Simone Jablonski | MathCityMap

Task of the Week: Circular Ring

Today’s Task of the Week focuses on the circular ring. The idea behind is to determine the desired surface area by the difference of two surfaces, which can be calculated easily. Task: Ciruclar Ring (Task number: 1943) Calculate the area of the circular ring. Give the result in cm². The area of the circular ring […]

Today’s Task of the Week focuses on the circular ring. The idea behind is to determine the desired surface area by the difference of two surfaces, which can be calculated easily.

Task: Ciruclar Ring (Task number: 1943)

Calculate the area of the circular ring. Give the result in cm².

The area of the circular ring can be calculated by determining the radius of the entire circle, as well as the radius of the small “missing” circle. In this case, the easiest way is to measure the diameters of both circles. Then one calculates the wanted area either with the formula of the area of the circular ring, or one calculates the area of the entire circle and deducts the small circular gap. In both cases, the wanted area results.

A similar task can be created by means of traffic signs, e.g. the passage prohibited sign and the question of the proportion of red color. In both cases, the circle plays a thematic main role, so that the topic can be used from class 9 onwards.

The new design of the app also reached the website and the prints. Stay up to date and download the new MCM flyer (available in German) here.

MCM in Erfurt

Doing outdoor mathmatics with MathCityMap works in any weather. Iwan Gurjanow and Matthias Ludwig visited the cathedral city Erfurt on Wednesday 21.03. and Thursday 22.03. On the 24th Days of the maths and science lessens of the ThiLLM, we were able to present MathCityMap. While the preparations on Wednesday took place in cold but sunny […]

Doing outdoor mathmatics with MathCityMap works in any weather. Iwan Gurjanow and Matthias Ludwig visited the cathedral city Erfurt on Wednesday 21.03. and Thursday 22.03. On the 24th Days of the maths and science lessens of the ThiLLM, we were able to present MathCityMap. While the preparations on Wednesday took place in cold but sunny weather, there were some brave teachers who ignored the sleet and solved MCM tasks at the campus of the University of Erfurt and later created own MCM tasks in the portal. Of course, in such a beautiful city, we were also searching for tasks in the city center. The finished trail in Erfurt’s old town will be presented here in the next few days.

Generic Tasks: Determining Quantities and Numbers

Determine quantities and numbers – an issue that is already relevant at primary level. For getting started in determining numbers, one should use regularly arranged objects like windows on a (high-rise) building, paving stones on a sideway or stones at a wall. When determining windows on houses, in many cases you can count the […]

Determine quantities and numbers – an issue that is already relevant at primary level. For getting started in determining numbers, one should use regularly arranged objects like windows on a (high-rise) building, paving stones on a sideway or stones at a wall.

Determine the number of windows on the house

When determining windows on houses, in many cases you can count the number of windows per row and the number of rows and get the result by multiplication. It is important to make clear whether you ask for windows or window panes, and whether all the windows of the building are relevant or, for example, only windows on the southern front.

Determine number of bricks

For walls and rectangular pavings there are several possibilities:

1. One determines the number n of the stones per 1m² and projects that to the total area A.

2. The length and height of the wall are determined in “stone units” and one counts the number of stones in length l and in width b.

Circular arranged stones with a gap

The level of difficulty increases when deviating from rectangular areas and e.g. asking for circular arranged stones. In addition, it can be difficult to determine the number of objects in which the regularity is interrupted in some places and one is forced to choose special solution methods.

You will find a detailed overview of our generic tasks on Determining quantities in the deposited PDF document.

Happy Pi Day

Friends of special dates and numbers might already have noted it in their calendar: Today is Pi Day. Based on the American spelling of today’s date (3/14) and the beginning of the number Pi with its first two decimals, the 14th March is perfect to celebrate Pi. Therefore, today everything at MCM revolves around the […]

Friends of special dates and numbers might already have noted it in their calendar: Today is Pi Day. Based on the American spelling of today’s date (3/14) and the beginning of the number Pi with its first two decimals, the 14th March is perfect to celebrate Pi. Therefore, today everything at MCM revolves around the circle and we would like to celebrate this with the help of one of our various tasks on the topic of the circle.

Task: Paving stones in a circle (Task number: 2007)

How many paving stones are in the red marked area?

Despite various approaches, the number Pi is central while solving the problem. On the one hand, it is possible to determine the number of paving stones in a certain area (for example one square meter) and to project them to the total area. The task can be solved particularly clever by considering a paving stone as a unit and expressing the radius of the circle by the number of stones.

This is just as one example of many tasks in which the number Pi is relevant in everyday life and for the math trail idea (e.g. traffic signs, advertising pillars, trees). In this sense: Happy Pi day!

By the way: the task is part of a trail around the Stuttgart’s stock exchange. They were created by our team and will be officially opened in April.

Welcome Greece!

Thanks to Georgios Fesakis, who educates maths teachers at Aegean University of Rhodos, MCM is now available in Greek. We wish all Greek users and students a lot of fun during creating and solving tasks in the Aegean sun. By the way: at Easter, the MCM team will visit Greece and help to take the […]

Thanks to Georgios Fesakis, who educates maths teachers at Aegean University of Rhodos, MCM is now available in Greek. We wish all Greek users and students a lot of fun during creating and solving tasks in the Aegean sun. By the way: at Easter, the MCM team will visit Greece and help to take the first steps.

Task of the Week: Height of the Building

Also this week, we would like to introduce you to a task with help of an interview with the task author, Johannes Schürmann. We would like to thank him for creating the task and his time to answer our interview questions. Task: Height of the Building (task number: 2339) Determine the height of the Oetker […]

Also this week, we would like to introduce you to a task with help of an interview with the task author, Johannes Schürmann. We would like to thank him for creating the task and his time to answer our interview questions.

Task: Height of the Building (task number: 2339)

Determine the height of the Oetker hall! Give the result in meters.

How did you come up with the idea to create this task for MathCityMap? How did you find out about MathCityMap?

In my studies, I became aware of MCM through a seminar I attended. The lecturer, Prof. Dr. Rudolf vom Hofe, told us about the project and so the idea to write a final thesis about the topic was born. As a result, Joerg Zender was invited to Bielefeld University for a lecture and I was able to create a mathtrail with Joerg at the university. When creating the trail and in conversation with Joerg, the idea of using MCM or digital media in teaching was strengthened. Thus, a school near the Bielefeld city center agreed on participating in a study and I was able to create a mathtrail adapted to the class content. So it turned out that I created the task.

Which competencies and topics play a role in solving the task?

The current topic which was taught in class were the intercept theorems. Accordingly, this should also be used in the task. However, the task is not so easy to solve with the intercept theorems, because of the local condition that the height differences are not easy to measure. Therefore, a second approach is given on the measurement and counting of the facade panels of the inner arches. Both approaches come up with a similar result. Space and form are the priority content with the skills problem solving, mathematical modeling as well as formal-technical work.

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

I tested the task for my survey of the thesis with students, or rather, let the whole trail run by the students. The specification while running was that the students should work on certain tasks. In the evaluation of the individual groups of students, it turned out that not all had decided for this task. Reasons for this would be purely speculative.

MCM scores at GDMV conference in Paderborn

As part of the joint meeting of GDM and DMV in Paderborn from 05.03. – 09.03.2018, MathCityMap was presented in various ways. First of all, on 06.03. Matthias Ludwig spoke on the Erasmus + project MoMaTrE (Mobile Math Trails in Europe), in which the cooperation partners and goals were presented on an international level. On […]

As part of the joint meeting of GDM and DMV in Paderborn from 05.03. – 09.03.2018, MathCityMap was presented in various ways. First of all, on 06.03. Matthias Ludwig spoke on the Erasmus + project MoMaTrE (Mobile Math Trails in Europe), in which the cooperation partners and goals were presented on an international level. On 08.03., Iwan Gurjanow presented his research results in the field of motivation and gamification (points and leaderboard) while running a math trail. In addition, Joerg Zender considered the Math Trail idea from the point of view of performance, which led to interesting discussions on 09.03.

A special highlight for the entire team is the prize which Daniel Birnbaum and Matthias Ludwig won at the poster session. On the poster, the future-oriented technology Augmented Reality was presented, as well as first ideas to use it in school and MCM.

During the entire conference, the participants had the opportunity to test a trail in the city center of Paderborn. Of course, we took the chance and ran the trail from the perspective of the task solver with lots of fun and ambition.

At this point, we want to thank Max Hoffmann and the students of the Pelizaeus-Gymnasium for creating the tasks! Likewise, we would like to thank all interested in the project for the exciting questions and discussions.

Task of the Week: Giant Keyhole

Our Task of the Week was created by Vanessa Präg, student at Goethe University Frankfurt, as part of a mathematics didactic course. In a short interview, she will tell us about her experiences. Task: Giant keyhole (Task number: 2550) The city wants to close the keyholes. For this, the holes are filled with concrete up […]

Our Task of the Week was created by Vanessa Präg, student at Goethe University Frankfurt, as part of a mathematics didactic course. In a short interview, she will tell us about her experiences.

Task: Giant keyhole (Task number: 2550)

The city wants to close the keyholes. For this, the holes are filled with concrete up to the respective edges. How much does the concrete weigh in a keyhole when the density of the concrete is 2.1g/cm³? First estimate and then calculate the weight of the concrete in kg.

How did you come up with the idea to create this task for MathCityMap? How did you get to know MathCityMap?

My lecturer, Mr. Zender, made me aware of MathCityMap. As part of a course, we as prospective teachers talked about what modeling in mathematics education means. For clarification, he let us run a small trail from MathCityMap and solve it, as well as create 2 tasks in MCM. I’ve been an avid geocacher for years and think it’s a good idea to set tasks which can be solved with mathematics at different places. If I have more time, I will certainly create more tasks.

The task itself came to me as I walked through our city looking for unusual objects for MCM. The keyhole immediately jumped in my eye.