toben
to romp
To move around, play, or run about in a wild, loud, and unrestrained way. Often used for children or animals.
Die Kinder toben nach der Schule im Garten.
The children romp around in the garden after school.

to romp / rage
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to romp
To move around, play, or run about in a wild, loud, and unrestrained way. Often used for children or animals.
Die Kinder toben nach der Schule im Garten.
The children romp around in the garden after school.

The verb 'toben' (to romp/rage) always describes a form of wild, loud, and uncontrolled energy. This energy can be playful (children), emotional (anger), natural (storm), or metaphorical (dispute).
Die Fans tobten vor Begeisterung im Stadion.
The fans went wild with excitement in the stadium.
When the subject is children, animals, or a group of people in a playful context, 'toben' means to move around loudly and wildly. Typical places for this are the garden, the playground, or the children's room.
Die Welpen toben den ganzen Tag durch die Wohnung.
The puppies romp through the apartment all day.
To express extreme anger, 'toben' is very often used with the preposition 'vor' (with/from). The fixed phrase is 'vor Wut toben' (to rage with anger).
Mein Chef tobte vor Wut, als er den Fehler bemerkte.
My boss raged with anger when he noticed the mistake.
In connection with forces of nature such as 'Sturm' (storm), 'Meer' (sea), or 'Gewitter' (thunderstorm), 'toben' is used metaphorically. It describes these forces raging with great intensity.
Das Meer tobte und die Wellen schlugen gegen die Felsen.
The sea was raging, and the waves were crashing against the rocks.
When the subject is an abstract conflict, such as 'Streit' (dispute), 'Debatte' (debate), or 'Kampf' (fight), 'toben' means that it is being carried out very intensely and emotionally.
Seit Wochen tobt eine Debatte über die neuen Umweltgesetze.
A debate about the new environmental laws has been raging for weeks.
to play
'spielen' and 'toben' can both describe what children or animals do for fun. 'Spielen' is general and can be calm or wild: with building blocks, cards, a ball, or outside. 'Toben' is more specific. It means that someone plays or runs around wildly, loudly, and with a lot of movement. Learners may confuse the words because 'toben' can be a kind of 'spielen'. If the activity is calm or normal, 'spielen' fits. If it is loud and wild, 'toben' fits better.

Draußen toben die Kinder im Schnee und lachen laut.
Outside, the children are romping around in the snow and laughing loudly.
Im Wohnzimmer spielt das Kind leise mit seinen Bauklötzen.
In the living room, the child is playing quietly with his building blocks.