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.
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.
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.
After all teachers had learned about the system, and the registration problems had been solved, the participants were able to create tasks by themselves. They found good objects to experience mathematics. The problems came later back in the classroom. Again, it was experienced that a precise formulation, the creation of hints and sample solutions are […]
After all teachers had learned about the system, and the registration problems had been solved, the participants were able to create tasks by themselves. They found good objects to experience mathematics.
The problems came later back in the classroom. Again, it was experienced that a precise formulation, the creation of hints and sample solutions are not formulated easily. Of course, there were also technical problems since not all teachers had the appropriate IT knowledge to exchange images between two devices or to edit them (for example a 90° rotation). Nevertheless, each group was able to integrate a task into the system.
We, the MCM project team, are a little proud that our idea and system also works in South Africa! But the participants enjoyed it as well as the final photo shows. MCM says thanks to RUMEP (Rhodes University Math Education Project).
Today’s “Task of the Week” was created by Markus Heinze in the trail “Schillergymnasium” in Bautzen and combines percentage calculation with a geometric question. Task: Percentage Calculation at the Entrance (task number: 1262) Determine how many percent of the entrance doors are made of glass. Mr. Heinze was kindly available for a short interview so that we can present […]
Today’s “Task of the Week” was created by Markus Heinze in the trail “Schillergymnasium” in Bautzen and combines percentage calculation with a geometric question.
Task: Percentage Calculation at the Entrance (task number: 1262)
Determine how many percent of the entrance doors are made of glass.
Mr. Heinze was kindly available for a short interview so that we can present his assessment and experience with the task. We would like to thank him very much!
How did you get the idea for this task?
I wanted to create different tasks for an 8th or 7th class. I had a free time but it rained right at that time. That’s why I stood at the entrance at first and thought about how to install the entrance door and so, the idea arose to connect triangular areas and percentage calculation.
Which mathematical skills and competencies should be addressed in the task?
On the one hand, of course, modeling and problem solving is of high importance, because I had noticed deficits in the competence test in this area among the students in the 8th class. But also the visual ability is strengthened, of course, since real objects are being worked with and the students receive an idea of areas and percentages.
Has the task already been solved by pupils? If so, what feedback was given?
The task was solved by students of a 9th class and they found it relatively simple but interesting, but this is also because they had not worked with the app before and were generally enthusiastic about the matter. I think for a 7th or 8th class it is suitable.
This week, we had the opportunity to present MathCityMap at a teacher training at Rhodes University in Grahamstown in South Africa. Matthias Ludwig followed the invitation of Prof. Dr. Marc Schäfer (chair of mathematics education, Rhodes University) and accepted the challenge to present and test MCM in South Africa. The area of Rhodes University offers a variety of objects […]
This week, we had the opportunity to present MathCityMap at a teacher training at Rhodes University in Grahamstown in South Africa.
Matthias Ludwig followed the invitation of Prof. Dr. Marc Schäfer (chair of mathematics education, Rhodes University) and accepted the challenge to present and test MCM in South Africa.
The area of Rhodes University offers a variety of objects which are suitable for good MCM tasks. Three routes with 6-7 tasks could be created. On Monday, the theory of outdoor mathematics and the basic idea of MCM were introduced. On Tuesday, almost all of the 50 teachers were able to install the MCM app on their Android smartphones. Some tried it with their Windows phones, but of course it did not work. None of the teachers owned an iPhone! Afterwards, it was time to solve the tasks, but it turned out that many participants were not able to navigate on a map at all. Some had not activated the GPS localization and searched the right direction. Thanks to the support of Clemens and Percy, we found the reason quickly.
It was a pleasure to observe the teachers during solving the tasks, and to see the joy when the MCM app rewarded a 100-point response and a green check. Overall, the concept of “doing mathematics outside” was completely new to the South Africans.
There was also a discussion about units, conversions and modeling. Especially the modeling process is relevant for MCM since one has to translate reality into a mathematical model to solve the tasks numerically.
The present Task of the Week is about polygons and geometrical figures. In particular, the prism with a hexagonal base surface plays a role. The task can be found in this form in Cologne, but can be transferred to similar objects without problems. Task: Flower Box (task number: 1189) What is the volume of the […]
The present Task of the Week is about polygons and geometrical figures. In particular, the prism with a hexagonal base surface plays a role. The task can be found in this form in Cologne, but can be transferred to similar objects without problems.
Task: Flower Box (task number: 1189)
What is the volume of the flower box? You may assume that the floor is as thick as the edge of the box. Give the result in liters.
As already mentioned, the base area can be assumed to be a regular hexagon. To determine the area of the base area, pupils can either use the formula for the area content of a regular hexagon or divide the area into suitable subspaces. They should note that the edge does not belong to the volume. The pupils then measure the height of the prism by subtracting the floor plate. Subsequently, the volume of the prism, which is converted into liters in the last step, is obtained by multiplication.
The task thus involves a geometric question, in which students can either apply their knowledge to regular polygons or to composite surfaces. In addition, spatial figures are discussed as well as the adaptation to real conditions by observing the edge. The task is recommended from grade 8 onwards.
The present Task of the Week leads to Münster and contains a question from the probability calculation. Task: Red or Green? (Task number: 428) The city of Münster is trying everything to make road traffic as smooth as possible. There is even a traffic light hotline, where you can make suggestions for improvement. Despite all […]
The present Task of the Week leads to Münster and contains a question from the probability calculation.
Task: Red or Green? (Task number: 428)
The city of Münster is trying everything to make road traffic as smooth as possible. There is even a traffic light hotline, where you can make suggestions for improvement. Despite all the good planning, walkers often come to red traffic lights. Often, the red traffic lights are noticed more often than the green traffic lights. Estimate how often a traffic light shows “green” if one passes the traffic light 100 times.
In order to solve the problem, students should first measure the duration of a green phase, as well as the duration of a red phase. The duration of a total phase then results over the length of a green phase and a red phase. In order to determine the probability of reaching the traffic light at green, the duration of the green phase is divided by the duration of a complete traffic light. Subsequently, the expectation value can be formed with a 100-time passing.
This approach leads to a theoretical solution which, however, should be questioned critically. The result as well as the randomness of the arrival can be influenced depending on the traffic light circuit and any traffic lights which have been traversed previously. However, the problem is a successful application of the probability calculation in everyday life and can be used with the first elaborations of the probability concept.
This week’s Task of the Week addresses, in particular, the modeling competence of the students. It is a question of approximating the weight of a stone as closely as possible by approximating the stone through a known body. Task: Stone (task number: 1048) What is the weight of the stone? 1cm³ weighs 2.8g. Give the […]
This week’s Task of the Week addresses, in particular, the modeling competence of the students. It is a question of approximating the weight of a stone as closely as possible by approximating the stone through a known body.
Task: Stone (task number: 1048)
What is the weight of the stone? 1cm³ weighs 2.8g. Give the result in kg.
In order to approach the object by means of a geometrical basic body, the students must refrain from slight deviations of the real object and the ideal body. In particular, a prism with a trapezoidal base side is suitable. If this step is done, the students determine the pages relevant to this body through measurements and then calculate its volume. The last step is the calculation of the weight with the given density as well as the conversion in kilograms.
With this task, it is especially nice to see that there is not always one correct result for mathematical questions. Through different approaches and measurements the pupils receive different results. In order to obtain the most accurate result as possible, the determined values must be within a defined interval. Translating from reality into the “mathematical world” also plays a decisive role here in the sense of modeling competence.
The task requires knowledge about the basic geometrical bodies and in particular about the prism with a trapezoidal base surface. It is therefore to be classified in spatial geometry and can be solved from class 7.
At the invitation of Stiftung Rechnen and EuroScience, Iwan Gurjanow and Matthias Ludwig spent two days in Kappeln in Schleswig-Holstein at the Baltic Sea to create MCM Mathtrails for a vacation project. The Stiftung Rechnen and EuroScience will hold from 08.07. – 12.08 the interactive exhibition Mathe Magie. To do this, the working group MATIS […]
At the invitation of Stiftung Rechnen and EuroScience, Iwan Gurjanow and Matthias Ludwig spent two days in Kappeln in Schleswig-Holstein at the Baltic Sea to create MCM Mathtrails for a vacation project.
The Stiftung Rechnen and EuroScience will hold from 08.07. – 12.08 the interactive exhibition Mathe Magie. To do this, the working group MATIS I was asked to create various MCM trails in the city at the Schlei. Of course, this was not a question for us: we would like to support the project and created 27 new tasks in Kappeln at the beginning of June.
The photo shows : Jeanette Schuppe-Krahn (EuroScience), Henning Mittelmann (Mittelmanns Werft), Matthias Ludwig, Iwan Gurjanow (both Goethe University), Bodo Meusel (EuroScience), Lara Zemite (Wirtschaft und Touristik Kappeln GmbH), Matthias Mau.
