Перед сном мама укачивает малыша на руках.

It means before sleep, which in natural English is usually before bed or at bedtime.

So in this sentence, Перед сном sets the time: this happens before the child goes to sleep.

Because the preposition перед normally takes the instrumental case.

• сон = sleep, nominative
• сном = sleep, instrumental

So:

• перед сном = before sleep
• compare: перед ужином = before dinner

This is just the normal case pattern after перед when it means before.

Укачивает means rocks/soothes by rocking, often with the idea of helping a child fall asleep.

So мама укачивает малыша is not just Mom is moving the baby back and forth. It specifically suggests she is rocking the child to calm him and get him sleepy.

A useful verb pair is:

• укачивать = imperfective
• укачать = perfective

In this sentence, укачивает is imperfective, which fits a repeated, habitual, or ongoing action.

Качать is a more general verb meaning to rock, swing, move back and forth.

Укачивать is more specific: it usually means to rock someone so they calm down or fall asleep.

So:

• мама качает малыша = Mom is rocking the baby
• мама укачивает малыша = Mom is rocking the baby to soothe him / lull him to sleep

The prefix у- adds that more goal-oriented, soothing sense here.

Because малыша is the accusative singular form, and the child is the direct object of the verb укачивает.

The dictionary form is:

• малыш = little child, baby, toddler

But with a masculine animate noun, the accusative singular usually looks like the genitive singular:

• nominative: малыш
• accusative: малыша

So:

• мама укачивает малыша = Mom rocks the child

Not necessarily exactly.

Малыш is an affectionate word for a small child. Depending on context, it can mean:

• baby
• little one
• little child
• toddler

So if the English translation says baby, that is often fine, but the Russian word itself is a bit broader.

На руках means in (someone’s) arms.

So:

• укачивает малыша на руках = rocks the child in her arms / while holding him in her arms

This is a very natural Russian expression for holding a child against your body in your arms.

Because на руках is the normal expression for being held in someone’s arms.

• на руках = in someone’s arms
• в руках = in someone’s hands

If you say в руках, it sounds more like holding an object in the hands. For a baby or small child, Russian normally says на руках.

Because Russian usually uses the plural in this expression: на руках = in one’s arms.

Literally, it is something like on the arms/hands, but idiomatically it means in the arms.

This is just the standard way Russian says it. The singular would not work the same way here.

Russian often leaves out possessive words like his, her, or their when the meaning is obvious from context.

Here, since мама is the subject, на руках naturally means in her arms.

Russian prefers not to add a possessive unless it is needed for contrast or clarity. So:

• мама укачивает малыша на руках = Mom rocks the child in her arms

Even without a separate word for her, the meaning is clear.

Укачивает is present tense, and in Russian the present tense can describe:

• something happening right now
• a habitual/repeated action
• a vivid scene in narration

So this sentence can mean:

• Mom is rocking the child in her arms before bed or
• Before bed, Mom rocks the child in her arms

The exact nuance depends on context.

Yes. Russian word order is fairly flexible.

This version:

• Перед сном мама укачивает малыша на руках.

puts the time phrase Перед сном first, which makes before bed the starting point of the sentence.

Other orders are possible, for example:

• Мама укачивает малыша на руках перед сном.
• Малыша мама укачивает на руках перед сном.

These all keep basically the same core meaning, but the emphasis changes. The original version is very natural and neutral.

In a sentence like this, мама usually feels more like mom than the more formal mother.

It is the normal everyday family word. Depending on translation style, you might render it as:

• Mom
• Mum
• Mother in a more neutral literary translation

But emotionally and stylistically, мама is usually closer to mom/mum.