task of the week | MathCityMap

Task of the Week: The Wall

Today’s Task of the Week is an example of a task that you can create with minimal effort using the Task Wizard. It is about determining the number of stones in a given rectangular area. The object here is a wall, but similar objects can also be pavements. Task: The Wall (task number: 1077) Determine […]

Today’s Task of the Week is an example of a task that you can create with minimal effort using the Task Wizard. It is about determining the number of stones in a given rectangular area. The object here is a wall, but similar objects can also be pavements.

Task: The Wall (task number: 1077)

Determine the number of stones of the wall front in the marked area.

In order to solve the problem, the students can proceed in various ways. On the one hand, it is possible to determine the number of stones in one square meter and to measure the length and height of the rectangular wall. In this solution, the accuracy can be increased by counting several square meters and then taking the mean value. On the other hand, the students can count the stones in terms of length and height and approximate the total number by means of a multiplication.

When you create such a task with the Task Wizard, you only have to enter the length and height and the number of stones in a square meter as well as add a photo and the location. The Task Wizard then automatically creates notes and a sample solution.

The task requires knowledge about the rectangle. It can be classified in the field of geometry and can be used from class 6 onwards.

Task of the Week: Old Oak Tree

How can the age of a tree be approached using mathematics? This question addresses the current Task of the Week. It is placed in this form in Kappeln, but can be easily and quickly transferred to other places. Task: Old Oak Tree (issue number: 1473) How old is this oak tree? It is known that […]

How can the age of a tree be approached using mathematics? This question addresses the current Task of the Week. It is placed in this form in Kappeln, but can be easily and quickly transferred to other places.

Task: Old Oak Tree (issue number: 1473)

How old is this oak tree? It is known that an oak with a diameter (in breast height) of 50 cm is about 110 years old.

In order to solve the problem, it is assumed that the growth of the oak is linear. This means that the average growth per year can be determined using the information in the text. Subsequently, the circumference in the height of the chest is measured and the diameter is determined by means of the relationship between the circumference and the diameter of a circle. This then leads to the age of the tree.

On the one hand, the problem can be classified in the geometric topic of the circle and, on the other hand, proportionality. If the relationship between the diameter and the circumference is already discussed at this time, the task can be used from class 6 onwards.

Task of the Week: Tank Filling

In today’s Task of the Week everything focuses on the geometrical body of a cylinder as well as the activities of measuring and modeling. The task is included in the Dillfeld Trail in Wetzlar. Task: Tank Filling (task number: 1098) Determine the capacity of the tank in liters. First of all, it is necessary to […]

In today’s Task of the Week everything focuses on the geometrical body of a cylinder as well as the activities of measuring and modeling. The task is included in the Dillfeld Trail in Wetzlar.

Task: Tank Filling (task number: 1098)

Determine the capacity of the tank in liters.

First of all, it is necessary to recognize the object as a cylinder and to ignore minor deviations from the idealized body. The students then measure the necessary length. Since the result is to be expressed in liters, it is sufficient to record the data already at this point in decimetres. Subsequently, the capacity is determined by means of the volume formula for cylinders.

For the task, the students must have already gained experience with the geometrical body cylinder and its volume. The task is assigned to the spatial geometry and can be used from class 9 onwards.

Task of the Week: Mushroom

Today’s Task of the Week focuses a geometric question at the Aasee in Münster. More specifically, the surface content of a hemisphere is calculated by the students. Task: Mushroom (task number: 1400) Determine the area of the mushroom. Give the result in dm². Round to one decimal. In order to solve the problem, the students have to […]

Today’s Task of the Week focuses a geometric question at the Aasee in Münster. More specifically, the surface content of a hemisphere is calculated by the students.

Task: Mushroom (task number: 1400)

Determine the area of the mushroom. Give the result in dm². Round to one decimal.

In order to solve the problem, the students have to approach and recognize the shape as a hemisphere. They then need the formula for the calculation of the spherical surface or here the hemispherical surface. For the determination, only the radius of the hemispheres is required. Since it can not be measured directly, this can be determined with help of the circumference.

The task requires knowledge of the circle and of the sphere and can therefore be applied from class 9 onwards.

Task of the Week: Hubland Bridge

Many of the tasks in the MCM portal are based on mathematical knowledge from secondary level I. Today’s Task of the Week shows that knowledge of secondary level II can be integrated in tasks as well. The task “Hubland Bridge I” is about the inflection point of a function as well as its properties. Task: […]

Many of the tasks in the MCM portal are based on mathematical knowledge from secondary level I. Today’s Task of the Week shows that knowledge of secondary level II can be integrated in tasks as well. The task “Hubland Bridge I” is about the inflection point of a function as well as its properties.

Task: Hubland Bridge I (task number 684)

At which stair (counted from below) is the inflection point?

First, the bridge must be modeled as a function. For the visual determination of the inflection point, the students use the characteristics of the inflection point. In this case, the property can help to describe the inflection point here as the point with maximum slope and without curvature. In the presence of the device, the maximum slope can also be determined using a gradiometer (see Hubland Bridge II). The point of inflection as a point without curvature can be determined optically by looking for the point at which the graph resembles a straight line. After the turning point has been determined, the students have to count the steps up to the point. Ideally, this is done several times and the mean value is formed.

The task can be assigned to the topic of analysis, more precisely the differential calculus. With the development of the characteristics of the turning point of a function, the task can be used from class 11 onwards.

Task of the Week: Percentage Calculation at the Entrance

Today’s “Task of the Week” was created by Markus Heinze in the trail “Schillergymnasium” in Bautzen and combines percentage calculation with a geometric question. Task: Percentage Calculation at the Entrance (task number: 1262) Determine how many percent of the entrance doors are made of glass. Mr. Heinze was kindly available for a short interview so that we can present […]

Today’s “Task of the Week” was created by Markus Heinze in the trail “Schillergymnasium” in Bautzen and combines percentage calculation with a geometric question.

Task: Percentage Calculation at the Entrance (task number: 1262)

Determine how many percent of the entrance doors are made of glass.

Mr. Heinze was kindly available for a short interview so that we can present his assessment and experience with the task. We would like to thank him very much!

How did you get the idea for this task?
I wanted to create different tasks for an 8th or 7th class. I had a free time but it rained right at that time. That’s why I stood at the entrance at first and thought about how to install the entrance door and so, the idea arose to connect triangular areas and percentage calculation.

Which mathematical skills and competencies should be addressed in the task?
On the one hand, of course, modeling and problem solving is of high importance, because I had noticed deficits in the competence test in this area among the students in the 8th class. But also the visual ability is strengthened, of course, since real objects are being worked with and the students receive an idea of areas and percentages.

Has the task already been solved by pupils? If so, what feedback was given?
The task was solved by students of a 9th class and they found it relatively simple but interesting, but this is also because they had not worked with the app before and were generally enthusiastic about the matter. I think for a 7th or 8th class it is suitable.

Task of the Week: Flower Box

The present Task of the Week is about polygons and geometrical figures. In particular, the prism with a hexagonal base surface plays a role. The task can be found in this form in Cologne, but can be transferred to similar objects without problems. Task: Flower Box (task number: 1189) What is the volume of the […]

The present Task of the Week is about polygons and geometrical figures. In particular, the prism with a hexagonal base surface plays a role. The task can be found in this form in Cologne, but can be transferred to similar objects without problems.

Task: Flower Box (task number: 1189)

What is the volume of the flower box? You may assume that the floor is as thick as the edge of the box. Give the result in liters.

As already mentioned, the base area can be assumed to be a regular hexagon. To determine the area of the base area, pupils can either use the formula for the area content of a regular hexagon or divide the area into suitable subspaces. They should note that the edge does not belong to the volume. The pupils then measure the height of the prism by subtracting the floor plate. Subsequently, the volume of the prism, which is converted into liters in the last step, is obtained by multiplication.

The task thus involves a geometric question, in which students can either apply their knowledge to regular polygons or to composite surfaces. In addition, spatial figures are discussed as well as the adaptation to real conditions by observing the edge. The task is recommended from grade 8 onwards.

Task of the Week: Red or Green?

The present Task of the Week leads to Münster and contains a question from the probability calculation. Task: Red or Green? (Task number: 428) The city of Münster is trying everything to make road traffic as smooth as possible. There is even a traffic light hotline, where you can make suggestions for improvement. Despite all […]

The present Task of the Week leads to Münster and contains a question from the probability calculation.

Task: Red or Green? (Task number: 428)

The city of Münster is trying everything to make road traffic as smooth as possible. There is even a traffic light hotline, where you can make suggestions for improvement. Despite all the good planning, walkers often come to red traffic lights. Often, the red traffic lights are noticed more often than the green traffic lights. Estimate how often a traffic light shows “green” if one passes the traffic light 100 times.

In order to solve the problem, students should first measure the duration of a green phase, as well as the duration of a red phase. The duration of a total phase then results over the length of a green phase and a red phase. In order to determine the probability of reaching the traffic light at green, the duration of the green phase is divided by the duration of a complete traffic light. Subsequently, the expectation value can be formed with a 100-time passing.

This approach leads to a theoretical solution which, however, should be questioned critically. The result as well as the randomness of the arrival can be influenced depending on the traffic light circuit and any traffic lights which have been traversed previously. However, the problem is a successful application of the probability calculation in everyday life and can be used with the first elaborations of the probability concept.

Task of the Week: Stone

This week’s Task of the Week addresses, in particular, the modeling competence of the students. It is a question of approximating the weight of a stone as closely as possible by approximating the stone through a known body. Task: Stone (task number: 1048) What is the weight of the stone? 1cm³ weighs 2.8g. Give the […]

This week’s Task of the Week addresses, in particular, the modeling competence of the students. It is a question of approximating the weight of a stone as closely as possible by approximating the stone through a known body.

Task: Stone (task number: 1048)

What is the weight of the stone? 1cm³ weighs 2.8g. Give the result in kg.

In order to approach the object by means of a geometrical basic body, the students must refrain from slight deviations of the real object and the ideal body. In particular, a prism with a trapezoidal base side is suitable. If this step is done, the students determine the pages relevant to this body through measurements and then calculate its volume. The last step is the calculation of the weight with the given density as well as the conversion in kilograms.

With this task, it is especially nice to see that there is not always one correct result for mathematical questions. Through different approaches and measurements the pupils receive different results. In order to obtain the most accurate result as possible, the determined values must be within a defined interval. Translating from reality into the “mathematical world” also plays a decisive role here in the sense of modeling competence.

The task requires knowledge about the basic geometrical bodies and in particular about the prism with a trapezoidal base surface. It is therefore to be classified in spatial geometry and can be solved from class 7.

Task of the Week: Alte Münz

In the present Task of the Week, the Roman numerals are looked at more closely, a spelling for the natural numbers which arose in Roman antiquity. Particularly on old buildings, a marking of the year of construction in Roman numbers is usual. The task is located in Wetzlar’s inner city and can be found in […]

In the present Task of the Week, the Roman numerals are looked at more closely, a spelling for the natural numbers which arose in Roman antiquity. Particularly on old buildings, a marking of the year of construction in Roman numbers is usual. The task is located in Wetzlar’s inner city and can be found in the trail “Mathe in Wetzlar”. There the Roman numerals are incorporated into a slogan on a house facade.

Task: Alte Münz (task number: 545)

In the inscription on the house “Alte Münz” (Eisenmarkt 9) some letters are strikingly capitalized. Add the values of the letters in the Roman numeric system.

The students must recognize the larger Roman numbers and note how many times they occur. Subsequently, the various Roman numerals are translated into the Arabic notation and added. The Roman numerals as a spelling for the natural numbers are usually worked out in class 5 and can be used from this point onwards. Here, the rules for calculation with Roman numerals are less important than the translation of Roman and Arabic numbers.