Sport treiben
to do sports
To be physically active; to regularly practice a sport.
Ich versuche, dreimal pro Woche Sport zu treiben.
I try to do sports three times a week.

to drive / drift
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to do sports
To be physically active; to regularly practice a sport.
Ich versuche, dreimal pro Woche Sport zu treiben.
I try to do sports three times a week.

The basic idea of 'treiben' is to set something or someone in motion, or to move passively oneself. This idea appears in many meanings, from driving animals to drifting on water.
Der Wind treibt die Wolken vor sich her.
The wind drives the clouds ahead of it.
The perfect tense of 'treiben' is usually formed with 'haben' (to have). However, if there is directed movement toward a destination, 'sein' (to be) is used.
Der Bauer hat seine Kühe auf die Weide getrieben.
The farmer drove his cows onto the pasture.
'Sport treiben' is a fixed expression and means to be physically active. The noun 'Sport' is the direct object here.
Um fit zu bleiben, sollte man regelmäßig Sport treiben.
To stay fit, you should do sports regularly.
In the meaning 'to move passively', the reflexive form 'sich treiben lassen' (to let oneself drift) is often used. This emphasizes that you give up control and let yourself be moved by water or by a mood.
Im Urlaub möchte ich mich einfach nur am Strand treiben lassen.
On vacation, I just want to let myself drift along at the beach.
When 'treiben' is used in the sense of 'to move ahead of oneself', the objects are usually groups of animals. Typical combinations are 'eine Herde treiben' (to drive a herd) or 'Vieh treiben' (to drive cattle).
Der Cowboy treibt die Rinderherde durch die Prärie.
The cowboy drives the herd of cattle through the prairie.
This meaning often follows the pattern 'jemanden zu etwas treiben' (to drive someone to something). The preposition 'zu' with the dative introduces the action or state that the person is pushed toward.
Die Neugier trieb sie dazu, das alte Buch zu öffnen.
Curiosity drove her to open the old book.
In this context, the subjects are always plants or parts of plants. The verb can also be used with an accusative object to say what is growing, e.g., 'Blüten treiben' (to produce blossoms).
Im Frühling treiben die Bäume neue Blätter.
In spring, the trees produce new leaves.
The combination 'Handel treiben' is a fixed expression for 'to do business'. It is often combined with a description of the trade, e.g., 'regen Handel treiben' (to engage in lively trade).
Die Hafenstadt treibt Handel mit der ganzen Welt.
The port city trades with the whole world.
The idiom 'es zu weit treiben' (to go too far) is a fixed unit. The pronoun 'es' is a fixed component here and cannot be replaced.
Mit dieser unfairen Bemerkung hast du es wirklich zu weit getrieben.
With that unfair remark, you really went too far.
'Unfug treiben' is a fixed collocation and means to do nonsense or play pranks. It is often used for children's behavior.
Pass auf, dass die Kinder im Garten keinen Unfug treiben.
Make sure the children don't get up to any mischief in the garden.
to do / make
'machen' and 'treiben' can be similar in some fixed expressions, for example 'Sport treiben' and 'Sport machen' (to do sports), or 'Unfug treiben' and 'Unsinn machen' (to get up to mischief / do nonsense). The important difference is: 'machen' is a very general verb for many activities. You cannot use 'treiben' freely for every activity; it only fits in certain combinations or special meanings. Learners may confuse the words because both sometimes have to do with activities. The safer rule is: if you do not know a fixed expression, 'machen' is usually more natural.

Seit dem Arztbesuch treibt Paul dreimal pro Woche Sport.
Since his visit to the doctor, Paul has been doing sports three times a week.
Am Wochenende machen wir einen Ausflug an den See.
At the weekend, we are taking a trip to the lake.