New: Try it out now Here is a tablet web app with reduced functionality.

With the Calculator app for iOS (iPad and iPhone/iPod Touch) The part-whole concept, which is the basis of the basic operations plus and minus, can be illustrated and explored interactively. The idea for this virtual tool was based on the ideas of Gerster & Schultz (2000) to promote part-whole understanding in children with arithmetic difficulties.

**Description of the app**

Two (partial) sets together make up a set. This is called addition calculation. And if you take away a part from a set, another part remains. This is called subtraction calculation. With this tool, you can interactively experience and research these relationships between partial sets and the total set.

- Use your fingers to touch the screen to place one or more tiles or to move them from side to side.
- Swipe over a number to hide or show it.
- Tap a number to sort the tiles on the board.
- Pull the shutter down and up again to cover one half of the tablet. This way you can create tasks for your study partner or check the task.
- Drag a tile up to delete it. Shaking the tray will empty it.

**Didactic principles and exemplary tasks**

The basic operations plus and minus are based on the concept that a set can be broken down into subsets and subsets can be put back together again (part-whole concept). In addition, two subsets are combined to form a total. In subtraction, a subset is removed from a set and another subset remains. Once children have understood these relationships between subsets and total, an important foundation for successful mathematical learning has been laid and the prerequisites for developing effective calculation strategies have been created. This virtual tool is a tool with which the part-whole concept can be illustrated, experienced and explored.

In order for the learning material to effectively promote the understanding of the part and the whole, appropriate tasks are required that encourage experimentation and reflection with the work material. Tasks that encourage the discovery of connections (operational tasks) are particularly suitable. Suitable tasks include:

- How can you place 6 tiles on the tray as quickly as possible with your hands?
- How can you arrange the tiles so that you can see how many there are as quickly as possible without counting?
- There are 4 tiles on one side and 3 tiles on the other side. How many tiles are there on both sides together? (Addition)
- What happens if I move 1 (2, 3, ...) tiles from one side to the other? (number decomposition, invariance)
- What happens to the partial amounts and the total amount when I remove a tile from the tray?
- How many different ways are there to distribute 10 tiles on both sides? (Number decomposition)
- There are 3 tiles on one side. How many do I have to add to the other side so that there are 7 tiles on the tray? (Supplementary tasks)
- There are 10 tiles on the tray. You can only see part of them. How many tiles are hidden? (Adding a quantity, subtraction)
- I put 8 tiles on one half of the tray. I then take 5 of the 8 tiles away and place them on the other side. How many are left? (Subtraction)
- The task 9 + 7 is on the tray. How can I move the tiles around so that I can immediately see what the result is? (Use neighboring tasks as a calculation advantage)
- The calculation tablet can also be used to introduce number walls or to clarify the relationships when difficulties arise.

**literature**

Gerster, H.-D & Schultz, Rita: Difficulties in acquiring mathematical concepts in early childhood education (research report). Available online at: http://nbn-resolving.de/urn:nbn:de:bsz:frei129-opus-161