Task of the Week | MathCityMap

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.

Task of the Week: The Stone Pillar

Jeniffer Sylaj Baptista is studying to be a teacher at the University of Luxembourg. In the interview, she tells us about her task “The Stone Pillar”, which she created in Sandweiler near the city of Luxembourg. How did you get in contct with the MathCityMap project? How do you use MCM and why? I use […]

Jeniffer Sylaj Baptista is studying to be a teacher at the University of Luxembourg. In the interview, she tells us about her task “The Stone Pillar”, which she created in Sandweiler near the city of Luxembourg.

How did you get in contct with the MathCityMap project? How do you use MCM and why?

I use the MCM project for university. I am studying “sciences de l’éducation” (teaching) at the University of Luxembourg. For the homework in the subject Didactics of Mathematics under the supervision of Yves Kreis, we have to create a Mathtrail with different tasks.

The MCM project is a great way to get students to see the mathematics in their environment and to solve mathematical problems in an exploratory way.

Describe your task. How can it be solved?

The task is: “How many stone faces does the stone column have in total?” Stone columns are built up into different stone tiers and these are then the same on each side. So all you really have to do is count the stone faces on one side and then multiply by the number of facets of the stone column, which in this example is 4.

What other tasks could be set on this interesting object?

For example, the volume of the entire stone column could be calculated in another task. Measuring the stone column could also be a small task.

Task of the Week: Hercules Fountain

Our new Task of the Week is located in Montesarchio, an Italian town near Naples. Here, the math teacher Angela Fuggi created the task “Hercules Fountain”. In the interview, she presents her task and gives us an insight in the ERASMUS+ programme “Maths Everywhere”. How did you get to know MathCityMap? In this last […]

Our new Task of the Week is located in Montesarchio, an Italian town near Naples. Here, the math teacher Angela Fuggi created the task “Hercules Fountain”. In the interview, she presents her task and gives us an insight in the ERASMUS+ programme “Maths Everywhere”.

How did you get to know MathCityMap?

In this last school year I participated in the Erasmus project “ERASMUS + Maths Everywhere”. From 16th to 22nd February my school, the Istituto di Istruzione Superiore “E.Fermi” in Montesarchio (Benevento, Campania, Italy) hosted a group of 10 teachers and 29 students from Greece, Latvia, Spain and Turkey.

The focus of the project meeting in Montesarchio was “Math in the street”. Mathematics was viewed in close connection with the geographical area and its artistic and cultural heritage. One of the main activities was a treasure hunt and it was at this moment that MathCityMap came into play. The path created with the related activities had to be loaded onto MathCityMap and for this reason I started to use the app.

Please describe your task. How could you solve it?

My task related to the fountain located in the main square of Montesarchio. The artistic work, dating back to the second half of the 19th century, consists of a circular base with a basin, surmounted by a sculptural group of four lions and on a podium the figure of the warrior Hercules, the same mythical character who also appears on the emblem of the municipality. The task formulation is as follows:

In Umberto I square (the most famous square in Montesarchio) there is a fountain with 4 lions that surround Hercules, the Olympian god. The 4 lions are arranged at the vertices of a square on the side L. The statue of Hercules is supported by a circular base placed above the lions. Seen from above, this base is inscribed in the square with the 4 lions at the top. After measuring the distance between two consecutive lions, and therefore the side of the square, calculate the area of the circular base that supports the statue of Hercules (m²).

How could you solve it? Which is the didactic aim of this task?

The distance between two consecutive lions is the side of square L=2m. The side of the square coincides with the diameter D of the inscribed circumference, L = D, D=2m. The area of the circumference is A=π⋅(D:2)²=π⋅(2:2)²≈3,14 m²

The didactic aims were to represent, compare and analyze geometric figures and to work with them, identifying variations, invariants and relationships, above all starting from real contexts.

Task of the Week: Checkmate!

Annika Grenz has created our new task of the week in Wolfsburg. The student teacher of the TU Braunschweig reports about her task in the following interview. How did you get to know MathCityMap? I came across the MathCityMap project during my master thesis for my teacher training at the TU Braunschweig. It deals […]

Annika Grenz has created our new task of the week in Wolfsburg. The student teacher of the TU Braunschweig reports about her task in the following interview.

How did you get to know MathCityMap?

I came across the MathCityMap project during my master thesis for my teacher training at the TU Braunschweig. It deals with the theoretical background of the project and the development of an own trail for the secondary school level I. I would like to create the trail and the individual tasks for a subject area that is not yet so often addressed in the already published tasks and trails, but which is still application-oriented. These conditions led to the area of percentage calculation.

Describe your task. How can it be solved?

The task is to calculate the height of a required chess piece (king) for an already existing chessboard in the pedestrian zone. For professional chess there are exact specifications for the size of a square with 58mm and for the height of the king with 9.5cm. The dimensions of the individual chess squares can be measured with the help of a folding rule/measuring tape. Certain percentage relations for chess boards and corresponding pieces are given in the task definition. These provide information about the size of the diameter of the chess piece in relation to the square as well as the height of the king in relation to the diameter of the piece.

What didactic goals do you pursue with this task?

The goal of the task is to show the students that not only the geometric content of the mathematics lessons, but also other or all other topics are useful and needed for them in their immediate environment and in the most diverse areas of life.

Do you have further comments about MathCityMap?

The MathCityMap project is a great opportunity to take students out into the fresh air, motivate them and let them discover mathematics in their everyday lives.

Task of the Week: Compass

Helen Irthum from Luxembourg gives us an interview about her task “Compass” in the following. The student teacher created our new task of the week during a university seminar. How did you find out about the MathCityMap project? How do you use MCM and why? I am a student of primary school teaching at […]

Helen Irthum from Luxembourg gives us an interview about her task “Compass” in the following. The student teacher created our new task of the week during a university seminar.

How did you find out about the MathCityMap project? How do you use MCM and why?

I am a student of primary school teaching at the University of Luxembourg. Due to the Covid-19 crisis, the courses at the university have changed a lot and it was sometimes impossible to write an exam. In our course “Didactics of Mathematics” my professors decided that we should create a math trail in small groups using MathCityMap for any elementary school in Luxembourg. In this way we students became aware of the project. Together with a partner, I created a trail for the elementary school in Roodt-sur-Syre, which consists of 11 tasks in total, including the task “Compass”. Here you can find the trail “Math Trail next to the School “Am Stengert” in Roodt-sur-Syre”.

Describe your task. How can it be solved?

Our task “Compass” is about the student standing in the middle of a large compass, which is on the ground in the schoolyard, so that the compass faces north. First, one must take 5 steps towards the north, then 7 steps towards the east, 3 steps towards the south, 4 steps towards the east and finally 1 step towards the north. The students should now determine what is exactly in front of them after following this step combination. With the help of the compass, the students can determine where each cardinal point is located and thus correctly perform the step combination.

What are the didactic goals of the task?

Our main didactic goal is to help the students to get to know the cardinal points of the compass. The students should try to help themselves with the compass on the ground. It was very important to us that the students get to know the points of the compass in reality in this way and can experience this on their own bodies.

Do you have any further comments about MCM?

We are very enthusiastic about the MathCityMap project, because we, as prospective teachers, feel it is very important to show the students the mathematics in their environment so that they can experience this on their own bodies. We believe that these trails can often make students even more enthusiastic about mathematics, as they can see that mathematics is not just in their classroom, but in their everyday life and environment.

Task of the Week: Conjunto escultórico

Our new Task of the Week was created on the Africian continent. However, the task is located on Spainish territory: In the Spanish exclave Ceuta, which is surrounded by Morocco, Margarita Gentil created the task “Conjunto escultórico” (engl.: “Sculptural ensemble”). In the following, Margarita gives us an interview about the task. How do you get […]

Our new Task of the Week was created on the Africian continent. However, the task is located on Spainish territory: In the Spanish exclave Ceuta, which is surrounded by Morocco, Margarita Gentil created the task “Conjunto escultórico” (engl.: “Sculptural ensemble”). In the following, Margarita gives us an interview about the task.

How do you get in contact with MathCityMap?

Long ago, my colleague Sergio González told me about this interesting project that he found on Twitter. We work as math teachers at IES Luis de Camoens in Ceuta and we have had the chance to create our first MathCityMap route thanks to a virtual workshop taught by Claudia Lázaro [MathCityMap Educator for Spain form the Spanish Teacher Association FESPM] at the online course “XI Miguel de Guzmán School of Mathematical Education”.

Please describe your task. Where is it placed? What is the mathematical question? How could you solve it?

The task Conjunto escultórico is formulated as follows: At Plaza de la Constitución, crossing the bridge, we can find a sculptural ensemble. They are stone copies of the originals from the 19th century sculpted in Carrara marble that can be admired inside the Palacio Autonómico (Town Hall). When they were placing these copies there was a great stir because nobody remembered which was the former order. How many possibilities exist to place these statues?

The participants will see that the ensemble is made up of 6 statues: Peace, Africa, Industry, Arts, Commerce and Labour. They must recognize the type of problem (count the number of different possibilities) and make use of the combinatorial knowledge acquired during the lessons at school (Permutations. 6! = 6 · 5 · 4 · 3 · 2 · 1 = 720). The different hints given to the participant help during the process that leads to the resolution.

Which didactic aims do you want to stimulate through this task?

The objective of this task is to identify basic combinatorial problems in a real context and find the appropriate strategy to solve them.

Do you have any other commentary on MathCityMap?

MathCityMap project is great because it fits the type of activities we like to do. Sergio and I have set up a group, CeutaMaths, and now we are working on new routes. But, most of all, we are looking forward to play them with our students.

Public trails in Ceuta:

Task of the Week: Ei ei Käptn

In Münster we find our new task of the week. Here the research assistant of the University of Münster Lea Schreiber has created some math problems in the zoo (trail code: 012859). Here we present the task “Ei ei Käptn”. How did you get in contact with MathCityMap? I work as a research assistant at […]

In Münster we find our new task of the week. Here the research assistant of the University of Münster Lea Schreiber has created some math problems in the zoo (trail code: 012859). Here we present the task “Ei ei Käptn”.

How did you get in contact with MathCityMap?

I work as a research assistant at the WWU Münster and came across the project at a conference. Since then I have been working with the app from time to time and create trails for my group of giftet students “Kleine Mathe-Asse” (see below for a project description). Additionally I participated in a workshop in Münster by the MathCityMap educators Matthias Ludwig and Iwan Gurjanow. I can well imagine using the app later in my math classes.

Describe your task. How can it be solved?

The task was created as part of an “excursion trail”, because the math students could not go on an excursion this year due to the Corona pandemic. Accordingly, I thought it would be a nice idea if the children could have the opportunity to do a little rally through the zoo on their own with the help of MCM. First of all, they have to find the information board about the African red-necked ostriches on which the information necessary to solve the actual task is written. This consists of finding out how many ostrich eggs are needed to bake a gigantic amount of pudding slices, if the remaining eggs could still be bought in the supermarket. Once the children have found out that 1 ostrich egg replaces about 25 chicken eggs, they can use the information from the recipe for the task (343 eggs) to determine how many ostrich eggs or normal eggs they need for baking. That would be 13 ostrich eggs (13 x 25 = 325 hen eggs) and 18 hen eggs. Since the children may also consider using only ostrich eggs and thus no supermarket eggs, a solution interval was given where the solution numbers 13 and 14 are correct.

What didactic goals do you pursue with this task?

For the solution of the task, different competences are required from the children/”Kleine Mathe-Asse”. On the one hand, they have to filter out the relevant information on the information board and from the task. In both cases, significantly more information is given than is actually necessary. Once they have done this, they have to come up with a solution strategy to get the number of ostrich eggs (e.g. by trying and approaching the 343 eggs). For this they need knowledge of division or multiplication and addition or subtraction. A mathematical sensitivity and the ability to structure on the pattern level are also helpful in order to quickly arrive at a solution or to think of a solution approach/strategy with meaningful number spaces. Less able-bodied children also have the chance to solve the task successfully by gradually extrapolating the 25 series up to 325 or 350. This takes a little more time, but ultimately gets them to the goal.

Information on the promotion of gifted children in Münster & Frankfurt:

Click here for the project “Mathe für kleine Asse” in cooperation with Lea Schreiber at the University of Münster. The Goethe University Frankfurt also offers a mathematical program for gifted students which is leaded by Simone Jablonski: “Die jungen Mathe-Adler Frankfurt”.

Task of the Week: Trapézio

The task “Trapézio” [engl.: “Trapezoid”] by Isabel Figueiredo, who was one of our partner in the MoMaTrE project from 2017-2020, is chosen to be our new Task of the Week. The task is located in the north of the Portuguese city of Porto. How do you use MathCityMap? Please describe our European project here in […]

The task “Trapézio” [engl.: “Trapezoid”] by Isabel Figueiredo, who was one of our partner in the MoMaTrE project from 2017-2020, is chosen to be our new Task of the Week. The task is located in the north of the Portuguese city of Porto.

How do you use MathCityMap? Please describe our European project here in a few sentences.

MathCityMap is a project of the working group MATIS I of Goethe University Frankfurt. It is co-funded by the Erasmus+ project MoMaTrE [Mobile Math Trails in Europe]. Currently, seven institutions from five countries are participating in this project that englobe a web portal and the MCM app. Unfortunately, the MoMaTrE project ended after three years at August 31th.

MathCityMap combines the well-known math trail idea with the current technological possibilities of mobile devices. I use MathCityMap for the dissemination and popularization of mathematics, to attract more students to continue their scientific and technological studies.

With the MathCityMap-Project we like to motivate students to solve real world tasks by using expedient mathematical modelling ideas outside the classroom in order to discover the environment that surrounds them from a mathematical perspective. Mathematics should be discovered and experienced and must be done on the spot.

Please describe your task. Where is it placed? What is the mathematical question? How could you solve it?

This task is placed in Maia, a Portuguese municipality in the district of Porto. In one of the entrances of this city there is a Monument located in the Jardim das Pirâmides. We ask for the area, in m², of the lateral surface that can be seen in the picture.

As the necessary data could not easily measured, the idea is to use a non-standard surface unit. The formula for the trapezoid area must be used, but the measurements to be used are determined by the rectangular plates that make up the structure. Students measure one of the plates and count the number of slabs on the trapezoid.

Which didactic aims do you want to stimulate through this task?

The task has as main objective to be able to apply the teaching content in the classroom to real objects and, thus, deepen the knowledge.
The advantage of this is that it is clear that prior knowledge is necessary to be able to see everyday life from a mathematical perspective by training an eye for simple geometric figures in architecture. Another advantage is to lead students to find a different way to solve problems and don´t give up in face of obstacles.

Do you have any other commentary on MathCityMap?

MCM project integrates advanced digital technology with the math trails concept to illustrate the use of a technologically supported outdoor trail to enhance the teaching and learning of outdoor mathematics.