Simone Jablonski | MathCityMap

Task of the Week: Slope of the Roof

Today’s Task of the Week leads us to South Africa. Matthias Ludwig created three trails in Grahamstown as part of a teacher training course. You can learn more about the background here. The task described is about determining a roof slope using a gradient triangle. Task: Slope of the Roof (task number: 1697) Calculate the […]

Today’s Task of the Week leads us to South Africa. Matthias Ludwig created three trails in Grahamstown as part of a teacher training course. You can learn more about the background here.

The task described is about determining a roof slope using a gradient triangle.

Task: Slope of the Roof (task number: 1697)

Calculate the slope of the roof. Give the result in percentage (%).

The task can be integrated in the topic of linear functions and their slope. The slope is determined by the quotient of vertical and horizontal length. For this purpose a suitable gradient triangle must be found. While the horizontal length can be determined by measuring, the height can be calculated using the number of stones. The task is therefore a successful combination of geometry and functions and can be used from class 8.

Task of the Week: The Wall

Today’s Task of the Week is an example of a task that you can create with minimal effort using the Task Wizard. It is about determining the number of stones in a given rectangular area. The object here is a wall, but similar objects can also be pavements. Task: The Wall (task number: 1077) Determine […]

Today’s Task of the Week is an example of a task that you can create with minimal effort using the Task Wizard. It is about determining the number of stones in a given rectangular area. The object here is a wall, but similar objects can also be pavements.

Task: The Wall (task number: 1077)

Determine the number of stones of the wall front in the marked area.

In order to solve the problem, the students can proceed in various ways. On the one hand, it is possible to determine the number of stones in one square meter and to measure the length and height of the rectangular wall. In this solution, the accuracy can be increased by counting several square meters and then taking the mean value. On the other hand, the students can count the stones in terms of length and height and approximate the total number by means of a multiplication.

When you create such a task with the Task Wizard, you only have to enter the length and height and the number of stones in a square meter as well as add a photo and the location. The Task Wizard then automatically creates notes and a sample solution.

The task requires knowledge about the rectangle. It can be classified in the field of geometry and can be used from class 6 onwards.

MoMaTrE – Mobile Math Trails In Europe

After one year of preparation we managed it: MathCityMap is the heart of the Strategic Partnership MoMaTrE. MoMaTrE is an acronym for Mobile Math Trails in Europe. The working group MATIS I led the application for this Erasmus + project. Currently, seven institutions from five countries are participating: Goethe University, Frankfurt Univerzita Konstantina Filozofa, Nitra, Slovakia Université Claude […]

After one year of preparation we managed it: MathCityMap is the heart of the Strategic Partnership MoMaTrE. MoMaTrE is an acronym for Mobile Math Trails in Europe. The working group MATIS I led the application for this Erasmus + project. Currently, seven institutions from five countries are participating:

Goethe University, Frankfurt
Univerzita Konstantina Filozofa, Nitra, Slovakia
Université Claude Bernard, Lyon, France
Instituto de Engenharia de Sistemas e Computadores, Investigação e Desenvolvimento, Lisbon, Portugal
Instituto Superior de Engenharia, Porto, Portugal
Autentek GmbH, Berlin (software company)
Federación Española de Sociedades de Profesores de Matemáticas, Santander, Spain

Within the next three years, the project has the following aims

Spread of mobile Math Trails across Europe
Further development of MathCityMap (including Gamification, mobile authoring tools, new task formats, educational Math Trail features)
Database for generic Tasks
Development and implementation of (international) training modules (shortterm curriculum)
Development and implementation of accredited seminars on outdoor mathematics (longterm curriculum)
Explore the use of mobile math trails and present the results at congresses and publications

Apart from the contentual reasons, the many supporting letters of our associate partners were responsible for the award. For example, we were able to convince the MNU, the Media Office of the DMV, Mathe im Leben, the DZLM, and the Stiftung Rechnen. From France are supported by the IREM, from Spain the Royal Spanish Society of Mathematics, from Portugal the Mathematicial Society as well as the Mathematics Teaching Association, and from Slovakia the Association of Slovak mathematicians and physicists.

The new MCM team

As MCM (see chart) continues to grow, we also need more employees. Since 15th August, seven people have been working in the MCM team. In the picture from left to right: Daniel Birnbaum (seconded teacher for computer science and sports, iOS app), Matthias Ludwig (head of the MCM project), Joerg Zender (research associate, momatre.eu), Simone […]

As MCM (see chart) continues to grow, we also need more employees. Since 15th August, seven people have been working in the MCM team.

In the picture from left to right:

Daniel Birnbaum (seconded teacher for computer science and sports, iOS app), Matthias Ludwig (head of the MCM project), Joerg Zender (research associate, momatre.eu), Simone Jablonski (research associate, public relations), Martin Lipinski (seconded teacher for math and sports, teacher training), Iwan Gurjanow (research associate, web portal and Android app). Moritz Baumann-Wehner (student, trainings, events) is unfortunately not in the picture.

If you have any questions regarding the project, please contact the listed persons:

ludwig at math.uni-frankfurt.de

gurjanow at math.uni-frankfurt.de

zender at math.uni-frankfurt.de

lipinski at math.uni-frankfurt.de

birnbaum at math.uni-frankfurt.de

jablonski at math.uni-frankfurt.de

MCM in Kappeln – a great success

Even in the summer holidays, MathCityMap is demanded. At the “Mathe Magie” exhibition in Kappeln, Iwan Gurjanow and Matthias Ludwig created various Mathtrails especially for the city of Kappeln. One can choose between the family trail and trails for different grades. Rebecca Nordmann from “Schleiboten” wrote a wonderful text about the Mathtrail which expresses the […]

Even in the summer holidays, MathCityMap is demanded. At the “Mathe Magie” exhibition in Kappeln, Iwan Gurjanow and Matthias Ludwig created various Mathtrails especially for the city of Kappeln. One can choose between the family trail and trails for different grades.

Rebecca Nordmann from “Schleiboten” wrote a wonderful text about the Mathtrail which expresses the mood in solving the tasks and which we want to share with you. We further want to thank for the photo taken by Rebecca Nordmann.

Task of the Week: Old Oak Tree

How can the age of a tree be approached using mathematics? This question addresses the current Task of the Week. It is placed in this form in Kappeln, but can be easily and quickly transferred to other places. Task: Old Oak Tree (issue number: 1473) How old is this oak tree? It is known that […]

How can the age of a tree be approached using mathematics? This question addresses the current Task of the Week. It is placed in this form in Kappeln, but can be easily and quickly transferred to other places.

Task: Old Oak Tree (issue number: 1473)

How old is this oak tree? It is known that an oak with a diameter (in breast height) of 50 cm is about 110 years old.

In order to solve the problem, it is assumed that the growth of the oak is linear. This means that the average growth per year can be determined using the information in the text. Subsequently, the circumference in the height of the chest is measured and the diameter is determined by means of the relationship between the circumference and the diameter of a circle. This then leads to the age of the tree.

On the one hand, the problem can be classified in the geometric topic of the circle and, on the other hand, proportionality. If the relationship between the diameter and the circumference is already discussed at this time, the task can be used from class 6 onwards.

Task of the Week: Tank Filling

In today’s Task of the Week everything focuses on the geometrical body of a cylinder as well as the activities of measuring and modeling. The task is included in the Dillfeld Trail in Wetzlar. Task: Tank Filling (task number: 1098) Determine the capacity of the tank in liters. First of all, it is necessary to […]

In today’s Task of the Week everything focuses on the geometrical body of a cylinder as well as the activities of measuring and modeling. The task is included in the Dillfeld Trail in Wetzlar.

Task: Tank Filling (task number: 1098)

Determine the capacity of the tank in liters.

First of all, it is necessary to recognize the object as a cylinder and to ignore minor deviations from the idealized body. The students then measure the necessary length. Since the result is to be expressed in liters, it is sufficient to record the data already at this point in decimetres. Subsequently, the capacity is determined by means of the volume formula for cylinders.

For the task, the students must have already gained experience with the geometrical body cylinder and its volume. The task is assigned to the spatial geometry and can be used from class 9 onwards.

MathCityMap goes to Namibia

From 17th July to 22nd July 2017, MathCityMap was presented at the National Institute for Educational Development in Okahandja to a select group of postgraduates and students from all over Namibia. Of course, we searched for special tasks. One of them focuses on the Camel Thorn Tree… …and another on the Namibian Desert Cactus. The […]

From 17th July to 22nd July 2017, MathCityMap was presented at the National Institute for Educational Development in Okahandja to a select group of postgraduates and students from all over Namibia. Of course, we searched for special tasks. One of them focuses on the Camel Thorn Tree…

…and another on the Namibian Desert Cactus.

The interest in the mobile mathtrails was very high and tasks were found and created diligently. We are looking forward to seeing more tasks in whole Namibia.

Task of the Week: Mushroom

Today’s Task of the Week focuses a geometric question at the Aasee in Münster. More specifically, the surface content of a hemisphere is calculated by the students. Task: Mushroom (task number: 1400) Determine the area of the mushroom. Give the result in dm². Round to one decimal. In order to solve the problem, the students have to […]

Today’s Task of the Week focuses a geometric question at the Aasee in Münster. More specifically, the surface content of a hemisphere is calculated by the students.

Task: Mushroom (task number: 1400)

Determine the area of the mushroom. Give the result in dm². Round to one decimal.

In order to solve the problem, the students have to approach and recognize the shape as a hemisphere. They then need the formula for the calculation of the spherical surface or here the hemispherical surface. For the determination, only the radius of the hemispheres is required. Since it can not be measured directly, this can be determined with help of the circumference.

The task requires knowledge of the circle and of the sphere and can therefore be applied from class 9 onwards.

Task of the Week: Hubland Bridge

Many of the tasks in the MCM portal are based on mathematical knowledge from secondary level I. Today’s Task of the Week shows that knowledge of secondary level II can be integrated in tasks as well. The task “Hubland Bridge I” is about the inflection point of a function as well as its properties. Task: […]

Many of the tasks in the MCM portal are based on mathematical knowledge from secondary level I. Today’s Task of the Week shows that knowledge of secondary level II can be integrated in tasks as well. The task “Hubland Bridge I” is about the inflection point of a function as well as its properties.

Task: Hubland Bridge I (task number 684)

At which stair (counted from below) is the inflection point?

First, the bridge must be modeled as a function. For the visual determination of the inflection point, the students use the characteristics of the inflection point. In this case, the property can help to describe the inflection point here as the point with maximum slope and without curvature. In the presence of the device, the maximum slope can also be determined using a gradiometer (see Hubland Bridge II). The point of inflection as a point without curvature can be determined optically by looking for the point at which the graph resembles a straight line. After the turning point has been determined, the students have to count the steps up to the point. Ideally, this is done several times and the mean value is formed.

The task can be assigned to the topic of analysis, more precisely the differential calculus. With the development of the characteristics of the turning point of a function, the task can be used from class 11 onwards.