Generic Tasks: Combinatorics
The so-called Generic Tasks offer a significant simplification when creating MathCityMap tasks. Generic tasks are tasks for objects that can be found, in a slightly modified form, in any place in the world. They are therefore tasks that can be implemented almost anywhere. Within the MoMaTrE project, several Generic Tasks, covering different topics, have been developed and implemented in the MCM web portal. You create a Generic Task by activating the so-called Task Wizard via the magic wand icon in the “Create task” section. Here you select the desired topic and object and enter only the data collected from your own object. The wizard then automatically creates a completely filled out task form with a ready-made sample solution, a suitable task text and appropriate hints. After inserting a task image, the task is thus ready for publication and can be used within a very short time.
In this and the following articles, we would like to introduce the various topics and objects for which Generic Tasks are currently available in the Task Wizard. First, we will take a look at the topic of combinatorics.
An object that can be found almost everywhere are stairs. Of course, a staircase can be used to design a wide variety of tasks. However, one combinatorial task that can be applied to any staircase is the following generic task:
“How many possibilities exist to go upstairs if one can take one or two steps within each move? The step sequences can be combined.”
There are several approaches to solving this task:
One approach is to write down the possibilities systematically.
Another approach to solving the problem is to use the Fibonacci series:
(1) 1 2 3 5 8 13 21 34 55 89 etc.
When creating the task, you only have to specify how many steps the staircase consists of on which you want to create this task. Everything else will be filled in automatically by the task wizard.
Another object for which a Generic Task from the combinatorics section was created and which can be found quickly is a bicycle stand. Here, the following task is generated by entering the number of existing bicycle racks and a quantity x of bicycles that you specify.
“x bikes should be locked at the stand. Each bike can be locked at the left or right. How many possibilities exist to lock the x bikes at the stand? It does not matter whether the bikes are locked “forwards” or “backwards”. You can assume that the stand is completely empty.”
Again, suitable sample solutions and hints are created by the wizard without any action on your part.
In the next article on Generic Tasks we will show you which possibilities for tasks regarding the topic “Slope” are already available in the task wizard of MathCityMap. Until then, we wish you a lot of fun and saved time when creating your own tasks!
