Simone Jablonski | MathCityMap

Mathtrail Seminar 2017

In this summer semester, students (for becoming a teacher in mathematics) at Goethe University Frankfurt again have the opportunity to take part in the Mathtrail seminar as a special event in order to get to know the advantages of outdoor mathematics. Before the participants will develop their own tasks and trails, they should experience how it […]

In this summer semester, students (for becoming a teacher in mathematics) at Goethe University Frankfurt again have the opportunity to take part in the Mathtrail seminar as a special event in order to get to know the advantages of outdoor mathematics. Before the participants will develop their own tasks and trails, they should experience how it feels to make mathematics outside the classroom. This Thursday , the course took place at the Mainufer near the ECB in order to run the trail in the “Im Schatten der EZB“, which was created and tested a year ago by the Mathtrail seminar, with help of the MCM app.

In the end, everyone agreed that a mathtrail can be a lot of fun and time can fly when one solves the math problem outside the classroom. However, it has also become clear that it is not so easy to develop good tasks, because the boundary between challenge and frustration can already be exceeded through a narrow solution interval.

In the coming weeks, students will be familiar with the MathCityMap system and then implement their own trail. We are curious!

P.S.: The weather was good as always! ?

Task of the Week: Hydrant sought

The current “Task of the Week” is about the hydrant sign, which might have been noticed frequently in everyday life. By means of them, hydrants can be quickly and precisely located, e.g. for fire-fighting operations. But how exactly is such a sign read? With this question, the students are confronted in the task “Hydrant sought” from the trail “Campus Griebnitzsee” […]

The current “Task of the Week” is about the hydrant sign, which might have been noticed frequently in everyday life. By means of them, hydrants can be quickly and precisely located, e.g. for fire-fighting operations. But how exactly is such a sign read? With this question, the students are confronted in the task “Hydrant sought” from the trail “Campus Griebnitzsee” in Potsdam.

Task: Hydrant sought (task number: 1047)

On the house is a reference to the next hydrant attached (red-white sign). How far is the hydrant from the sign in meters? Determine the result to the second decimal place.

In order to solve the problem, the sign must at first be interpreted correctly. If the students do not know it, the hints help them. The indication on the sign is to be read so that one runs a certain length in meters in one direction (left/right) and then turns at right angles and again runs the length of the second number in meters. The situation can thus be described and solved using a right-angled triangle. The two indications on the hydrant sign (in the picture, they are made unrecognizable in order to ensure the presence of the pupils) are the cathets, while the direct distance corresponds with the hypotenuse. This can be determined by means of the Theorem of Pythagoras. Further, the solution can be determined and valued through measuring the distance to the hydrant. The problem is therefore to be assigned to geometry and can be used as a practical application for this from class 9 onwards with the development of the Theorem of Pythagoras. Since hydrant signs can be found in many places, the task can easily be transferred to other sites and allows mathematical operations in the environment in an easy way.

MathCityMap App for iOS

We are pleased to announce that the MathCityMap app is now also available for iOS smartphones, such as the iPhone. You can find the app either by searching in the app store for: “mathcitymap” or by clicking on the following logo: Have you discovered bugs or would you like further features? Please contact us: info (at) mathcitymap.eu!

We are pleased to announce that the MathCityMap app is now also available for iOS smartphones, such as the iPhone. You can find the app either by searching in the app store for: “mathcitymap” or by clicking on the following logo:

Have you discovered bugs or would you like further features? Please contact us: info (at) mathcitymap.eu!

Task of the Week: On large Feet

This week we would like to present the task “On a big Foot”. It is located close to the main railway station in Hamburg and is part of the trail “In and around St. Georg”. Task: On large feet (task number: 647) These figures are created by the contemporary German sculptor Stephan Balkenhol. I would […]

This week we would like to present the task “On a big Foot”. It is located close to the main railway station in Hamburg and is part of the trail “In and around St. Georg”.

Task: On large feet (task number: 647)

These figures are created by the contemporary German sculptor Stephan Balkenhol. I would like to know from you: What shoe size does the man have? For shoe sizes, there are four common systems worldwide. In Germany, European shoe sizes are the usual measure. They are based on the so-called “Parisian Stitch”. The stitch is a length measure with which a shoemaker specifies the length of a stitch and thus also the shoe size of the complete shoe. A French stitch or Parisian stitch is ⅔ centimeters long. The shoe last is a piece of wood, plastic or metal which is modeled on the shape of a foot and used to build a shoe. Since the feet should have some space, the length of the shoe last corresponds approximately to the foot length + 15 mm.

For the task, the pupils first measure the length of the man’s shoe and calculate the length in “stitches” so that the European shoe size can be specified. A major component of the task is the measurement and conversion of quantities. In doing so, the unity of the stitch, which should be unknown to most students, is used. It can be used from class 6 onwards. In addition, the first proportional basic ideas can be formulated for the conversion and could be a suitable transition to the proportionality and the rule of three.

The task was created by Dunja Rohenroth. She has already been able to test this task with her students and sees in this task the special advantage that the result cannot be solved by means of an internet search. The aspects of the presence and activity of the pupils are thus particularly emphasized.

Task of the Week: Serpent Surface

Today’s “Task of the Week” leads to Lyon, France, included in the trail “IFE”. It deals with an area calculation of a particular kind and shows in an exciting way which varied mathematical ideas are in everyday objects. Task: Serpent Surface (task number: 1129) The metal railing of the fire stairs is in the form of a […]

Today’s “Task of the Week” leads to Lyon, France, included in the trail “IFE”. It deals with an area calculation of a particular kind and shows in an exciting way which varied mathematical ideas are in everyday objects.

Task: Serpent Surface (task number: 1129)

The metal railing of the fire stairs is in the form of a serpent line. Calculate the surface area in m².

Before the students can begin to solve the problem, preliminary considerations are necessary, e.g. whether the slope of the railing is relevant or which formulas can be used to determine the length of the railing. The pupils should recognize the course of the serpent line as circular. In the case of two rotations of the staircase, the length of the railing corresponds to the double circumference of the circle with the step length as radius. With help of the circumference and height of the railing, the surface area of the serpent surface can be determined.

This is a geometric problem which combines the subcategories “space and form” and “measuring” by recognizing geometric structures in the environment as well as measuring the sizes and using them for calculations. The task is assigned in particular to the theme “circle” and can thus be used with treatment of the formula for the circle circumference from class 8 onwards.

In addition, the task shows that many objects can motivate a wide range of questions. Besides the question of the surface area, it would for example be possible to calculate the slope of the railing.

Workshop

On Thursday, May 18, 2017, an interactive workshop on MathCityMap will be given at the Goethe University campus. Mathematics on the road With this slogan, we presented the project MathCityMap in Frankfurt a year ago in a small teacher training course. Since then, many things have happened: Over 1000 tasks have been created by numerous […]

On Thursday, May 18, 2017, an interactive workshop on MathCityMap will be given at the Goethe University campus.

Mathematics on the road

With this slogan, we presented the project MathCityMap in Frankfurt a year ago in a small teacher training course. Since then, many things have happened:

Over 1000 tasks have been created by numerous enthusiastic “Mathtrailers” worldwide.
MathCityMap is currently available in nine different languages.
Further, exciting research and development results could be achieved in the MCM team.
We have received numerous suggestions from users and implemented them as innovations.

In the workshop, we would like to inform you about MCM and introduce you to the new possibilities offered by MCM. Please bring your smartphone and – if possible – a laptop, because we say: Participation is more than just taking part!

As part of the workshop, you will be able to gain experience with mathematics on the street around the Westend campus. In addition, your own ideas are developed into tasks and immediately tested with the MathCityMap app. Click here to register.

This event is accredited by IQ (Hessen) as LFB.

Time: 18.05.2017 15:00-18:00

Place: House of Finance, Campus Westend, Room “Shanghai” (room 1.28), Theodor-W.-Adorno-Platz 3, 60323 Frankfurt am Main

MCM presents itself at the MNU in Aachen

On Saturday, 8th April 2017, Matthias Ludwig and Joerg Zender will give a lecture about the MathCityMap project. The tasks around the new auditorium building have already been designed and wait to be solved. We are looking forward to numerous listeners and MCM contributors.

On Saturday, 8th April 2017, Matthias Ludwig and Joerg Zender will give a lecture about the MathCityMap project. The tasks around the new auditorium building have already been designed and wait to be solved. We are looking forward to numerous listeners and MCM contributors.

Task of the Week: Illumination of the Castle Garden

This week the “Task of the Week” focuses on a typical application of the intercept theorems. In particular, it is about the height determination of objects using the interception theorems. This task type can be transferred to many different objects and can therefore be found in further MathCityMap trails. The here described example is about […]

This week the “Task of the Week” focuses on a typical application of the intercept theorems. In particular, it is about the height determination of objects using the interception theorems. This task type can be transferred to many different objects and can therefore be found in further MathCityMap trails. The here described example is about the height determination of the lanterns in the garden of Erlangen’s castle.

Task: Illumination of the Castle Garden (task number: 709)

Determine the height of the two-armed lamps in the castle garden in the unit cm.

To solve the problem, the second intercept theorem is required. For this purpose, the pupils position themselves a few meters away from the object and fix the object. The intercept theorem can then be applied using the measuring stick. For this, the eye height as well as the distance to the object must be measured. With the arm outstretched, the measuring stick is held so that its tip coincides with the upper end of the lantern. The length of the arm and the scale length, which corresponds to the height of the lantern from the height of the eye, lead to the height of the lantern.

This is a problem-solving situation in which initially missing values have to be determined by a suitable initial situation. The application of the interception theorem can in this case be facilitated through the preparation of a sketch. The task is particularly suited to show students the practical application of the interception theorem and to give a meaningful content to the calculus.

Task of the Week: Weight of the Quai 43

The current “Task of the Week” from the trail “La Doua” in Lyon, France, shows that the MathCityMap project is already implemented internationally. Originally, the task is in French and will be translated for the Analysis. Task: Weight of the Quai 43 (Task Number: 855) The building “Quai 43” has the shape of an ocean […]

The current “Task of the Week” from the trail “La Doua” in Lyon, France, shows that the MathCityMap project is already implemented internationally. Originally, the task is in French and will be translated for the Analysis.

Task: Weight of the Quai 43 (Task Number: 855)

The building “Quai 43” has the shape of an ocean liner, which is built on ten concrete columns. Determine the weight of the building in tons (reinforced concrete weights 2.5t/m³).

To approximate the weight, it is necessary to calculate the volumes of the individual walls and floor slabs. To do so, the length and width of the building are determined through measuring. Afterwards, the area and the perimeter of the building (idealized as a rectangle) can be calculated. The building includes two floors and therefore the area can be counted three times. To determine the volume of the walls and floor slabs, it is further necessary to determine the height of the building and the thickness of a wall/floor slab. Afterwards, the students can calculate the different volumes through the formula of a cuboid. With help of a multiplication with the density, the approximate weight of the building can be found.

This task is a geometric and architectural problem which includes measuring of lengths as well as determining of field volumes. Especially modelling is in the center as the form of the building is approximated to a cuboid. Afterwards, the students have to consider which walls and floor slabs are relevant for the building’s weight. The task can be used from grade 7, especially in the context of cuboids and compound fields.

This task is only one of many examples which show that the MathCityMap project is an international project which stands out due to its universal use at several locations.

Task of the Week: Monument Erlangen/Brüx

This time, the “Task of the Week” is part of the trail “Rund um den Erlangener Schlosspark”. It is called “Monument Erlangen /Brüx” with task number 704. Thematically, the task can be integrated into the topic parables and is therefore suitable from grade 9. Task: Monument Erlangen/Brüx Examine whether the “curve” in the lower quarter […]

This time, the “Task of the Week” is part of the trail “Rund um den Erlangener Schlosspark”. It is called “Monument Erlangen /Brüx” with task number 704. Thematically, the task can be integrated into the topic parables and is therefore suitable from grade 9.

Task: Monument Erlangen/Brüx

Examine whether the “curve” in the lower quarter of the stone monument is a parable y= -ax². If not, enter a=0 as solution, otherwise enter the calculated value of a.

The task was written by Jürgen Hampp. In the following interview, he gives an insight into the idea behind the task and the aim of the task. At this point, we would like to take the opportunity to thank Mr. Hampp for his answers.

What made you consider including this task into the trail?

My concern was to develop a trail which is on the one hand easy to access in walking distance from our school, the Christian-Ernst-Gymnasium in Erlangen, and on the other hand leads through mostly car-free areas. Of course, the possible objects are limited. Under this perspective, the monument Erlangen/Brüx has an optimal position, the measuring is riskless – one does not have to climb etc. – and only simple resources are needed.

Where do you see the characteristic of the task? Which skills and ideas are especially supported?

I want to train the “mathematical view”, e.g. the recognition of mathematical objects in everyday life, and the activity with these objects with help of the methods which are known from class. This object mainly supports the competence branch K3 “Mathematical modelling”. Here, quadratic functions (topic in grade 9) present themselves. I did not want to use the common tasks with water fountains as they might be out of use, the water pressure may vary and the measuring is difficult. For me, the special attraction of this task is that a plain solution – as for usual schoolbook exercises – does not exist. Inaccurate measuring at the object or discrepancies at the object require skillful forming of averages and approximated values.