Tag: linear function

Task of the Week: Man walking to the Sky

Author Simone JablonskiDate
Task of the Week

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.

Task of the Week: Climbing Wall

Author Simone JablonskiDate
Task of the Week

Today’s “Task of the Week” leads to Hamburg, more precisely to the school Am Heidpark. Here, one can find the trail “Am Heidpark” which is a good example to show that already a schoolyard can be made for a MathCityMap trail. The selected “Task of the Week” is called “Climbing Wall” with task number 668.

Task: Climbing Wall

Determine the slope of the climbing wall in percent.

The task enables a suitable embedding of the topic slope of linear functions. The slope of the climbing wall can be determined by recourse of the gradient triangle. In the coordinate system, the slope of a linear function can be calculated with help of two points on it. It is necessary to determine the difference of the y-coordinates (dy) and the difference of the x-coordinates (dx) and divide them afterwards. Corresponding in the real context, it is necessary to measure the height difference (dy) as well as the difference in length (vertical; dx). Afterwards, the slope can be calculated with help of a division and the conversion into percent. The task can be used from grade 8 and supports a basic understanding of the slope of a linear function and its determination with help of a gradient triangle. The task is especially suitable in the beginning of the topic as it already “predefines” a right-angled gradient triangle. Further tasks could for example involve the slope of a stair handrail. The task is a connection of algebra and geometry and can be related to the branches measuring and functional correlation.