Каждому ребёнку дали по одному мандарину, и малышка сразу начала улыбаться.

Because каждому ребёнку is in the dative case, and here it means to each child.

• каждый ребёнок = every child as the subject
• каждому ребёнку = to each child

In this sentence, the children are the receivers of the tangerines, so Russian uses the dative:

• дать кому? = to give to whom?
• каждому ребёнку = to each child

So the structure is basically:

• Каждому ребёнку дали... = They gave each child...

Russian often uses a 3rd person plural verb with no subject to mean something like they in an indefinite sense.

So:

• дали literally = they gave
• but it often means someone gave or people gave

This is very common in Russian when the speaker does not name who did the action, either because it is obvious, unimportant, or unknown.

So here:

• Каждому ребёнку дали по одному мандарину
  = Each child was given one tangerine
  or more literally
  = They gave each child one tangerine

English often prefers a passive translation, but Russian naturally uses this plural verb.

This means one tangerine each.

The preposition по is often used for distribution:

• по одному = one each
• по два = two each
• по три = three each

So:

• дали по одному мандарину = gave one tangerine to each person

This is a very common Russian pattern.

A few examples:

• Студентам дали по книге. = The students were given a book each.
• Детям купили по мороженому. = They bought each child an ice cream.

Because по in this distributive meaning commonly takes the dative case.

So:

• один мандарин = nominative
• одному мандарину = dative

That is why you see:

• по одному мандарину = one tangerine each

This can feel strange to English speakers, because English does not mark this kind of structure with case. In Russian, though, по + dative is a normal way to express distribution.

The dictionary form is ребёнок, with ё, and here the dative singular is ребёнку.

Important points:

• ё is pronounced like yo
• in everyday writing, Russians often write е instead of ё
• so you may see ребенку, but it is the same word

For learners, it is useful to remember the real pronunciation:

• ребёнок = roughly rye-BYON-ak
• ребёнку = roughly rye-BYON-koo

So yes, ё is correct, even if it is sometimes omitted in normal text.

Малышка is nominative singular, because it is the subject of начала улыбаться.

It means something like:

• little girl
• small girl
• sometimes toddler or little one, depending on context

It comes from малыш / малышка, words related to being small or little. Compared with девочка, малышка sounds more affectionate and emphasizes that she is very young or little.

So in this sentence:

• малышка сразу начала улыбаться = the little girl immediately began to smile

Yes, малышка is singular. The sentence first talks about a group, then singles out one child from that group.

So the logic is:

1. Each child was given one tangerine
2. And the little girl immediately began to smile

This is perfectly natural. Russian, like English, can move from a general group statement to one specific person in that group.

Because начала улыбаться means began to smile, while улыбнулась means smiled or gave a smile.

The difference is about how the action is presented:

• начала улыбаться = focuses on the beginning of the smiling
• улыбнулась = presents the smile as a more complete single action

So:

• малышка сразу начала улыбаться = the little girl immediately started smiling
• малышка сразу улыбнулась = the little girl immediately smiled

Both are possible in many contexts, but they are not exactly the same.

After начать (to begin), Russian normally uses an imperfective infinitive to describe the action that starts.

So:

• начать улыбаться = to begin smiling

The imperfective aspect is natural here because it presents smiling as a process or ongoing action, not as one finished event.

This is a very common pattern:

• начал читать = began reading
• начала говорить = began speaking
• начали смеяться = began laughing

Сразу means:

• immediately
• right away
• at once

In this sentence, it modifies начала улыбаться:

• малышка сразу начала улыбаться = the little girl immediately began to smile

Russian word order is fairly flexible, so сразу could appear in different places with only small differences in emphasis, for example:

• Малышка сразу начала улыбаться.
• Сразу малышка начала улыбаться.
• Малышка начала сразу улыбаться.

The first version is the most neutral and natural here.

Russian word order is more flexible than English word order, and the first position often shows what the speaker wants to emphasize or set as the topic.

Starting with Каждому ребёнку puts focus on the recipients:

• Каждому ребёнку дали по одному мандарину
  = As for each child, they were given one tangerine each

If you started with Дали, the sentence would still be grammatical:

• Дали каждому ребёнку по одному мандарину

But the original version sounds more natural if the speaker wants to highlight that every child got one.

Not naturally in English. A word-for-word translation helps show the grammar, but it does not make good English.

A more natural translation would be:

• Each child was given one tangerine, and the little girl immediately began to smile.
• or They gave each child one tangerine, and the little girl immediately started smiling.

English usually needs either:

• a subject like they
• or a passive structure like was given

Russian does not need that in the same way.

Russian has no articles.

So nouns like:

• ребёнку
• мандарину
• малышка

can mean a child / the child, a tangerine / the tangerine, a little girl / the little girl, depending on context.

In this sentence, English naturally uses:

• each child
• one tangerine
• the little girl

Russian leaves that information to context instead of using articles.

Yes. Мандарин is the normal Russian word for the fruit often called:

• tangerine
• mandarin
• mandarin orange

in English.

In everyday translation, tangerine is often the most natural choice, but mandarin orange is also correct depending on the context and the variety of fruit meant.

Here are the main dictionary forms:

• каждому → каждый = each, every
• ребёнку → ребёнок = child
• дали → дать = to give
• одному → один = one
• мандарину → мандарин = tangerine / mandarin orange
• малышка → малышка = little girl, little one
• сразу = immediately
• начала → начать = to begin
• улыбаться = to smile

Looking up the dictionary forms is especially helpful in Russian, since many words change form because of case, number, gender, tense, and aspect.