Task of the Week: Man walking to the Sky

This week, we focus on a task that can be used to realize linear functions in the environment. It was created by Kim Biedebach in Kassel.

I became aware of MathCityMap during a didactics lecture as part of my teaching studies that I attended. The idea for the task actually came to me by chance. I am from Kassel and had in mind that I have to design a modelling task for the lecutre. When I passed the figure, I spontaneously decided that this might be a suitable task.

Task: Man walking to the Sky (Task Number 3832)

How many meters is the man on the pole above the ground?

For this, the pole on which the man steps up is interpreted as a linear function. The point at which the pole starts on the ground is chosen as point (0, 0) for the sake of simplicity. Now, the slope must be determined as the quotient of the change in vertical and the change in the horizontal. If one starts from the chosen origin, and walks e.g.one meter to the side and measures the height there, the slope can be determined.

Afterwards, the slope can be used to determine the equation of function. Then the distance from the origin to the human on the ground has to be determined (corresponds to the x-coordinate). This is best done by positioning oneself under the man and measuring the distance to the origin. By inserting into the function equation the height can be calculated.

The task makes the linear relationship of x and y coordinates particularly clear. Also the slope concept is discussed. Of course, alternative approaches can be chosen, such as using the intercept theorems.