Tag: archway

Task of the Week: Archway

Author Simone JablonskiDate
Task of the Week

Created during a teacher training in Erfurt, today’s Task of the Week fokuses on the topic Archway. The topic allows different questions and problems. Some weeks ago, we already presented an archway task on the weight of an archway’s stones. Today, the maximal height of an archway is focused.

Task: Archway (Task Number: 3090)

Determine the maximal height of the archway at the Krämerbrücke. Give the result in meters with two decimals.

The most elegant solution of this task is to divide the archway into a rectangle and a semi-circle.

With this hint, it is necessary to determine the point at which the semi-circle begins and the rectangle ends. With the height of the rectangle and the radius of the semi-circle (best determined through the diameter), the height of the archway results. In case the topic circle should be highlighted even more, it is possible to ask for the circumference of the archway. Here, the relation of diameter and circumference is further focused.

Task of the Week: Archway

Author Simone JablonskiDate
Task of the Week

In today’s Task of the Week, we would like to present a task from a MathTrail, which was developed within a project for talented students by the University of Paderborn in cooperation with the Paderborner Pelizaeus-Gymnasium. You can find more information here. We would like to present the selected task in a short interview with Max Hoffmann, member of the project. At this point, we would like to thank for the cooperation and the interview.

Task: Archway (task number: 1303)

Calculate the volume of the stones that create the archway! Give the solution in cubic meters. (Only the round part of the arc is meant).

How did you get the idea of ​​using this object in a task?

While searching for tasks for a mathematical walking tour through the beautiful Paderborn inner city, the students independently selected this archway near the Paderquelle. The first idea was to calculate the area of ​​the stones around the archway. I had the feeling that this kind of questioning was a typical task the students knew from their math books. After some thought, the suggestion came to modify the task so that the volume of the stones from which the archway is formed should be calculated.

What kind of mathematical activities and competences do you want to promote?

The task addresses modeling competencies (representation of the situation through two semicircles) and requires the selection and determination of appropriate measured variables. In terms of content, the known formulas for the circle are necessary for solving the problem.

Have you already processed the task with pupils or received feedback in other forms?

The task was developed by a small group and the other students of the project also solved the problem and liked it. The results of the first group were confirmed. In addition, the group presented the task at the final project event at the University of Paderborn and received positive feedback.