По мере того как хлеб становился горячее в тостере, мама разливала чай по чашкам.

It means something like as, while, or more literally in proportion as. It introduces two actions or processes that develop alongside each other.

So in this sentence, the idea is:

• the bread was getting hotter
• at the same time, the mother was pouring tea into cups

It often suggests a gradual change happening step by step.

Because the sentence describes ongoing, unfolding actions in the past, not single completed events.

• становился = was becoming / was getting
• разливала = was pouring

This is very natural when two actions are happening at the same time.

If you used perfective verbs, the focus would shift to completed results, which would not fit the same smooth background description as well.

Становился is imperfective, so it shows a process: the bread was getting hotter.

Стал would mean became, as a more complete or single change. Compare:

• хлеб становился горячее = the bread was getting hotter
• хлеб стал горячее = the bread got hotter / became hotter

Because По мере того как usually describes something developing gradually, становился fits better.

For the same reason: разливала presents the action as in progress.

• разливала = was pouring
• разлила = poured, finished pouring

Here the sentence paints a scene in progress, so imperfective is the natural choice.

Горячее is the comparative form of горячий, so it means hotter.

• становился горячее = was getting hotter
• становился горячим = was becoming hot

These are close, but not identical:

• горячее emphasizes increase in degree
• горячим emphasizes reaching the state hot

In this sentence, the speaker wants the idea of gradual increase, so горячее is a very good choice.

Горячее here is the comparative form of the adjective горячий.

Comparative forms in Russian usually do not change for gender, number, or case in this kind of predicate use. So even though хлеб is masculine singular, you still say:

• хлеб становился горячее
• суп становился горячее
• булочки становились горячее

The form горячее stays the same.

Because становиться is the normal Russian verb meaning to become or to get.

For learners, it is best to treat становиться as a whole dictionary word. The -ся here is not something you should translate literally as oneself. In modern Russian, становиться simply means become / get.

Its perfective partner is стать.

Because в with the prepositional case is used for location: in the toaster.

• тостер = toaster
• в тостере = in the toaster

Here the bread is located inside the toaster, so the location use of в is correct.

If there were motion into the toaster, Russian would normally use в + accusative instead.

По чашкам means something like into the cups, with a sense of distribution among multiple cups.

The noun is in the dative plural:

• чашка = cup
• чашкам = to/among the cups

After по, this structure often means distributed across several items. So:

• разливать чай по чашкам = to pour tea into the cups, cup by cup

This is very idiomatic Russian.

You can say в чашки, and it would also make sense. But the nuance is a little different.

• в чашки focuses more on direction: into the cups
• по чашкам focuses more on distribution: among the cups, cup by cup

With разливать, по чашкам is especially natural because the verb itself already suggests pouring something out into several containers.

Both verbs can be possible in similar contexts, but they are not exactly the same.

• наливать = to pour, to fill
• разливать = to pour out into multiple containers, to distribute liquid

Since the sentence mentions чашкам in the plural, разливала is very fitting: the mother was pouring tea out among the cups.

So разливала чай по чашкам sounds especially natural.

In Russian past tense, verbs agree with the subject in gender and number.

• хлеб is masculine singular, so: становился
• мама is feminine singular, so: разливала

This is a very important feature of Russian past tense:

• masculine: usually no final -а
• feminine: usually -а
• neuter: -о
• plural: -и

Yes. Russian word order is flexible, and the basic meaning would stay the same. For example, you could also hear:

• Мама разливала чай по чашкам, по мере того как хлеб становился горячее в тостере.

The original order is natural because it sets up the background process first and then gives the simultaneous action. But Russian often changes word order for emphasis, rhythm, or style.