Task of the Week – Page 2

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.

Task of the Week: Ahoy sailors!

The student teacher Jill Groos created the task “Ahoy sailors!” in Stadtbredimus, Luxembourg, which we present today as the new Task of the Week. In our interview Jill Groos explains how the task can be solved and gives us insights into her teacher training. How did you get to know MathCityMap? I am a student […]

The student teacher Jill Groos created the task “Ahoy sailors!” in Stadtbredimus, Luxembourg, which we present today as the new Task of the Week. In our interview Jill Groos explains how the task can be solved and gives us insights into her teacher training.

How did you get to know MathCityMap?

I am a student at the University of Luxembourg in the Bachelor of Teacher Education. The MathCityMap project was presented to me by our professors at the university. In this summer semester, in the subject “Didactics of Mathematics”, our semester project was to design a math trail with MathCityMap.

Please describe your task. How could you solve it?

My task is about first and second graders building a paper boat. Then the boat is let into the water on one side of the bridge and students are asked to count how long the boat takes to come out on the other side of the bridge. The task is solved by counting, to be more precisely by counting seconds.

Which didactic goals do you want to promote with this task?

The children should take a closer look at the familiar tower and recognise that they can find numbers everywhere, even “in real life”. In our daily life we are surrounded by numbers!

Do you have any further comments on MathCityMap?

The didactic goals of this task are in the areas of learning to count, problem solving and learning to tell time. It is important that the children can work out a solution for an existing problem, learn how to count seconds and learn to count in total.

Task of the Week: The Climbing Blocks of the Mennea Park

In Turin, Italy, we find our new task of the week. Here the teacher Michela Viale created the task “I blocchi da arrampicata del Parco Mennea” (engl.: “The climbing blocks of the Mennea Park”), in which the visible surface of stapled dodecahedrons should be calculated. Michela, how did you discover the MathCityMap project? I got […]

In Turin, Italy, we find our new task of the week. Here the teacher Michela Viale created the task “I blocchi da arrampicata del Parco Mennea” (engl.: “The climbing blocks of the Mennea Park”), in which the visible surface of stapled dodecahedrons should be calculated.

Michela, how did you discover the MathCityMap project?

I got in contact with MCM four years ago, when I was attending a math online course at the university of Torino, Math Department, where I had to create my first MathCityMap task. By participating another MOOC in the spring of 2020, I created my own math trail on MCM.

I am a teacher at middle school (from 11 to 14 years old) and I love to create “real problems” for my students. By using MCM I can organize outdoor mathematical problem solving for my students.

Describe your task. How can it be solved?

My task is placed in a park in Turin (Parco P. P. Mennea). It is a climbing block for children made up of three dodecahedra. Since the blocks are stapled on top of each other, they have some common sides, which are therefore not visible. I ask to children to calculate the area of the visible sides (the surface they could paint). They have to recognize the dodecahedron, count the number of the sides they could paint, calculate the area of one side (which is a regular pentagon).

What didactic goals do you pursue with the task?

I want to stimulate different didactic aims: recognize solids and plane figures around us, measure them, calculate their surface. In general, I think MCM is very useful to improve Math competences. I’ll create a new math trail during my holidays in Sardinia in August.

Task of the Week: The Solar Pyramid

Our new Task of the Week is located in Spanish capital Madrid. There, Juan Martinez created the task “Puerta N.O. Parque Juan Carlos I (Pirámide Solar)” [engl.: Entrance to the park Juan Carlos I (Solar Pyramid)]. The task author Juan Martinez is a member of the Spanish maths education association FESPM, which is one of […]

Our new Task of the Week is located in Spanish capital Madrid. There, Juan Martinez created the task “Puerta N.O. Parque Juan Carlos I (Pirámide Solar)” [engl.: Entrance to the park Juan Carlos I (Solar Pyramid)].

The task author Juan Martinez is a member of the Spanish maths education association FESPM, which is one of our project partners in out Erasmus+ projects MoMaTrE and MaSCE³. Both aim to the further development of the MathCityMap system in order to show students the “hidden” mathematics in their own environment.

The task formulation is as follows: Entering the Juan Carlos I Park, through this door we observe on the left a Solar Pyramid. What is the total area of the roof, using one square solar panel as a unit? The pyramid has four triangular sides of equal size. We count 25 whole solar panels on the base side and 15 vertically stacked panels. Taking the cut panels into account, we can calculate that the sides of the pyramid are composed of approximately 830 solar cells.

This task is to approximate the lateral area of a pyramid using a non-standard surface unit. Since the object is quite large, the students should use the triangular area formula to calculate the number of solar collectors und recognize this procedure as an effective counting method.