**– an experimental environment for understanding multiplication and division.**

The virtual tool is intended to help students gain a deeper understanding of multiplication and, as an exchange operation, division. To do this, they can experiment with different representations of multiplication, explore and establish connections, and thereby promote an understanding of multiplication.

The app includes the following display options:

- a point field (changeable by tapping or moving your finger),
- the corresponding multiplication equation (individual fields can be covered and all numbers can be changed),
- a number line,
- a representation of multiplication as continued addition
- the corresponding division term (swap operation)
- a times table with all multiplication tasks.
- a voice output.

The displays can be individually configured and customized, partly within the app, but mostly in the global settings. This means that the teacher (global settings) or the student themselves (within the app) can flexibly change displays and adapt them to the student's current level and the task.

#### Possible activities

Basically, using the app in class makes sense when the child has already had hands-on experience with multiplication, i.e. has learned about multiplication through concrete action situations. The app can help to explore and understand connections between representations and between different multiplication tasks and to develop clever calculation strategies and mental images from them. Whether this succeeds depends largely on the stimulating tasks offered in parallel to using the app. For example, the following exercises can be offered:

- Place a specific multiplication problem on the multiplication field with as few clicks (fingertips) as possible.
- Change a task by moving your finger so that the task ... is created.
- Cover the result of the task. Now the learning partner changes the task slightly. How has the result changed.
- Press the arrow to display the swap task. What exactly has changed? Why has the result stayed the same even though the bundles have changed? Explain.
- Set up series of tasks (e.g. 4×3, 5×3, 6×3, …). Describe what changes with each step on the points field (/ number line / addition task).
- How are multiplication and division problems related to each other? Observe how the numbers change? Can you explain why this is the case?
- One partner slowly changes the task on the point field by moving the finger, the other only hears the voice output and has to say whether the finger was moved up / down / left / right.
- One child covers part of the screen (eg the dots field and the task so that only the number line is visible). The partner has to say what the corresponding multiplication / division task is called.
- …

Have fun experimenting and learning with the app!