Category: Generic Tasks

Generic Tasks: Velocity

Author MathCityMap AdminDate
Generic Tasks

The new article on Generic Tasks is dedicated to a task from the ” Velocity ” category. With the help of the task wizard, this task can be created in the shortest possible time, as always, and the corresponding object can be found everywhere in your environment, especially in urban areas. You can read the first article on Generic Tasks, which also tells you how to get to the task wizard and what Generic Tasks are, here.

The object we are going to look at in this article is escalators. They are often found in public buildings or at the entrances to subway stations or train stations. The task that is available for escalators in the task wizard is:

“Determine the speed of the escalator. Give the result in meter per second. Give the result with two decimal places.”

Required for creating the task are the time duration, which the escalator needs to travel a well-defined distance. In addition, you can select whether the speed should be specified in m/s or in km/h. Based on the entered data, the wizard fills in the rest of the task form and only a picture needs to be added to complete the task.

 

 

In the next article we will deal with the probably most special category of Generic Tasks, the so-called GPS tasks. Until then, have fun and save time when creating MCM tasks with the Task Wizard!

 

Generic Tasks: Growth

Author Philipp LarmannDate
GeneralGeneric Tasks

This Generic Tasks article is about the wizard task from the “Growth” topic. As always with our Generic Tasks, the tasks can be created in no time with the help of the task wizard, and this time you can find the corresponding objects everywhere in your environment with even greater certainty than usual. The first article on Generic Tasks, which also tells you how to get to the Task Wizard and what Generic Tasks are, can be found here.

The objects we are looking at in this article on growth are, of course, trees. Whether in the countryside or in the city, the next MCM task is never far away. The task that is stored in the task wizard is:

“Determine the age of this tree. A tree with a diameter of approximately 40cm (measured in 130cm height) is about 72 years old. One can assume that the diameter grows proportionally. Give the result in years.”

To create the task, we need the circumference of the tree at a height of approx. 130 cm and the type of tree, i.e. whether it is an oak, a maple or a sycamore, since different trees naturally grow at different rates. The task can then be solved via the fact that the growth takes place almost linearly, so we can determine the growth of the tree per year via proportionality.

 

 

The next article on the issue of Generic Taks will deal with the topic of velocities, for which we will take a closer look at the escalator. Until then, have fun and save time when creating MCM tasks with the Task Wizard!

 

Generic Tasks: Volume and Weight

Author Philipp LarmannDate
Generic Tasks

The new article on Generic Tasks is dedicated to tasks in the category “Volume and Weight”. As always, you can create these tasks in no time using the task wizard, and you will find the corresponding objects everywhere in your surroundings. The first article on Generic Tasks, which also tells you how to get to the task wizard and what Generic Tasks are, can be found here.

First, we would like to look at the object category of cuboids. Especially in public places or near buildings you can find stones or stone seats that can be approximated as cuboids. In the first picture of this article such a seat is shown as an example. The task, which is available in the task wizard, reads:

“How much does the stone weigh? 1m³ weighs 2600kg. Give the result in kg.”

Required for creating the task are the length, width and height, and optionally the density of the stone. If you do not have the density of the material, the wizard will give you an average value for the weight of a cubic meter of stone. Based on the entered data, the wizard fills in the rest of the task form and only a picture needs to be added to complete the task.

 

 

Another object that can be found in many cities is the fountain, with a fountain basin that can be modeled as a cylinder. The focus of this task is on determining the capacity of the fountain basin in liters, which is why the corresponding problem definition of the Generic Task, which is created by the Wizard, is as follows:

“How many liters of water are in the fountain?”

The data needed to create the task in this case are the radius of the fountain basin, which in practice can be easily determined by the circumference of the fountain, and the height of the basin.

In the next article on the topic of Generic Taks, we will turn to a classic wizard task. The focus will be on the growth rate of trees. Until then, we hope you have fun and save time when creating MCM tasks with the Task Wizard!

 

Generic Tasks: Number

Author Philipp LarmannDate
Generic Tasks

In this article on Generic Tasks, we would like to introduce you to two tasks from the “Number” category. As always, you can find the corresponding objects everywhere and the tasks can be created in no time using the task wizard. The first article on Generic Tasks, which also tells you how to get to the Task Wizard and what Generic Tasks are, can be found here.

The first object category we want to talk about here are paved areas or walls. Especially in city centers or public places you can often find areas that are paved with stones. In the picture below you can see an example of a semicircular area, which was laid out with paving stones. The task, which is provided for this in the task wizard, reads:

“With how many paving stones was the area shown laid out?”.

The values needed to create the task with the wizard are only the size of the total area and the average number of stones on a square meter. Starting from this data, the wizard fills in the complete task form and only a picture needs to be added to complete the task. Similarly, there is a task in the wizard that asks for the number of bricks that make up a wall.

 

 

 

 

 

 

 

 

 

 

 

 

Another object for which a Generic Task can be created in the Wizard is the typical advertising pillar. After manually entering the circumference and height of the area that can be placarded, the task here is:

“How many DIN A0 posters can be placed on the advertisement pillar without overlapping? DIN A0: length = 84cm; height = 119cm.”.

An interesting aspect of this problem is that it can only be solved correctly if the condition of not overlapping, which is necessary in reality, is taken into account. If you divide the surface of the cylindrical column by the surface of a poster, you get a result which is mathematically reasonable, but which turns out to be wrong in the validation on the real situation.

In the next article about Generic Taks we will have a look at the tasks in the wizard, which are available for the topic “Volume and Weight”. Until then, we hope you have fun and save time when creating MCM tasks with the task wizard!

 

 

Generic Tasks: Slope

Author Philipp LarmannDate
Generic Tasks

In the last article on Generic Tasks, which you can read here, we already showed you how you can use Generic Tasks to save time when creating tasks in your surroundings. In this context we showed you the Generic Tasks implemented in the system for the topic Combinatorics. Another theme that the task wizard can help with is slopes.

The objects for which Generic Tasks were created and which can also be found almost everywhere are ramps and handrails of staircases. Since, for example, ramps are not allowed to have a slope greater than six percent for use by wheelchairs, it makes sense to design an MCM task that asks exactly what the slope is.

To create the task, you only have to insert the data measured at the ramp into the task wizard and specify whether the result of the task is to be determined in percent or in degrees. The resulting task text is quite simple: “Determine the slope of the ramp in percent (degrees).

 

 

 

 

 

 

 

 

 

 

 

The creation of tasks with the wizard for handrails works in the same way. The sample solution and the hints are again created in a suitable way and only the task image has to be inserted.

In the next article on Generic Tasks we will deal with the creation of tasks on the topic “Number”. Until then, we wish you again a lot of fun and success in creating new tasks with MathCityMap!

 

Generic Tasks: Combinatorics

Author Philipp LarmannDate
Generic Tasks

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!