tasks | MathCityMap

Visit of the Project Seminar “Math Trails”

On 12.10.2017, the MathTrails project seminar from the Theodosius-Florentini-Schule Gemünden visited the MathCityMap team in Frankfurt. Marie-Noelle Klug, a participating student in the project, has thankfully provided us a great report as well as photos, which give an insight into how the students have experienced the day: The P-Seminar “MathTrails” led the students of the […]

On 12.10.2017, the MathTrails project seminar from the Theodosius-Florentini-Schule Gemünden visited the MathCityMap team in Frankfurt. Marie-Noelle Klug, a participating student in the project, has thankfully provided us a great report as well as photos, which give an insight into how the students have experienced the day:

The P-Seminar “MathTrails” led the students of the Q11 of the Theodosius-Florentini-Schule Gemünden to Frankfurt to get to know the origin of the project MathCityMap and to get the necessary information about the seminar.

We arrived at the Goethe University in Frankfurt around 10:30 am, where we were welcomed by Iwan Gurjanow and Joerg Zender. Afterwards we were introduced to the concept of MathCityMap in detail and we got useful tips for dealing with the materials we needed to test a trail. Then we started in groups of three with our smartphones, on which we had previously installed the app MathCityMap, and made a small trail with different tasks. For example, we had to calculate the shoe size of the T Rex statue. We had a stick, measuring tape and a pocket calculator. Now one had to become creative and come to own solutions, whereby the app also provides up to three hints.

© Marie-Noelle Klug

After all the groups finished the trail, we got together again and held a brief feedback round. Afterwards, we received the criteria and tips for the creation of our own tasks for a trail, what we could then test again in our small groups.

For example, the task was to “calculate the inner surface of the O”

© Marie-Noelle Klug

Several tasks were created in each group, which allowed us to create the first own trail of our group on the web portal.

In conclusion, the excursion was a great success for the students and many questions were answered. The class is now very well prepared for the project and hopes for a successful end result.

Task of the Week: Lamp

With two trails in Salzburg, we can now welcome Austria as the 9th country with a MCM Trail. The current task of the week presents a task in the field of the surface of a cylinder. It is located in the trail at the natural sciences faculty of the Paris-Lodron University in Salzburg. Task: Lamp […]

With two trails in Salzburg, we can now welcome Austria as the 9th country with a MCM Trail. The current task of the week presents a task in the field of the surface of a cylinder. It is located in the trail at the natural sciences faculty of the Paris-Lodron University in Salzburg.

Task: Lamp (task number: 1908)

How large is the black painted surface of a lamp without the base plate? Give the result in m². Round to two decimal places.

The pupils first recognize the lamp as cylindrical and then determine the black surfaces. For this, it is necessary to divide the lamp into two cylinders. For the upper small cylinder, the shell surface as well as the cover are calculated, for the lower cylinder only the shell surface. Height and radius need to be measured. Subsequently, the individual surfaces are added and the total painted surface area is obtained.

The task can be assigned to the subject area of geometry and, in particular, geometrical bodies (cylinders) and can be used from class 9 onwards.

Math Trail at Heidelberg University

The MathCityMap idea lives from its active users and task creators in different places. Today, we would like to present a new trail at the University of Heidelberg that Mr. Niccolò Rigi-Luperti created there. In a short interview, for which he was thankfully available, we would like to let him speak for himself and give […]

The MathCityMap idea lives from its active users and task creators in different places. Today, we would like to present a new trail at the University of Heidelberg that Mr. Niccolò Rigi-Luperti created there. In a short interview, for which he was thankfully available, we would like to let him speak for himself and give us an insight into the background to the trail creation.

How did you hear about MathCityMap?

Through my job as a scientific assistant in the project “MINTmachen!”. There, we bring students closer to MINT subjects through e.g. holiday courses, workshops at the Girls-Day or possible BOGY-stays at the university (www.mintmachen.de). My boss (Dr. Michael Winckler) had learned from MathCityMap and asked me to get to know the app to see if and how we could integrate it into our work.

How did you get the idea to create your own trail? Have you created this for a particular event or target group?

It seemed to me the best way to get a feeling for the app and the job. According the target group, I was thinking of math-physics-computer science first semesters, which should solve small group tasks in the introductory days for mutual learning. In my opinion, this is a very good way to do this, especially because they are doing maths together and seeing different campus locations.

What mathematical content and skills are required in your trail?

In the order of the four tasks: simple probability calculation, precise counting of objects, trigonometry and potential & kinetic energy, combinatorics.

Which of the tasks is your “favorite task” and why?

The third task, “wheelchair“. I think it is nice to see the slope as a large acceleration ramp. It is the only physical task, and it can be solved in different ways, but they are of varying complexity. The easiest way to do this is to use energy conservation. Doing so, you solve the problem quite efficiently, it is only necessary to do a few line transformations as well as a single length measurement.

Task of the Week: Water in the Fountain

A popular MathCityMap task is concerned with the volume of fountains and how many liters of water are contained. The question can be used for a wide range of geometric themes, depending on the shape of the selected fountain (rectangular, circular, …). The Task of the Week is a particular challenge because the fountain has […]

A popular MathCityMap task is concerned with the volume of fountains and how many liters of water are contained. The question can be used for a wide range of geometric themes, depending on the shape of the selected fountain (rectangular, circular, …). The Task of the Week is a particular challenge because the fountain has to be modeled with help of different geometric bodies.

Task: Water in the Fountain (task number: 1420)

How many liters of water are in the illustrated fountain?

The illustrated fountain can be modeled using a cuboid and a cylinder (divided into two parts). If this has been recognized, the necessary quantities must be collected and the individual volumes calculated. Finally, the conversion in liters is required. The task with cylinders can be used from class 9 onwards; simpler fountain shapes are already possible from class 6 onwards.

Depending on the structure of the well, the collection of the data can be a challenge and the students have to become creative. For example, the circumference of a circle can be helpful for the determination of the diameter. Not at least through such considerations, a flexible handling of mathematical formulas and correlations is promoted.

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!

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: 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: 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.

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.