springen
to jump
To push oneself off the ground or another surface with one's legs and move through the air for a brief moment.
Die Kinder springen vor Freude in die Luft.
The children jump into the air for joy.

to jump
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to jump
To push oneself off the ground or another surface with one's legs and move through the air for a brief moment.
Die Kinder springen vor Freude in die Luft.
The children jump into the air for joy.

As a verb of movement or change of state, 'springen' (to jump/crack) always forms the perfect tense with the auxiliary verb 'sein' (to be). This applies to all meanings of the word.
Die Katze ist auf den Schrank gesprungen.
The cat jumped onto the cupboard.
When the subject is a brittle material such as glass, porcelain, or a wall, 'springen' means that it gets a crack or breaks. In this case, the verb is intransitive.
Die alte Vase ist gesprungen, als ich sie bewegt habe.
The old vase cracked when I moved it.
In the meaning of 'sich abstoßen' (to push oneself off), 'springen' is often combined with prepositions that indicate direction. Typical examples are 'in' (accusative), 'über' (accusative), or 'von' (dative).
Er ist mutig vom Fünfmeterbrett gesprungen.
He bravely jumped from the five-meter diving board.
To express a sudden, quick movement, 'springen' is often used in fixed expressions. Common combinations are 'aus dem Bett springen' (to jump out of bed) or 'ins Auto springen' (to jump into the car).
Als der Bus kam, sprang sie schnell auf und rannte zur Haltestelle.
When the bus came, she quickly jumped up and ran to the stop.
When 'springen' means to leave something out in a sequence, it is often used with the preposition 'zu' + dative to indicate the new target. It describes a direct change.
Der Professor ist von Kapitel 2 direkt zu Kapitel 5 gesprungen.
The professor jumped directly from chapter 2 to chapter 5.
to run
'rennen' and 'springen' both describe fast movement with the body. 'rennen' means moving forward very quickly on foot, usually over a distance. It can also mean that someone is in a big hurry. 'springen' means pushing off with the legs and being in the air briefly. Sometimes it can also mean a very quick, sudden movement. Learners may confuse the words because both are fast and active. The important point is: when you 'rennen', the movement stays on the ground; when you 'springen', there is a jump into the air.

Das Kind springt im Park über eine kleine Pfütze.
The child jumps over a small puddle in the park.
Tom rennt zur Haltestelle, weil der Bus gleich kommt.
Tom is running to the bus stop because the bus is about to arrive.