task of the week | MathCityMap

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.

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

In this task, I see the competences “problem solving”, “modeling” and “working with mathematics symbols and techniques”. Communicating is also part of the task since on the one hand, the information from the task must be understood and implemented correctly, and on the other hand, the students should communicate with each other their solution proposals. Correct measurement of lengths, as well as the knowledge of the body and its volume play an important role. What surprised me was how heavy concrete is in a comparatively small volume. Therefore, I thought it would be interesting for the students, if they can assess the weight reasonably well.

Task of the Week: Parabolic Slide

Although the focus of many MCM tasks is on lower secondary maths, some upper secondary level tasks can also be realised. So our current Task of the Week, which was created in the context of a teacher training at the commercial schools Hanau. Task: Parabolic Slide (task number: 2241) The shape of the slide is […]

Although the focus of many MCM tasks is on lower secondary maths, some upper secondary level tasks can also be realised. So our current Task of the Week, which was created in the context of a teacher training at the commercial schools Hanau.

Task: Parabolic Slide (task number: 2241)

The shape of the slide is the part of a parabola. Determine the compression factor. 1m equals 1 unit of length. You can assume that the slide is almost horizontal at the end.

The slide is approximated according to the task with the help of the equation f (x) = ax² of a parabola. To solve the task, the students first have to transfer the situation to a suitable coordinate system. Since only the compression factor is asked, it is not necessary to specify this in the task. It makes sense to set the coordinate system so that the origin lies at the lower end of the parabola, but leaves out the horizontal end. Through such a choice, it is sufficient to determine another point on the slide, so the change in the x- and y-coordinate. By inserting this into the equation, the compression factor a results.

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: Height of the Building

Through cooperation with the MOOC Working Group of the University of Turin, we are looking forward to the first MCM tasks in Italy, which is part of today’s Task of the Week. Task: Height of the Building (task number: 2045) Determine the height of the building. Give the result in meters. The height can be […]

Through cooperation with the MOOC Working Group of the University of Turin, we are looking forward to the first MCM tasks in Italy, which is part of today’s Task of the Week.

Task: Height of the Building (task number: 2045)

Determine the height of the building. Give the result in meters.

The height can be approximated in various ways, e.g. by estimation or the intercept theorems. The task can be solved elegantly by looking for structures and patterns in the building facade. In this building, the horizontal strips, which can be found up to the roof, are noticed directly. For the total height, it is therefore only necessary to determine the height of a horizontal strip, as well as to count the number of strips. Minor deviations from the pattern can be approximated using estimates.

With this method, the task can already be solved by class 6 students. In the case of older pupils, the different solutions can be discussed and assessed with regard to simplicity and accuracy.

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.