Я хочу кое-что тебе показать после урока.

Both can mean something, but they are not exactly the same.

• что-то = something / I don’t know what / some kind of thing
• кое-что = something specific, but I’m not saying exactly what

In this sentence, кое-что suggests that the speaker has a particular thing in mind and is deliberately keeping it vague for now.

So Я хочу кое-что тебе показать feels like:

• I want to show you something
• and the speaker knows what that thing is.

If you said Я хочу что-то тебе показать, it would sound a bit less specific and can feel more like I want to show you something or other.

Because in Russian, кое- is a particle that is normally attached by a hyphen to pronouns like:

• кое-кто = someone
• кое-что = something
• кое-какой = some kind of

So кое-что is just the standard spelling.

Because тебе is the dative case, and the verb показать uses the pattern:

• показать что? = to show what?
• показать кому? = to show to whom?

In this sentence:

• кое-что is the thing being shown
• тебе is the person receiving it

So:

• Я хочу показать тебе кое-что
• literally: I want to show to you something

Why not the other forms?

• ты = nominative, used for the subject
• тебя = accusative/genitive, not the form needed here
• тебе = dative, correct after показать for the person you show something to

Because after хочу (I want), Russian normally uses an infinitive:

• хочу читать = I want to read
• хочу пойти = I want to go
• хочу показать = I want to show

This is like English want to + verb, except Russian does not use a separate word for to before the infinitive.

So:

• хочу показать = want to show

This is a question of aspect.

• показать = perfective
• показывать = imperfective

Here, показать is used because the speaker means one complete action: showing something once, after the lesson.

So the idea is:

• I want to show you something as a single finished event.

If you used показывать, it could suggest:

• a repeated action,
• an ongoing process,
• or a more general activity of showing.

Compare:

• Я хочу тебе показать... = I want to show you...
• Я хочу тебе показывать... = I want to be showing you... / I want to show you regularly...

In this sentence, the perfective показать is the natural choice.

Because после requires the genitive case.

The basic form is:

• урок = lesson / class

After после (after), it becomes:

• после урока = after the lesson/class

This is a very common pattern:

• после работы = after work
• после фильма = after the film
• после встречи = after the meeting

So урока is simply the genitive singular form of урок.

Yes. Russian word order is more flexible than English because case endings show the grammatical roles.

The sentence as written:

• Я хочу кое-что тебе показать после урока.

is natural and neutral.

But you could also hear:

• Я хочу тебе кое-что показать после урока.
• После урока я хочу тебе кое-что показать.
• Кое-что я хочу тебе показать после урока.

These all mean roughly the same thing, but the emphasis changes.

For example:

• После урока at the beginning emphasizes when
• тебе earlier can slightly emphasize to you
• кое-что earlier can highlight the something

English usually depends much more on fixed word order; Russian uses word order partly for emphasis and information flow.

Both are possible.

Russian often allows either:

• хочу тебе показать
• хочу показать тебе

Both are grammatical and natural. The difference is usually about rhythm, style, or slight emphasis, not basic meaning.

In everyday speech, хочу тебе показать is very common and sounds very natural.

Because Russian has no articles like a, an, or the.

Russian speakers do not normally mark definiteness with a separate word. Instead, the meaning comes from context.

So после урока can mean:

• after the lesson
• after class
• after a lesson

depending on the situation.

In this sentence, context usually makes it sound like after the lesson / after class.

Yes. In real usage, урок often corresponds to lesson or class, depending on context.

So после урока may naturally be understood as:

• after the lesson
• after class

This is especially common in school or teaching contexts.

Yes, it is completely natural.

It sounds like something a teacher, classmate, or friend might say. The sentence is straightforward and conversational:

• Я хочу = personal intention
• кое-что = something specific but not named
• тебе = to you
• показать = show
• после урока = after the lesson/class

So overall, it is a very normal piece of everyday Russian.