tasks | MathCityMap

Task of the Week: Grass Field

At the beginning of the year, MCM was successfully presented in Mumbai. Of course, in this context the first Indian Math Trail was created, from which our current task of the week originates. Task: Grass Field (Task number: 2459) Calculate the area of the grass field. Give the result in m²! First, a mathematical model […]

At the beginning of the year, MCM was successfully presented in Mumbai. Of course, in this context the first Indian Math Trail was created, from which our current task of the week originates.

Task: Grass Field (Task number: 2459)

Calculate the area of the grass field. Give the result in m²!

First, a mathematical model has to be found that represents the area most accurately. This is best done by dividing the total area into several individual areas. The obvious choice is the division into two halfcircles and a rectangle. For this, the rectangular side lengths and the circle’s radius must be measured, the areas calculated and all partial areas added.

The task belongs to the topic of compound surfaces, whereby calculations on the circle must already be known in order to solve the task as exactly as possible. In the German school system, it would therefore be solvable from class 8.

Task of the Week: Glass Roofing

Today’s object – found in Hamburg – requires the recognition of different quadrilateral shapes as well as a fitting division into several subareas. Task: Glass roofing (task number: 2148) How many square meters of glass were used for the entire roof? The glass roofing consists of a rectangular roof surface (can be divided into three […]

Today’s object – found in Hamburg – requires the recognition of different quadrilateral shapes as well as a fitting division into several subareas.

Task: Glass roofing (task number: 2148)

How many square meters of glass were used for the entire roof?

The glass roofing consists of a rectangular roof surface (can be divided into three small rectangles), a rectangular area next to the entrance and three trapezoids on each side. To solve the task, all measurements for the rectangles and trapezoids must be made. Afterwards, the students calculate the individual areas and by adding the entire content of the glass. Due to the individual bars, the decomposition of the surfaces is almost predetermined. Nevertheless, the task requires the recognition of geometric shapes as well as a suitable mathematization of the tasks by formula knowledge of rectangle and trapezoid. This geometric question can be assigned to compound surfaces and can be solved from class 8 onwards.

Task of the Week: Slope of the Helix

In the new year, we would like to continue introducing interesting tasks and topics from the MathCityMap task portal. It starts with a task from Qatar, which was created as part of a presentation of MathCityMap. Task: Slope of the Helix (Task number: 2243) Calcaulate the slope of the hailrail of this circular ramp. Give […]

In the new year, we would like to continue introducing interesting tasks and topics from the MathCityMap task portal. It starts with a task from Qatar, which was created as part of a presentation of MathCityMap.

Task: Slope of the Helix (Task number: 2243)

Calcaulate the slope of the hailrail of this circular ramp. Give the result in percentage!

Despite the architectural peculiarity of the building, the task can be solved in a familiar way. One can use the definition of the slope as a quotient of vertical and horizontal change. In particular, with the help of the balusters, distance and horizontal change can be easily detected.

Thus, the task fits thematically in the area of ”slope” – a topic that occurs again and again in almost every location at MathCityMap, whether at railings, ramps or stairs. The task can be solved from grade 7 and serves as a basis for the recognition of functional relationships.

Task of the Week: Packing Station

With a task from the Christmas Trail, we would like to present the last “Task of the Week” this year and draw attention to the possibility of addressing probabilities in the context of MCM. Task: Packing Station in the Westend (task number: 779) You should pick up two packages for the boss. You do not […]

With a task from the Christmas Trail, we would like to present the last “Task of the Week” this year and draw attention to the possibility of addressing probabilities in the context of MCM.

Task: Packing Station in the Westend (task number: 779)

You should pick up two packages for the boss. You do not know their size. You guess behind which of the yellow boxes they could be (in each box can only be one package). What is the likelihood that the packages will really be behind the ones you picked?

First of all, it has to be clarified how many boxes there are. Then one can calculate the probability of picking the first box and the second box correctly. In this case, combinatorial considerations are necessary as to whether the order plays a role. As answer format, multiple choice was chosen for this task, whereby the correct solution can be expressed in terms of two possible answers: once as a fraction and once as an estimate with percent, which underlines the equivalence of both forms. The task is recommended from grade 9 onwards.

With this task, the MCM team says goodbye to the Christmas break and wishes all users a Merry Christmas and a Happy New Year. We are curious to see how we can further develop the MCM project in the new year and look forward to an exciting time!

Task of the Week: Arched Greenhouse

As a task creator for MathCityMap, it is important to look at the environment through “mathematical glasses”. Thus, buildings become cuboids, lawns become polygons or – as in the current task of the week – greenhouses become half cylinders. Task: Arched greenhouse (task number: 1950) Calculate the material requirement for plastic for the greenhouse. Give […]

As a task creator for MathCityMap, it is important to look at the environment through “mathematical glasses”. Thus, buildings become cuboids, lawns become polygons or – as in the current task of the week – greenhouses become half cylinders.

Task: Arched greenhouse (task number: 1950)

Calculate the material requirement for plastic for the greenhouse. Give the result in m².

When solving the task, students’ mathematical view is also taught. This involves the recognition of the object as a lying half cylinder. Once this has been achieved, radius, the circumference of the semicircle and height must be measured, so that the material consumption can be calculated. This corresponds to the surface of the half cylinder, which can be determined by means of formulas for the area of a circle and the surface of a cylinder.

Task of the Week: Red Area

In this year’s autumn, numerous tasks were created in Wilhelmsburg, district of Hamburg. The tasks are very convincing – especially in the context of the MCM concept – through their interdisciplinary and thematic diversity, which we would like to illustrate exemplary in our current Task of the Week. Task: Red area (task number: 1964) Determine […]

In this year’s autumn, numerous tasks were created in Wilhelmsburg, district of Hamburg. The tasks are very convincing – especially in the context of the MCM concept – through their interdisciplinary and thematic diversity, which we would like to illustrate exemplary in our current Task of the Week.

Task: Red area (task number: 1964)

Determine the red area on which the ping-pong table stands. Give the result in m².

It quickly becomes clear that the entire area can not be approximated by a single geometrical object, or that this is only possible with significant losses in accuracy. It is therefore appropriate to divide the area searched into disjoint subspaces, which can be calculated using formulas. This is best done using a drawing. A particular challenge are the curved edges, where estimations and approximations are necessary. According to measurements and calculations, the total area is obtained by adding the area contents of all partial surfaces.

The area can be described using rectangles and triangles. In addition, the principle of the decomposition and additivity of surface content is necessary for solving the problem. The task can be used from class 7 onwards.

Task of the Week: Tafelberg’s Monument

As a few weeks ago, the Task of the Week leads us to the African continent, more precisely to the approximately 1000-meter-high Tafelberg in Cape Town. There you can find a monument of stone, which is also an ideal object for a MCM task. Task: Tafelberg’s Monument (task number: 1791) Calculate the mass of the […]

As a few weeks ago, the Task of the Week leads us to the African continent, more precisely to the approximately 1000-meter-high Tafelberg in Cape Town. There you can find a monument of stone, which is also an ideal object for a MCM task.

Task: Tafelberg’s Monument (task number: 1791)

Calculate the mass of the stone monument. Give the result in kg. 1 cm³ of granite weighs 2,6 g.

First, the shape of the stone has to be considered more closely. When choosing a suitable model, a prism with a trapezoidal base can be used. For this, it is necessary to ignore minor deviations from the ideal body as well as to operate with the stone mentally. The required data are then determined and the required weight of the stone is obtained by means of the area content formula of a trapezoid, the volume formula of a prism and the given density.

The task shows that over the last few years, MCM has developed into an international platform for authentic “outdoor” mathematic tasks and has already been set up in many prominent places. We are looking forward to further tasks and are looking forward to the countries and regions in which new MCM tasks will emerge.

MCM in Wetzlar

On 14.11.17, Iwan Gurjanow and Simone Jablonski presented MathCityMap as part of an internal teacher training at the Werner-von-Siemens school in Wetzlar. 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 […]

On 14.11.17, Iwan Gurjanow and Simone Jablonski presented MathCityMap as part of an internal teacher training at the Werner-von-Siemens school in Wetzlar. 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 different geometrical problems. As final product, the participants created their own tasks in the portal and merged them into a trail for the school.

We would like to thank the participants for their cooperation and feedback and look forward to numerous MCM tasks in and around Wetzlar.

Are you interested in teacher training on MCM? Feel free to contact us!

Task of the Week: Brick in the Wall

As a part of a teacher training at the Johanneum Gymnasium Herborn, a modeling task was created, which we would like to present to you today as the “Task of the Week”. Task: Brick in the Wall (task number: 2040) The wall in the schoolyard should be sprayed. It is planned to save color for […]

As a part of a teacher training at the Johanneum Gymnasium Herborn, a modeling task was created, which we would like to present to you today as the “Task of the Week”.

Task: Brick in the Wall (task number: 2040)

The wall in the schoolyard should be sprayed. It is planned to save color for the hole in the wall. Calculate the area to be sprayed in m². Enter the result with two digits.

The challenge in this task is to approach the existing hole in the rectangular wall as precisely as possible. Different models can be chosen for this purpose. On the one hand, one could assume the hole as a circle and determine an average diameter. More precisely, however, the result is obtained by approaching the hole as an ellipse and measuring the axes.

The task requires a certain amount of creativity and shows that the clear mathematics in the environment outside the classroom reaches its limits. The pupils acquire modeling competences, especially in the skillful choice of a mathematical model. The various solutions and results of the pupils thus form an ideal basis for discussing appropriate models. The problem can be applied with the treatment of circle and ellipse from class 9 onwards.

Task of the Week: Jacobean Pilgrim

Today, we would like to introduce you a task from Speyer, which was created there by Katalin Retterath. It is about the famous Way of St. James, which leads through the city to Santiago de Compostela. Task: Jacobean Pilgrim (task number: 1614) Measure/estimate the step of the Jacobean Pilgrim. How many steps would he have […]

Today, we would like to introduce you a task from Speyer, which was created there by Katalin Retterath. It is about the famous Way of St. James, which leads through the city to Santiago de Compostela.

Task: Jacobean Pilgrim (task number: 1614)

Measure/estimate the step of the Jacobean Pilgrim. How many steps would he have to take if he were to travel the 2,500 kilometers to Santiago de Compostela?

How did you get the idea to create MathCityMap?

I am a consultant for teaching development in mathematics at the Pedagogical State Institute in Rhineland-Palatinate. For a number of years, we have been developing mathematical rallies, which are well received by both our pupils and the training events. First we experimented with LearningApps, then with Actionbound – both were OK, but not really satisfactory. We have become acquainted with MathCityMap and we would like to introduce the MathCityMap project here.

What are the mathematical competences and contents associated with the task?

Students must estimate and/or measure, work with large numbers. The task is solved by a group – thus, communicating plays a great role and if the students explain their their solution to one another (which would be desirable), then also argue.

Has the task already been tested by students or did you receive feedback in other forms?

The task itself has been tested by students (many different classes), but still with Actionbound. The students were able to solve the problem without major (content) difficulties – with the units and number of zeros, however, it was not so good. I have only entered two-three tasks at MathCityMap to test the software. A test of the tool will be considered in spring.

The MCM team thanks for the interview and is looking forward to further tasks in Speyer!