. It is clear that the area can be identified as a triangle, but it is also clear that it is not possible to measure directly any of the three heights of the triangle, because of the presence of plants and shrubs in the flowerbed inside the traffic island, which make it inaccessible. Therefore, to solve the task, it is possible to use trigonometry, and in particular to generalize of the formula for calculating the area of a right-angled triangle. By measuring the lengths of two sides of the triangle with a ruler or string, and measuring the angle between them with a goniometer, the student will be able to calculate the area required. An alternative way of solving the problem can be based on the use of the formula: A = ½*a*c*sin

What are the learning objectives of this task? What could students learn while working on this task?

From the didactic point of view, the task requires for a reflection about the best and most practicable way of solution (which sometimes does not coincide with the initial idea). The task is an invitation for the student to critically compare different solving strategies, to reflect on the necessity of knowing several methods and formulas that allow to reach the same objective, since often each of them is based on different assumptions and needs, in our case on the impossibility of making an internal measurement of the geometric figure.

Do you have any other comments on MathCityMap?

I believe that MathCityMap truly offers an authentic context for learning mathematics and I am sure I will continue to use it in the near future.

Task of the Week: The Ring

Dominik Enders, a student of the German grammer school (Gymnasium) in Bad Neustadt, created our new Task of the Week (the task “Ring”). In the interview, he explains why the students at his school create their own MCM tasks. How do you use MCM and why? I participate in a project, led by teacher […]

Dominik Enders, a student of the German grammer school (Gymnasium) in Bad Neustadt, created our new Task of the Week (the task “Ring”). In the interview, he explains why the students at his school create their own MCM tasks.

How do you use MCM and why?

I participate in a project, led by teacher Ms Gleichmann, in which we create math trails for pupils from younger classes, which you can tackle in your free time or on hiking days.

Describe your task. How can it be solved?

My problem is about a ring-shaped piece of sports equipment on a playground, of which you are supposed to find the area of the upper side. Assume that the edges of the ring are smooth, i.e. without indentations.

First you have to calculate the area of the circle up to the outer edge of the ring (tape measure/inch stick and pocket calculator are required) by determining the radius and then
calculate the area of the circle. Using the same procedure, calculate the smaller area of the circle enclosed by the inner edge of the ring. Then you only have to subtract the smaller area from the larger one to get the area of the top of the ring.

What didactic goals do you pursue with the task?

The task refers to the teaching content of the 8th grade and represents an application of the pupils’ knowledge on the topic of the area of a circle. The circle-ring is more demanding, but this can be mastered by using the area formula for two circles. The reference of mathematics in the 8th grade to a piece of sports equipment on a playground, which the pupils know from their everyday experience, should be motivating. By measuring lengths (radii), the topic of sizes from Year 5 is also addressed, as well as the importance of measuring accuracy.

Note: The task “Shoe size of the statue” was also created by a pupil of the Rhön-Gymnasium. It was the 15,000th task at MCM – great!

Task of the Week: Chinese Multiplication

Our new assignment of the week shows how MathCityMap can support Distance Learning. In this interview, our student assistant Franzi Weymar explains how she uses MathCityMap in the context of the gifted education program “Junge Mathe-Adler Frankfurt”. How do you use MCM with the math eagles? The Junge Mathe-Adler Frankfurt are a project for mathematically […]

Our new assignment of the week shows how MathCityMap can support Distance Learning. In this interview, our student assistant Franzi Weymar explains how she uses MathCityMap in the context of the gifted education program “Junge Mathe-Adler Frankfurt”.

How do you use MCM with the math eagles?

The Junge Mathe-Adler Frankfurt are a project for mathematically particularly interested as well as gifted students. Normally, the students are offered the opportunity to deal with mathematical problems and topics outside of the school setting every two weeks at the Institute for Didactics of Mathematics and Computer Science at Goethe University Frankfurt. However, the pandemic situation this year required special circumstances, as the usual face-to-face sessions could not take place. Using the MCM platform, it was possible to design trails with thematically coordinated tasks for both home and outdoor use. This made it possible to offer the students a versatile and varied range of activities and to successfully implement extracurricular, mathematical support during this special time.

Describe your task. How can it be solved?

In general, the trail “Rechentricks für die Mathe-Adler” [engl.: “Calculation Tricks for the Mathe-Adler”], from which the task “Chinesische Rechenmethode_Aufgabe 1” [engl.: “Chinese Multiplication_Task 1”] is taken, deals with calculation tricks for fast multiplication.

The Chinese multiplication method is about multiplying two two-digit numbers together in a simple and quick way by visualizing them through a figure. The tens and ones digits are first mapped into corresponding numbers of slanted lines. By counting the intersections of the lines from left to right, the place values of the result can be read from the hundreds place to the ones place. In the task selected here, the students should now try to read off the result of the multiplication task shown (22-22) by counting the intersections and assigning them to the corresponding place values. The hints and the sample solution serve as help and explanation for the students to be able to solve the task or to understand it well. Previously, the Chinese multiplication was explained by means of an example task.

What can students learn here?

By working through the trail on the various calculation tricks, students can learn simple and quick procedures for solving multiplication tasks, which can also be useful to them in their everyday school life. In addition, the thematization of the cultural reference of the different arithmetic tricks promotes the examination of mathematical topics from other countries, because mathematics can be found everywhere.

To what extent can the MCM@home concept help organize homeschooling in mathematics?

Within the MCM@home concept, the Mathe-Adler team is offered the possibility of setting up a digital classroom in addition to the interactive learning setting for students. This means that at the same time as the Young Mathe-Adler session would normally take place in presence, a learning space, the so-called Digital Classroom, is activated for a selected time slot with the respective tasks. This ensures that we as the Mathe-Adler team can see the learning progress of the participating students in real time, can respond to questions and comments from the students during the session via the chat portal, and thus, despite the distance learning, there is a direct exchange with them. In addition, students always receive direct feedback on their learning success through hints and the sample solution provided. Homeschooling in mathematics can thus be organized in an appealing, versatile and simple way using the MCM@home concept.

Task of the Week: Climbing Frame

Patrick Rommelmann has created our new task of the week on the schoolyard of the Regenbogen-Gesamtschule Spenge – the task “Climbing Frame”. The task is located in the theme-based math trail “Route RGeS”, which focuses on the repetition of cylinders. Mr. Rommelmann has already tested the trail with a 10th grade class. How did […]

Patrick Rommelmann has created our new task of the week on the schoolyard of the Regenbogen-Gesamtschule Spenge – the task “Climbing Frame”. The task is located in the theme-based math trail “Route RGeS”, which focuses on the repetition of cylinders. Mr. Rommelmann has already tested the trail with a 10th grade class.

How did you come across the MathCityMap project? How do you use
MCM and why?

I became aware of the MathCtityMap project during my mathematics didactics training at Bielefeld University. At the university, a math trail has already been created, which I worked on in a seminar.
In the seminar for writing my master thesis the MathCityMap project came up again and I decided to create a math trail and test it with a school class. After positive feedback, I have now published the tasks so that other teachers can work on the math trail with their classes.

Describe your task. How can it be solved?

In this task, we are to determine the length of the lowest blue rope. The beauty of this task is that there are different possible solutions. The rope forms the shape of a circle. Therefore, the radius of the circle can be measured and then the circumference of the circle can be calculated.
A more intuitive solution option is to measure the entire circumference of the circle. However, this can take quite a long time if the many, individual sections have to be measured one after the other. A clever variant can be chosen here if only one section is measured and this is multiplied by the number of all sections.

What didactic goals are you pursuing with the task?

In particular, the variety of solutions should create an openness of the task. Open tasks are particularly well suited for heterogeneous learning groups, which are also increasingly found at this comprehensive school. In addition, the MathCityMap task had the typical didactic aspect of modeling on real objects.

What other tasks could be investigated on this exciting object be investigated?

Starting with questions about the circle, further questions about the shape of the climbing frame as a cone could arise at the climbing frame. In addition, the pole to which the climbing frame is attached could also be investigated. The pole has the shape of a cylinder, so for example with given density and weight, the length of the pole could be determined. The result could be used to check how secure the climbing scaffold is in the ground. Of course, the necessary information would have to be obtained beforehand.

Further comments on MCM?

As you can see from this nice example, mathematical questions can be found on many objects in our world. With MathCityMap, an app has been created that can successfully establish the application connection of mathematics to the objects.