Category: Task of the Week

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).

This week MCM is talking with Christian Mercat about the Task of the Week located in Nabeul, Tunisia.

What is the task about?

There are video surveillance cameras that can be monitored in the lobby over the shoulder of the guard. The task is to find the opening angle of the camera. It happens to be 90° so there are many ways to validate that but to actually measure it, it’s not that easy and pretty cool. One has to identify a left plane, a right plane, find some points on it, for example elaborate an isosceles triangle with the camera as the vertex, then apply some trigonometry, or report theses values on a sketch, in order to evaluate the angle, whether through calculus or with the help of a protractor. It was really fun because the students had to collaborate in order to identify the left and right planes, shouting in the corridor, one looking at the monitor, the other moving slowly to the left or right.

For what purpose was the task created?

The purpose of the task is to measure an angle. But the issue here is that the observer can not be physically at the center of the angle. Therefore the usual ways to measure an angle, using for example your hand span with your stretched arm, doesn’t work here. Moreover the camera is too high, therefore constructing a sketch is not that easy, in order to be accurate, one has to  deal with several angles  or distances, in different planes, for example  one has to apply the Pythagoras theorem in order to get a distance.

What do you like about MathCityMap?

Here the geolocalisation is not that necessary since a simple picture is clear enough to locate the camera we are talking about. What I like is that we can have hints that guide you when you are stuck and you have retroaction so that you can refine your first guess.