Category: Task of the Week

This time the task is located in Grahamstown, South Africa.

Calculate the area of the hexagonshaped table. Give the result in units of m².

The task can be solved in different ways. Once you can divide the area into six equilateral triangles. It is also possible to divide the area into a rectangle and two triangles.

This time the task is in Bratislava, Slovakia.

Dmitri Ivanovitch Mendeleïev (Дмитрий Иванович Менделеев) set up the periodic table of the elements arranged as rays around the sculpture of his portrait.

Calculate the volume of this sculpture in cubic meters.

The sculpture has the shape of a hemisphere. Therefore, the volume can be calculated using the diameter.

Today, MCM talks with Jörg Kleinsteuber (MCM Educator) about the task of the week in Apolda, Germany.

If the wooden crocodile would come to life and eat, the goldfish would have “bad cards”. Decide what amount of food would need a mature 6 meter specimen compared to a crocodile the size of the wooden crocodile.

What is the task about?

The beautifully carved wooden model is a small version(centric extension) of a crocodile. Since the length of a full-grown crocodile is a multiple of the model, this unusual task can be created from it. Already in the book “Gulliver’s Travels” by Jonathan Swift, the 12x larger Gulliver got the clothing (surface) of 144 Lilliputians and his food portion would have been enough for 1728 by the Winzlings. This mathematical effect of the stretch factor on the area and the volume is always amazing. I chose Multiple Choice as the answer format because I did not want to measure exactly, but to understand and apply knowledge.

For what purpose was the task created?

The task was created for a workshop with teachers on the SINUS-Landtag https://www.schulportal-thueringen.de/sinus_thueringen in Apolda (in the Hotel Am Schloss https://www.hotel-apolda.de/).

When we went to the conference, I got a shock – the crocodile was gone … and thus the task is no longer solvable.

The conference manager spoke therefore with the hotel staff and the caretaker then took the crocodile from hibernation from the basement (great service, thank you!)

So the participants could still solve this unusual task; It was a tough nut, but it was fun.

Afterwards, I even thought about exchanging the photo so that the size of the crocodile can be used to determine its size, even if it sleeps in the cellar in winter.

What do you like about MathCityMap?

What fascinates me about MCM is the combination of classical mathematics with digital support. Mathematics does not have to mean complicated bills and expensive applications. Small tasks with practical relevance, in which the students themselves have to become ACTIVE by measuring, modeling, estimating, and discussing in small groups offer plenty of potential for student activities.

The possibility of using the smartphone as a support is self-evident for students and at the same time motivating. At the same time this reduces my effort in the care, because the APP provides feedback in the form of hints, model solutions and also offers gamification (points). A great mix!

The new “digital classroom” allows me to chat with students while they are completing tasks (answer questions) and I can see their walkways while they’re on the trail.

In the follow-up in the classroom we had very stimulating discussions about the tasks.

Thank you for the interview and your commitment to MCM!

This time we present a task from Speyer, Germany. The object is a popular sculpture by the artist Wolf Spitzer.

“Sigillum”, bronze 1994, seal stamp – planetary gear that turns on its own axis and touches the nearby museum wall. The Sigillum represents the preservation of history and culture.

The shape of the figure is often interpreted by the local people as a mushroom, hence the name of the task. Geometrically, these are two conntected cylinders.

Calculate the volume and give the result in liters! One liter equals 1 dm³.

For the big cylinder it is difficult to measure the circumference. In contrast, it is easy to raise the diameter. For the small cylinder it is not difficult to measure the circumference. It is therefore very likely that when working on the task, there are different ways to calculate the volume of the two part-bodies.

If one raises the measured values ​​in decimeters, the result is obtained directly as the sum of the two volumes.

The task of the week is this time aboutthe Ernst-Abbe monument in Jena, Germany.

How often does the volume of the sphere fit into the truncated pyramid?

To solve the problem, the sphereand the truncated pyramid must be measured in order to calculate their volume. Then divide both sizes. The interesting thing about this task is that the solution interval contains a special number .

This time the task of the week is on the site of the VW Autostadt in Wolfsburg.

Everything is a little smaller on the traffic training ground than it really is. A “No entry” sign usually has a diameter of 42cm. How much bigger is a normal shield than the one used here?

To solve the problem, one has to measure the diameter of the shield first. Later on the areas of both shields have to be calculated and put into proportion. The result is the scaling factor of the area.

The task is Apolda, Germany.

Determine by what percentage the first circle with the dark stones is larger than the inner circle (light stones).

To get the solution of the task, one can make different models. On the one hand it is possible to count the light and dark stones and calculate the ratio. Another possibility is to calculate the area of a circle and a annulus.

It is not enough to calculate only the ratio of both stone types. To get the right result, the ratio must be converted to percent and then reduced by 100. Only then someone knows how many percent larger the annulus is than the inner circular area.

Thanks to MCM Educator Jörg Kleinsteuber for this task.

The Rosetta is located in Erfurt, Germany.

Determine the inner circumference of the rosette. (dyed red). Give the result in meters to two decimals!

To solve the task, one must first consider how to determine the diameter of the circle. This can not be measured in the classical sense. However, it is possible to count the number of stone rows and to get to the diameter by multiplying with the height of a stone. One problem here is that the height of the stones is not uniform and has to be formed through a suitable mean value.

The task was created during the MoMaTrE project during a meeting with our partners in Nitra, Slovakia.

In a courtyard of the philosopher Konstantin-University Nitra, the atrium, there is the so-called insect hotel. The front of this object is protected by a fence and the underlying wood painted in the colors of the Slovak flag. The task is to calculate the proportion of the red color. However, the basic space consists not only of the painted surfaces, but includes the whole fence. Therefore, we decided in the task to motivate them as a random experiment.

The front side of the insect hotel is protected by a fence with the shape of little squares. These squares could be seen as pixels. One pixel is chosen randomly. Calculate the probability that the chosen pixel contains red color. Enter the result in percent.

The meshes of the fence are square and we have considered these as pixels. How big is the probability that the selected pixel contains red in the purely random choice of a pixel? To get the number of pixels, you can count them or calculate them as the compound area of ​​a rectangle and a trapezoid. Then you have to count the red pixels. The result is then the Laplace probability “favorable by possible cases” since the probability for each pixel is the same.

Today MCM is talking with Cécile Nigon about the Task of the Week located in Saint-Étienne, France.

What is the task about?

We want to put the children as robots that have to move following a sequence of orders / instructions. The goal for them is to predict precisely where the robot will be at the end of the movement of the robot. The children can move their body to find the answer.

For what purpose was the task created? 

Programming has recently emerged inside the academic programm for elementary schools in France. Programming a movement on a paper or on a screen or on floor with little robots (“turtles”) is a usual exercise. But executing the orders with our body directly in a real space enable to live the situation fully (and maybe understand it better)

In our previous route, the tasks concerned perimeter, area, volume, the pupils told us that they would have liked of other tasks. We chose programming.

 What do you like about MathCityMap?

To give the opportunity to young people to do maths outside. To create activities that correspond to  their motivation (fondness, interest, etc).