Simone Jablonski | MathCityMap

Task of the Week: Bench

The determination of the weight of an object has often been part of a Task of the Week. However, today’s task is a particular challenge because the object consists of different materials with different densities. Task: Bench (task number: 1803) There are benches in front of the H7. How much does a bench seat weigh […]

The determination of the weight of an object has often been part of a Task of the Week. However, today’s task is a particular challenge because the object consists of different materials with different densities.

Task: Bench (task number: 1803)

There are benches in front of the H7. How much does a bench seat weigh when the wood weighs 690 kg per m³ and the concrete weighs 2400 kg per m³? Give the result in kg.

The best way to solve this problem is by dividing the bench into three parts: the two concrete feet, the concrete seat and the wooden seat. A cuboid can be used as a model for all parts. Then the students take the necessary measurements and calculate the weight of concrete and wood first separately. The total weight of the bench is then calculated by addition.

The task requires knowledge about the cuboid as well as its volume. In addition, the concept of density should be known to the pupils. Within solving this task, this can be sharpened. The task is recommended from class 7.

MoMaTrE Kick Off at ENS Lyon

On Thursday, 5th October 2017, the EU project MoMaTrE officially started in the House of Mathematics at the École Normal Superieure Lyon. MoMaTrE is the acronym for Mobile Math Trails in Europe and that is exactly what we want to do within the next 3 years: to spread the Math Trail idea with the help […]

On Thursday, 5th October 2017, the EU project MoMaTrE officially started in the House of Mathematics at the École Normal Superieure Lyon. MoMaTrE is the acronym for Mobile Math Trails in Europe and that is exactly what we want to do within the next 3 years: to spread the Math Trail idea with the help of new technologies in Europe. All project partners from five EU countries (France, Germany, Portugal, Slovakia, Spain) were represented and prepared the first milestones for the various subprojects. One thing is already clear: MCM will play a central role in MoMaTrE and will be further developed. It should be noted that future versions of the app will contain educational features, that there will be 100 generic tasks as well as an app for authors with which one can create MCM tasks on site.

On the picture you can see from left to right

On the stairs: Matthias Ludwig (GU, Frankfurt), Immanuel Scheerer (Aut, Berlin), Johannes Scheerer (Aut, Berlin), Christian Mercat (UCBL, Lyon)

Below: Ana Moura (IPP, Porto) , Claudia Lazaro (FESPME, Santander), Patrik Berger (UCBL, Lyon), Carmen Monzo Gonzalez (FESPME, Santander), Iwan Gurjanow (GU, Frankfurt), Joerg Zender (GU, Frankfurt), Pedro Santos (INESC-ID, Lisbon), Amelia Caldeira (IPP, Porto), Imrich Jakab (CPU, Nitra), Sona Ceretkova (CPU, Nitra).

Task of the Week: Spider Web

While searching for suitable MathCityMap tasks, creativity and a focus for mathematics in the environment are required. This is also shown by the current Task of the Week, created by Stefan Rieger, in which a climbing frame is converted into a math task. Task: Spider web (task number: 1662) How many meters of rope does […]

While searching for suitable MathCityMap tasks, creativity and a focus for mathematics in the environment are required. This is also shown by the current Task of the Week, created by Stefan Rieger, in which a climbing frame is converted into a math task.

Task: Spider web (task number: 1662)

How many meters of rope does this spider web consist of?

Thankfully Mr. Rieger was available for a short interview, so he could give an insight into the idea behind the task.

How did you get the idea to create this task for MathCityMap?

Three of us were walking around the schoolyard, looking for interesting tasks. This task offered itself directly, because it is challenging and can be solved by younger students.

What competencies and topics play a role in the problem solving?

Here, it will be important that the group works together when it tries to solve the task. There are several people needed for measuring and recording. Accurate measurement and safe handling of the measuring tape will be necessary to solve the problem. Since it is intended as a task for the grades 5/6, the measuring (here non-straight lines) will be relevant. Of course, older students can use knowledge from the circle calculation.

Have you tested the task with students or received other feedback on the task?

No. The task will be tested in the next school year with grade 5 as well as in the course of a further teacher training with colleagues. However, he climbing children had a lot of fun to help me as a climber for checking the measurements.

We are pleased that MathCityMap finds more and more task authors from different regions and the task portal is expanded by a variety of tasks!

University of Turin uses MathCityMap

At the invitation of Prof. Dr. Ferdinando Arzarello from the Department of Mathematics at the University of Turin, Iwan Gurjanow and Matthias Ludwig presented the functionality and possibilities of MCM to the Massive Open Online Course (MOOC) working group. First, the idea of Math Trails was demonstrated to the colleagues from Piemont, using the example […]

At the invitation of Prof. Dr. Ferdinando Arzarello from the Department of Mathematics at the University of Turin, Iwan Gurjanow and Matthias Ludwig presented the functionality and possibilities of MCM to the Massive Open Online Course (MOOC) working group.

First, the idea of Math Trails was demonstrated to the colleagues from Piemont, using the example of their own city. Subsequently, Iwan Gurjanow described the technical possibilities. In a short MCM-Trail, created by the MCM team around the mathematical institute, the participants themselves were able to enter the MCM activity. Thanks to Eugenia Taranto and the collaboration of Virginia Alberti, Sara Labasin and Roberta Ferro, the app and the portal are now also available in Italian. The next morning was used to discover tasks at the Basilica of Superga and then integrate them into the MCM system. The colleagues from Turin were so enthusiastic that from January 2018 onwards a MOOC course on the topic of MCM will be offered by the University of Torino for Italian mathematics teachers. We are looking forward to this cooperation.

The Logo of the Massive Open Online Course of the University of Turin

MCM in Herborn

On 28.09.17, Daniel Birnbaum, Martin Lipinski and Simone Jablonski presented MathCityMap as part of an internal teacher training at the Johanneum Gymnasium in Herborn. First, the theoretical basis for Math Trails as well as the MCM concept were presented to the participants. With the help of the criteria for good MCM tasks, the participants were […]

On 28.09.17, Daniel Birnbaum, Martin Lipinski and Simone Jablonski presented MathCityMap as part of an internal teacher training at the Johanneum Gymnasium in Herborn. First, the theoretical basis for Math Trails as well as the MCM concept were presented to the participants. With the help of the criteria for good MCM tasks, the participants were then themselves active and searched for possible tasks at the schoolyard. After a change of perspective, the participants learned about the app by means of a trail in the schoolyard, consisting of combinatorial and geometrical problems.

We would like to thank the participants for their cooperation and feedback and look forward to numerous MCM tasks in and around Herborn. Are you interested in teacher training on MCM? Feel free to contact us!

Task of the Week: Europe Tower

The current Task of the Week deals with one of the many landmarks of Frankfurt: the Europe tower, also known as “asparagus”. The related task is to estimate the own distance to the tower using the intercept theorems. Task: Europe Tower (task number: 1595) Determine the distance from your location to the Europe Tower. Give […]

The current Task of the Week deals with one of the many landmarks of Frankfurt: the Europe tower, also known as “asparagus”. The related task is to estimate the own distance to the tower using the intercept theorems.

Task: Europe Tower (task number: 1595)

Determine the distance from your location to the Europe Tower. Give the result in meters. Info: the pulpit has a diameter of 59 m.

The first challenge is to find a suitable solution. With the aid of the intercept theorems, the task can be solved with the use of one’s own body. The arm and thumbs are streched so that the pulpit of the tower is covered with one eye opened. Afterwards the distance to the tower can be calculated with help of the thumb width and the arm length or distance from thumb to eye.

The task is a successful example of “outdoor mathematics” by using the theoretical formulas (here: intercept theorems) in an authentic application in the environment. To solve the problem, the students need knowledge about the intercept theorems. The task can thus be assigned to geometry and can be solved from class 9 onwards.

Task of the Week: Shaft Cover

The current Task of the Week is about an everyday object, which is suitable for various tasks around the circle and can be used due to its frequent occurrence in almost every trail. More specifically, it is about the shaft cover of a canal and its dimensions and weight. Task: Shaft Cover (task number: 1804) […]

The current Task of the Week is about an everyday object, which is suitable for various tasks around the circle and can be used due to its frequent occurrence in almost every trail. More specifically, it is about the shaft cover of a canal and its dimensions and weight.

Task: Shaft Cover (task number: 1804)

In the center of the shaft cover, concrete is given. 12 liters of concrete are used per lid. What is the height of the concrete cylinder? Give the result rounded to one decimal place in cm.

To solve the problem, it is first necessary to recognize that the volume of the center of the shaft cover is given. In addition, the shaft cover has to be recognized as a cylinder apart from minor inaccuracies. Using the formula for the volume of a cylinder and the measured radius, the students can identify the required height. In general, the modeling competence and handling of mathematical objects in reality is trained. In addition, the flexible handling of formulas and the choice of suitable units play an important role in order to solve the problem. The problem can be grouped into the complex circle and cylinder and thus plays a role in geometric questions. The task can be used from class 9 onwards.

Task of the Week: Block of concrete at Camps Bay

The current “Task of the Week” is about determining the mass of a concrete sculpture in Camps Bay near Cape Town, the capital of South Africa. The special feature of this sculpture is that it is a composite geometric figure whose components are modeled and calculated individually. Task: Block of concrete at Camps Bay (task […]

The current “Task of the Week” is about determining the mass of a concrete sculpture in Camps Bay near Cape Town, the capital of South Africa. The special feature of this sculpture is that it is a composite geometric figure whose components are modeled and calculated individually.

Task: Block of concrete at Camps Bay (task number: 1811)

Calculate the mass of this concrete sculpture. 1cm³ weighs about 2.8g. Enter the result in tons!

In order to solve the problem, it is necessary to divide the sculpture into three basic parts: a cuboid and two cylinders. Then, the necessary lengths are measured and the volumes of the bodies are calculated and added. In the last step, the total volume of the sculpture is multiplied with the density of concrete, which leads to the total weight of the sculpture.

This kind of task can easily be transferred to similar objects, whereby the degree of difficulty can be varied according to the composition of the figure. This type of task teaches the geometric view and understanding of composite bodies.

Lecture in Bielefeld

At the invitation of Rudolf vom Hofe, there was a lecture on the MathCityMap project as part of a seminar on didactics of algebra at the 25th July 2017. In front of nearly 20 listeners, current results from studies and the technical background were presented. After the lecture, there were many detailed questions about the […]

At the invitation of Rudolf vom Hofe, there was a lecture on the MathCityMap project as part of a seminar on didactics of algebra at the 25th July 2017. In front of nearly 20 listeners, current results from studies and the technical background were presented. After the lecture, there were many detailed questions about the web portal as well as the app, and the listeners could test the prepared trail at the University of Bielefeld.

The trail was created in collaboration with Johannes Schürmann. An interesting task from the trail is about the bench in front of the lecture hall 7, which is composed of several cuboids and materials.

Task of the Week: Archway

In today’s Task of the Week, we would like to present a task from a MathTrail, which was developed within a project for talented students by the University of Paderborn in cooperation with the Paderborner Pelizaeus-Gymnasium. You can find more information here. We would like to present the selected task in a short interview with […]

In today’s Task of the Week, we would like to present a task from a MathTrail, which was developed within a project for talented students by the University of Paderborn in cooperation with the Paderborner Pelizaeus-Gymnasium. You can find more information here. We would like to present the selected task in a short interview with Max Hoffmann, member of the project. At this point, we would like to thank for the cooperation and the interview.

Task: Archway (task number: 1303)

Calculate the volume of the stones that create the archway! Give the solution in cubic meters. (Only the round part of the arc is meant).

How did you get the idea of using this object in a task?

While searching for tasks for a mathematical walking tour through the beautiful Paderborn inner city, the students independently selected this archway near the Paderquelle. The first idea was to calculate the area of the stones around the archway. I had the feeling that this kind of questioning was a typical task the students knew from their math books. After some thought, the suggestion came to modify the task so that the volume of the stones from which the archway is formed should be calculated.

What kind of mathematical activities and competences do you want to promote?

The task addresses modeling competencies (representation of the situation through two semicircles) and requires the selection and determination of appropriate measured variables. In terms of content, the known formulas for the circle are necessary for solving the problem.

Have you already processed the task with pupils or received feedback in other forms?

The task was developed by a small group and the other students of the project also solved the problem and liked it. The results of the first group were confirmed. In addition, the group presented the task at the final project event at the University of Paderborn and received positive feedback.