На завтрак мама дала детям по одному сырнику и по чашке чая.

На завтрак is an idiomatic way to say for breakfast.

Here, на is used with the accusative case to show purpose or occasion. You will often see the same pattern in phrases like:

• на обед = for lunch
• на ужин = for dinner

Завтрак is accusative singular. Since it is an inanimate masculine noun, its accusative form is the same as its nominative form.

Мама is the subject of the sentence, so it is in the nominative case.

The verb дала is the past tense of дать = to give. In Russian past tense, the verb agrees with the subject in gender and number:

• дал = masculine singular
• дала = feminine singular
• дало = neuter singular
• дали = plural

Since мама is feminine singular, the verb is дала.

Дала is perfective, from дать. It presents the action as a completed event: the mother gave the children breakfast.

If you used давала, that would be imperfective and would suggest a repeated action, a process, or background description, depending on context. In this sentence, the speaker is talking about one completed act, so дала is the natural choice.

Детям is the indirect object, meaning the people who received something.

After verbs like дать = to give, Russian usually puts:

• the thing given in one structure
• the recipient in the dative case

So:

• мама дала детям... = mother gave the children...

Also, детям is the dative plural form of дети = children.

Here по has a distributive meaning: each, apiece, or one each.

So дала детям по одному сырнику и по чашке чая means that the giving was distributed among the children:

• each child got one syrnik
• each child got a cup of tea

This is a very common use of по in Russian.

Because after distributive по, Russian uses forms that fit this construction, and here that means dative singular:

• одному = dative singular of один
• сырнику = dative singular of сырник

So по одному сырнику literally has the structure one syrnik each.

A native English speaker often expects something closer to one syrnik, but Russian marks the phrase differently because of по.

It is singular because the phrase means one per child, not several as one group.

Russian often uses the singular in distributive expressions with по when each person gets one item:

• детям по одному сырнику = the children got one syrnik each

Even though the total number of syrniki is more than one, the grammar focuses on the amount received by each individual child.

Both are possible, but по чашке чая is very natural and common.

Russian often leaves out одной when the meaning one each is already clear from по and the singular noun:

• по чашке чая = a cup of tea each
• по одной чашке чая = one cup of tea each

The version with одной is more explicit. The version without it sounds a bit lighter and more idiomatic in many contexts.

Two different things are happening here.

First, чашке is in the dative because of distributive по:

• по чашке = a cup each

Second, чая is in the genitive because Russian often uses the genitive after a container or measure noun to show what it contains:

• чашка чая = a cup of tea
• стакан воды = a glass of water
• бутылка молока = a bottle of milk

So:

• по чашке = dative because of по
• чая = genitive because it depends on чашка

It means that each child got one.

The repeated по makes the meaning distributive:

• по одному сырнику = one syrnik each
• по чашке чая = one cup of tea each

So the sentence does not mean there was only one syrnik total and one cup of tea total. It means the items were given individually to the children.

It is repeated to show that both parts are distributive:

• по одному сырнику
• по чашке чая

This makes it very clear that each child received each item separately.

Russian sometimes allows one по to cover more than one phrase in certain contexts, but repeating it here is very natural and clear.

Yes. Russian word order is flexible, because case endings carry a lot of the grammar.

The order here is natural and neutral:

• На завтрак sets the scene
• мама gives the subject
• дала gives the action
• детям gives the recipients
• по одному сырнику и по чашке чая gives what each child received

You could rearrange parts of the sentence for emphasis, but this version sounds straightforward and normal.