multiplication – MathCityMap

Dörthe Ludwig created in Dresden the task “Majestätische Steine” (engl.: “Majestic Stones”) which we now choose as our new MathCityMap Task of the Week. In the interview, Dörthe Ludwig explaines how she uses MCM to foster her daughter’s mathematical interest.

How did you discover the MathCityMap project? How do you use MCM and why?

I am a teacher at a secondary school and attend a 4-semester extra-occupational training course at the TU Dresden. In a didactics seminar we were introduced to the MCM project in a lecture.

Since my daughter (3rd grade) was not so interested in a maths at this time, we searched together for tasks that can be found in our own environment. Now we want to create a route that she can solve together with her friends (and as many others as possible). She is already looking forward to it!

Please describe your task. How can it be solved?

The task is to skilfully determine the number of cobblestones on a certain parking lot at the primary school. The stones are placed in such a way that it results in a simple multiplication task, but it requires multiplication beyond the small 1×1. So you can simply calculate the number, or you can break the task down into subtasks that you can calculate in your head. In this case, one must not forget to add the partial results.

What didactic goals do you aim for with the task?

To be honest, my main didactic goal was to show my daughter that mathematics can be fun even if you don’t see the solution directly, but have to make a little effort to do so. It seems to have been successful! Of course I hope that many more children will enjoy solving the problem and will be proud of themselves in the end!

Further comments on MCM?

I am enthusiastic and I will try to create many MCM tasks in Dresden. I would also like to take my students out into the fresh air and create some tasks around our school in the future.

Our new task of the week is in the Grand Duchy of Luxembourg! In Schifflange, Yves Kreis, senior lecturer at the University of Luxembourg, has created the task “Windows“. In the following interview he reports about the use of MathCityMap for his university teaching.

Hello Yves, you use MathCityMap for your teaching at the University of Luxembourg. How does it work exactly?

MathCityMap was presented by Gregor Milicic from the MCM team Frankfurt at the conference “Pedagogical Innovations in STEAM Education Conference” in Linz in January. My colleague Ben Haas and I found the project directly interesting. When we were forced to change our evaluation because of the COVID-19 pandemic, we decided to work out an MCM trail in groups of 2-3 students with subsequent self-evaluation and peer-review of 3 trails from other students.

You have also created some sample tasks . Please describe your task “Window”. How can it be solved? What is the aim of this task?

The task is to determine the number of square windows of a glass lift tower. On one side there are 2 rows of 12 windows each. Only 3 sides are made of glass; the fourth side is the school building. According to this there are 3 ⋅ 2 ⋅ 12 = 72 square windows. The task can be solved by all pupils from class 3 on. The aim is for the children to recognise the patterns and use multiplicative structures instead of simply counting all the windows.

Do you have any further comments on MCM?

MCM has managed to transfer an old idea (mathematical trails) into today’s digital age. A connection to AR (e.g. GeoGebra 3D Calculator) would be very useful from my experience, as many students have planned such tasks.

More information about the use of MathCityMap in Luxembourg:

Interview with Lorenzo Salucci, the 5,000 MathCityMap users & students at the University of Luxembourg

Our current task of the week leads us to the Austrian state Steiermark. In Graz, Rosina Haider and Ursula Skrabitz created many interesting MathCityMap tasks. Professor Haider answered some questions about the MathCityMap app.

How did you get in contact with the MathCityMap app?

During the conference “Forschen. Lernen. Lehren an öffentlichen Orten” in Münster, Germany, I tested the MathCityMap app. Back in Graz, I was able to arouse my colleague’s interest in the app.

How do you use the MathCityMap app?

We use MCM in the context of our teaching at Kirchliche Pädagogische Hochschule Graz. The students of primary teacher training get the possibility to work on a trail. Afterwards, they have to create their own MCM task – at best their own trails – in small groups. The tasks are used in the math class of a primary school which is associated to our university.

Please describe your task. How could students solve the task.

The question of the task „Parkbänke aus Holzlatten“ (engl. „benches out of wooden slats“) is how long a single wooden slat would be, if the wooden slats of six benches were placed one after another. To answer the question, the kids have to count the number of benches as well as the number of wooden slats one bench consists of. Of course, they have to measure how long one of the slats is. Finally, the students should analyse the fictive length of the single wooden slat.

Which didactic aims are stimulated through your task?

The students

… find out the number of the installed wooden slats on an individual path.
… are able to add and multiplicate mentally or in writing within the range up to 1000
… can deal with the unit meter and
… are able to get on with their solving process on their own or by using the given hints.

Do you have any other commentary on MathCityMap?

We are enthusiastic about the MathCityMap app and are going to create some more interesting MCM trails.

Our new Task of the Week is located in the United States. On the campus of the University of California Santa Cruz the PhD student for mathematics education Julianne Foxworthy created the task “So many stairs!”. She gave us an interview about this task and her usage of MathCityMap.

How did you get in contact with MathCityMap? How do you use MCM?

I discovered the app when I met Iwan Gurjanow [MCM team of the Goethe University Frankfurt] at PME in Sweden last year. I used to teach math to 10-13 year-olds, and I used math trails with them (low-tech version!) and they loved them.

I created the “MBAMP Math Trail“ that this task is a part of for a professional development program for teachers of young students (6-9 year-olds). The teachers were all very interested in using math trails with their students. In the future, I’m planning on creating a series of math trails for various ages at our town’s famous beach boardwalk, so look out for that one!

Please describe your task. How could it be solved?

“So many stairs!” is a very simple task aimed at very young children. The question is, how many steps will you climb altogether, if you and two friends decide to race up the stairs all the way to the door of the library.

The problem solver needs to count all the stairs leading to the library and then, and this will be the tricky part for the youngsters, determine how many stairs will be walked by themselves and their friends.

The teachers who tried the task gave me very helpful feedback about being very clear with my language. The word “step” could be a stair (that’s what I intended) or it could mean a step taken by a person. The second meaning could result in a different answer (e.g., what if a person took the stairs two at a time?).

While during the past few weeks we often presented tasks which can be solved from secondary level, the present Task of the Week shows that the MathCityMap project can already be used from primary school.

Task: Number of Windows (task number: 1191)

How many window panes can be seen on this front of the house?

To solve the problem, it is possible to count the window panes. However, this takes a long time so that the students at best have the idea to count only the panes in a row as well as the number of rows and solve the task by means of a multiplication. The basic representation of the multiplication is addressed as a repeated addition. Further, the students must be aware that the number of window panes and not the windows is asked. For a window, therefore, three panes must be submitted if the students firstly count the number of windows.

The task can be classified in the areas of multiplication and number and can be solved from class 4.

Tag: multiplication

Task of the Week: Majestic Stones

Task of the Week: Windows

Task of the Week: Benches out of Wooden Slats

Task of the Week: So many stairs!

Task of the Week: Number of Windows