tasks | MathCityMap

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: 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.

MathCityMap in Wetzlar

It is a sunny Saturday morning in an industrial area near Wetzlar. The Mathematics Center Wetzlar invited students of the Q2 to a mathematics competition. The teachers had the opportunity to participate in the “MathCityMap – Mathematics on the Road” workshop and to get to know our project. After a short theoretical introduction to the […]

It is a sunny Saturday morning in an industrial area near Wetzlar. The Mathematics Center Wetzlar invited students of the Q2 to a mathematics competition. The teachers had the opportunity to participate in the “MathCityMap – Mathematics on the Road” workshop and to get to know our project. After a short theoretical introduction to the subject of outdoor mathematics and mathtrails, the participants (with a measuring stick, measuring tape and smartphone) went to solve mathematical questions in the industrial area of Dillfeld. For example, they had to find out the capacity of a tank or determine the slope of a metal ramp. After this, they had the possibility to formulate own tasks for objects in the environment and to create them in the MCM web portal. The result was a new mathtrail consisting of the newly created tasks of the teachers.

We hope that the participants had a lot of fun and some ideas for their own lessons. We are already looking forward to tasks and trails that will follow from this event. At this point, we would like to thank for the invitation to this event!

Are you interested in workshops on outdoor mathematics with MathCityMap? Take a look at our event page.

MathCityMap in Meißen

Being part of the “Day of Mathematics and Natural Sciences” in Saxony, the MathCityMap team held a course on outdoor mathematics with MCM. The “Sächsische Bildungsinstitut” (SBI) invited to this event on 9th March 2017 in Meißen at Schloss Siebeneichen. 24 participants took part in the workshop and were able to solve mathematical problems and questions […]

Being part of the “Day of Mathematics and Natural Sciences” in Saxony, the MathCityMap team held a course on outdoor mathematics with MCM. The “Sächsische Bildungsinstitut” (SBI) invited to this event on 9th March 2017 in Meißen at Schloss Siebeneichen. 24 participants took part in the workshop and were able to solve mathematical problems and questions around the castle. For example, one had to find out how high the tower of the castle is or how many liters of water fit into the pool. In the second part of the course, the teachers were able to search for own mathematical tasks in the environment and to create them in the portal.

We hope that the participants had a lot of fun and got some ideas for their own lessons. We are already looking forward to tasks and trails that will follow from this event.

Are you interested in workshops on outdoor mathematics with MathCityMap? Take a look at our event page.