На этом уроке мы не будем писать, а будем читать вслух.

With урок, Russian usually uses на when talking about something happening during a lesson/class.

• на уроке = in class / during the lesson
• на этом уроке = in this lesson / during this class

Using в этом уроке would more likely suggest inside the lesson as a unit of content, for example inside a textbook lesson, not the normal idea of what happens in class.

So here на этом уроке means during this lesson.

This is the prepositional case.

The preposition на often takes the prepositional case when it means on / at / in a location or setting.

So:

• этот урок = this lesson
• на этом уроке = in/during this lesson

Both words change:

• этот → этом
• урок → уроке

This is the normal masculine singular prepositional pattern.

Because писать is an imperfective verb, and the future of imperfective verbs is normally formed with:

• быть in the future + infinitive

So:

• будем писать = we will be writing / we will write
• не будем писать = we will not write

This is called the compound future.

Russian does this because imperfective verbs describe an action as a process, activity, or repeated action, not as a completed result.

Because the sentence is talking about the activity done in class, not about producing a finished result.

• писать = to write, to be writing, to do writing
• написать = to write something and finish it

In a classroom sentence like this, the speaker means:

• we will not be doing writing
• we will be doing reading aloud

So the imperfective писать fits better than the perfective написать.

For the same reason: читать is imperfective and focuses on the activity of reading.

• будем читать = we will read / we will be reading
• прочитаем = we will read and finish it

Here the teacher is describing what kind of work the class will do, not saying they will finish reading a particular text. So будем читать is the natural choice.

Here а marks a contrast:

• не будем писать, а будем читать = we will not write, but rather read

It is not exactly the same as но.

• но often means but in the sense of contradiction
• а often means whereas / while / but instead

In this sentence, а is very natural because the speaker is contrasting one class activity with another.

So the meaning is:

• not writing, but reading aloud instead

Sometimes Russian can omit repeated words, but here repeating будем sounds natural and clear:

• мы не будем писать, а будем читать вслух

This gives a nice balance:

• не будем писать
• будем читать

If you remove the second будем, the sentence may sound less complete or shift the structure. Repeating it makes the contrast stronger and cleaner.

Читать вслух means to read aloud.

• читать = to read
• вслух = aloud, out loud

So будем читать вслух means we will read out loud, not silently.

This is a very common expression in Russian:

• читать вслух
• сказать вслух = to say out loud

Because in modern Russian вслух functions as a fixed adverb meaning aloud.

Even though it historically comes from older elements, learners should just remember it as a normal adverb:

• вслух = aloud
• про себя = silently / to oneself

So:

• читать вслух = read aloud
• читать про себя = read silently

Because in context, Russian often leaves the object unstated if it is obvious or unimportant.

So:

• писать can mean to do writing
• читать can mean to do reading

In a classroom context, this sounds perfectly natural. The sentence is about the type of activity, not about a specific thing being written or read.

If needed, you could add an object:

• будем читать текст вслух = we will read the text aloud

But it is not necessary here.

Russian word order is flexible, but this order is very natural:

• На этом уроке sets the scene first: during this lesson
• мы gives the subject: we
• не будем писать, а будем читать вслух gives the contrast

Other orders are possible, but they change the emphasis. For example:

• Мы на этом уроке не будем писать, а будем читать вслух
  More emphasis on we.

• Читать вслух на этом уроке мы будем, а не писать
  Much stronger contrast, more marked style.

The original sentence is the most neutral and teacher-like.

Not always. Russian often drops subject pronouns when the verb ending already shows the subject.

So you could say:

• На этом уроке не будем писать, а будем читать вслух.

This still clearly means we will not write, but will read aloud.

However, including мы can make the sentence:

• clearer
• slightly more explicit
• more natural in some teaching or explanatory contexts

So мы is optional here, but perfectly normal.