tasks | MathCityMap

The MathCityMap Task Formats

The MathCityMap team has recently developed several new task formats! By now, MathCityMap offers nine task formats plus the possibility to create subtasks. All task formats are shortly presented in the following. Furthermore, we make available an Example Trail including all task formats. This trail can be viewed in the web browser here respectively by […]

The MathCityMap team has recently developed several new task formats! By now, MathCityMap offers nine task formats plus the possibility to create subtasks. All task formats are shortly presented in the following.

Furthermore, we make available an Example Trail including all task formats. This trail can be viewed in the web browser here respectively by the code 065522 in the MathCityMap app.

The interval is the ‘classic’ MathCityMap task format. It is to be used whenever measurements are necessary, e.g., to determine a length, an area or a volume.

Interval

The format Exact Value can be used for counting tasks or for combinatorial problems: How many windows do you spot on the house wall? How many possibilities do I have to lock my bike at this bicycle stand?

Exact Value

To raise more than one questions on a measuring activity, the task format Vector (Interval) can be used. Example: Determine the length, width and height of the pictured cuboid. Also, the task format can be applied for questions concerning spatial geometry.

Vector (Interval)

NEW TASK FORMAT!

Analogously, we offer the Vector (Exact Value) format which can be used to set several counting tasks or combinatorial problems at once.

Vector (Exact Value)

NEW TASK FORMAT!

If several numbers are the expected solution in a task, but the order in which the numbers are to be entered is not important, the Set task format can be used. In the app, only the numbers are entered into input fields. An example of a Set task can be found in the math trail above mentioned.

Set

NEW TASK FORMAT!

The Information Station is a task format without an input field in the app. It is implemented to offer important facts, e.g., to historical buildings, persons or realities during the math trail.

Information Station

NEW TASK FORMAT!

Another new task format is Fill In The Blanks: Within this format, gap texts can be easily worked on outside the classroom, e.g., to analyse objects outdoors in technical language, to deal with data from information boards or to raise questions on data of historical realities.
Note: Please use the “strict” mode if a number should be filled into the gap.

Fill In The Blanks

NEW TASK FORMAT!

Also, available data can be queried within the Multiple Choice format like in a quiz. Thereby, at least two answer options must be given, of which at least one is correct.

Multiple Choice

The GPS Task format allows users to create tasks in which the students have to find a pre-defined position (e.g., the middle of the given points) or position themselves in a pre-defined figure (e.g., building a equilateral triangle)
Note: This type of task works best in more rural areas since the GPS signal is often too weak in cities.

GPS Task

Lastly, we offer the possibility to pre-structure more complex tasks by dividing them up into optionally or mandatory Subtasks. One example for using Subtasks is given in the upper mentioned trail.

Subtask

NEW TASK FORMAT!

Task of the Week: Columns in the Parc

This week, Carmen Monzo, teacher in Spain gives us an inside into her task “Colums in the Parc”. It is created in a parc in Albacete, which ” is full of mathematical elements, though people are not aware of them until they are in math-vision mode.” Task: Columns in the Parc (Task Number: 3981) Calculate […]

This week, Carmen Monzo, teacher in Spain gives us an inside into her task “Colums in the Parc”. It is created in a parc in Albacete, which ” is full of mathematical elements, though people are not aware of them until they are in math-vision mode.”

Task: Columns in the Parc (Task Number: 3981)

Calculate the lateral surface (in m²) of one of the columns of this structure.

“I especially love this structure. Parallel and perpendicular lines can be easily identified, as well as a set of columns (cylinders) whose lateral surface can be easily calculated by using a folding ruler or a measuring tape, and a calculator to introduce the data and the formula. The height of the cylinder is easy to get, but to calculate the radius of the base as accurate as posible, students first have to measure the circumference and then divide by 2*pi.

As this structure has a dozen columns, the activity can be done by around 20 students, comparing their results and thinking about the importance of the accuracy when measuring. To solve this task, students should have previously studied 2D and 3D shapes, the concept of the lateral surface and some formula to calculate it.

As a secondary mathematics teacher, I think that our students need to handle things, measure, count, touch, feel, use their senses… MathCityMap provides the motivation students and teachers need to do those things with the help of the mobilephone technology.”

MathCityMap at New Horizons in Teaching Science Workshop in Italy

On 18 June 2018, the “New Horizons in Teaching Science” workshop was held in Messina, Sicily. On this occasion, Eugenia Taranto spoke about the MathCityMap project and the collaboration with the Math MOOC UniTo (Massive Open Online Course University Turin) project. Many different tasks, which were prepared by Sicilian teachers within the MOOC “Relations and […]

On 18 June 2018, the “New Horizons in Teaching Science” workshop was held in Messina, Sicily.

On this occasion, Eugenia Taranto spoke about the MathCityMap project and the collaboration with the Math MOOC UniTo (Massive Open Online Course University Turin) project.

Many different tasks, which were prepared by Sicilian teachers within the MOOC “Relations and Functions”, were shown.

A lot of interest was shown and we hope that the number of Sicilian and Italian tasks will continue to increase!

Task of the Week: Flowerpot

In case you search in our MathCityMap portal, you might notice that flowerpots enable various geometric tasks. Solely through the high frequency and the different shapes (cylinder, prismn with hexagonal area, etc.), the question how many liters of soil fit into the flowerpot, can be realised. In today’s Task of the Week, the flowerpot has […]

In case you search in our MathCityMap portal, you might notice that flowerpots enable various geometric tasks. Solely through the high frequency and the different shapes (cylinder, prismn with hexagonal area, etc.), the question how many liters of soil fit into the flowerpot, can be realised. In today’s Task of the Week, the flowerpot has the shape of a truncated cone.

Task: Flowerpot (Task number: 1219)

How many liters soil fit into the flowerpot, when it is filled until the top?

The formula for the volume of a truncated cone might not be known by all students. Therefore, they need strategies in order to solve the task, e.g. by means of the difference of a big and a small come. Further challenges are the determination of the small radius with help of the circumference and the consideration of the edge/bottom, which is obviously not filled with soil.

Task of the Week: Sculpture “Thinker”

After we opened the first MATHE.ENTDECKER (math explorer) trails at Stuttgart’s stock exchange at the 12th of April (read more here), we want to present you one of the included tasks. The object is the sculpture “Thinker”, a prominent symbol of Stuttgart. Task: Sculpture “Thinker” (Task number: 2018) Determine the height of a person with […]

After we opened the first MATHE.ENTDECKER (math explorer) trails at Stuttgart’s stock exchange at the 12th of April (read more here), we want to present you one of the included tasks. The object is the sculpture “Thinker”, a prominent symbol of Stuttgart.

Task: Sculpture “Thinker” (Task number: 2018)

Determine the height of a person with this head size. Give the result in meters.

An interesting question with forces the creativity of the students as the propotion of head size and body size might be unclear. The students can determine this proportion at their own bodies, at best with all group members and the mean. Afterwards, the head size of the sculpture is measured and related to former values. A previous estimation in comparison to the real height might be surprising.

Task of the Week: Scale of the Krämerbrücke

We all know them: city and site maps, illustrations and drawings that depict a real object to scale. Especially at sights, they offer the chance to calculate this scale, as in our Task of the Week at the Krämerbrücke in Erfurt. Task: Scale of the Krämerbrücke (Task number: 3108) Determine the scale 1: x in […]

We all know them: city and site maps, illustrations and drawings that depict a real object to scale. Especially at sights, they offer the chance to calculate this scale, as in our Task of the Week at the Krämerbrücke in Erfurt.

Task: Scale of the Krämerbrücke (Task number: 3108)

Determine the scale 1: x in which the Krämerbrücke is drawn (engraved) on this steel plate. Give the number x.

First, it has to be clarified how the scale is defined: One unit of length corresponds to x units of length in reality. In this example, the real length of the Krämerbrücke is indicated on the plate, so it is only necessary to measure their length on the plate and to compare the two values. Of course, the task can also be formulated on objects where the actual size or length has to be measured.

By the way: Do you already know the new metadata function “About this object”? This allows you to enter interesting sidefacts about sights and objects, so that cultural-historical references can be realized.

Task of the Week: Circular Ring

Today’s Task of the Week focuses on the circular ring. The idea behind is to determine the desired surface area by the difference of two surfaces, which can be calculated easily. Task: Ciruclar Ring (Task number: 1943) Calculate the area of the circular ring. Give the result in cm². The area of the circular ring […]

Today’s Task of the Week focuses on the circular ring. The idea behind is to determine the desired surface area by the difference of two surfaces, which can be calculated easily.

Task: Ciruclar Ring (Task number: 1943)

Calculate the area of the circular ring. Give the result in cm².

The area of the circular ring can be calculated by determining the radius of the entire circle, as well as the radius of the small “missing” circle. In this case, the easiest way is to measure the diameters of both circles. Then one calculates the wanted area either with the formula of the area of the circular ring, or one calculates the area of the entire circle and deducts the small circular gap. In both cases, the wanted area results.

A similar task can be created by means of traffic signs, e.g. the passage prohibited sign and the question of the proportion of red color. In both cases, the circle plays a thematic main role, so that the topic can be used from class 9 onwards.

Task of the Week: Height of the Building

Also this week, we would like to introduce you to a task with help of an interview with the task author, Johannes Schürmann. We would like to thank him for creating the task and his time to answer our interview questions. Task: Height of the Building (task number: 2339) Determine the height of the Oetker […]

Also this week, we would like to introduce you to a task with help of an interview with the task author, Johannes Schürmann. We would like to thank him for creating the task and his time to answer our interview questions.

Task: Height of the Building (task number: 2339)

Determine the height of the Oetker hall! Give the result in meters.

How did you come up with the idea to create this task for MathCityMap? How did you find out about MathCityMap?

In my studies, I became aware of MCM through a seminar I attended. The lecturer, Prof. Dr. Rudolf vom Hofe, told us about the project and so the idea to write a final thesis about the topic was born. As a result, Joerg Zender was invited to Bielefeld University for a lecture and I was able to create a mathtrail with Joerg at the university. When creating the trail and in conversation with Joerg, the idea of using MCM or digital media in teaching was strengthened. Thus, a school near the Bielefeld city center agreed on participating in a study and I was able to create a mathtrail adapted to the class content. So it turned out that I created the task.

Which competencies and topics play a role in solving the task?

The current topic which was taught in class were the intercept theorems. Accordingly, this should also be used in the task. However, the task is not so easy to solve with the intercept theorems, because of the local condition that the height differences are not easy to measure. Therefore, a second approach is given on the measurement and counting of the facade panels of the inner arches. Both approaches come up with a similar result. Space and form are the priority content with the skills problem solving, mathematical modeling as well as formal-technical work.

Have you tested the task with students or received any other feedback on the task?

I tested the task for my survey of the thesis with students, or rather, let the whole trail run by the students. The specification while running was that the students should work on certain tasks. In the evaluation of the individual groups of students, it turned out that not all had decided for this task. Reasons for this would be purely speculative.

Task of the Week: Giant Keyhole

Our Task of the Week was created by Vanessa Präg, student at Goethe University Frankfurt, as part of a mathematics didactic course. In a short interview, she will tell us about her experiences. Task: Giant keyhole (Task number: 2550) The city wants to close the keyholes. For this, the holes are filled with concrete up […]

Our Task of the Week was created by Vanessa Präg, student at Goethe University Frankfurt, as part of a mathematics didactic course. In a short interview, she will tell us about her experiences.

Task: Giant keyhole (Task number: 2550)

The city wants to close the keyholes. For this, the holes are filled with concrete up to the respective edges. How much does the concrete weigh in a keyhole when the density of the concrete is 2.1g/cm³? First estimate and then calculate the weight of the concrete in kg.

How did you come up with the idea to create this task for MathCityMap? How did you get to know MathCityMap?

My lecturer, Mr. Zender, made me aware of MathCityMap. As part of a course, we as prospective teachers talked about what modeling in mathematics education means. For clarification, he let us run a small trail from MathCityMap and solve it, as well as create 2 tasks in MCM. I’ve been an avid geocacher for years and think it’s a good idea to set tasks which can be solved with mathematics at different places. If I have more time, I will certainly create more tasks.

The task itself came to me as I walked through our city looking for unusual objects for MCM. The keyhole immediately jumped in my eye.

Which competencies and topics play a role in solving the task?

In this task, I see the competences “problem solving”, “modeling” and “working with mathematics symbols and techniques”. Communicating is also part of the task since on the one hand, the information from the task must be understood and implemented correctly, and on the other hand, the students should communicate with each other their solution proposals. Correct measurement of lengths, as well as the knowledge of the body and its volume play an important role. What surprised me was how heavy concrete is in a comparatively small volume. Therefore, I thought it would be interesting for the students, if they can assess the weight reasonably well.

Task of the Week: Parabolic Slide

Although the focus of many MCM tasks is on lower secondary maths, some upper secondary level tasks can also be realised. So our current Task of the Week, which was created in the context of a teacher training at the commercial schools Hanau. Task: Parabolic Slide (task number: 2241) The shape of the slide is […]

Although the focus of many MCM tasks is on lower secondary maths, some upper secondary level tasks can also be realised. So our current Task of the Week, which was created in the context of a teacher training at the commercial schools Hanau.

Task: Parabolic Slide (task number: 2241)

The shape of the slide is the part of a parabola. Determine the compression factor. 1m equals 1 unit of length. You can assume that the slide is almost horizontal at the end.

The slide is approximated according to the task with the help of the equation f (x) = ax² of a parabola. To solve the task, the students first have to transfer the situation to a suitable coordinate system. Since only the compression factor is asked, it is not necessary to specify this in the task. It makes sense to set the coordinate system so that the origin lies at the lower end of the parabola, but leaves out the horizontal end. Through such a choice, it is sufficient to determine another point on the slide, so the change in the x- and y-coordinate. By inserting this into the equation, the compression factor a results.