Temperówka jest w szufladzie, bo rano dzieci jej szukały przed lekcją.

Because the verb szukać normally takes the genitive, not the accusative.

• jej = genitive of ona / it (here referring to temperówka)
• ją = accusative

So:

• dzieci jej szukały = the children were looking for it

This is one of those verbs whose object case has to be learned with the verb. In careful standard Polish, szukać kogo? czego? is the pattern.

Temperówka is in the nominative singular, because it is the subject of the sentence.

The basic dictionary form is:

• temperówka = pencil sharpener

In this sentence:

• Temperówka jest... = The pencil sharpener is...

So it stays in its base form.

Because w meaning in takes the locative when it describes a location.

• szuflada = drawer
• w szufladzie = in the drawer

So:

• Temperówka jest w szufladzie = The sharpener is in the drawer

A useful contrast:

• w szufladzie = in the drawer, located there
• movement into something is usually expressed differently, for example do szuflady

Because the preposition przed takes the instrumental in this meaning.

• lekcja = lesson, class
• przed lekcją = before class

The instrumental singular ending here is:

• lekcja → lekcją

So this is simply the form required by przed.

Because dzieci takes the non-masculine-personal plural form in the past tense.

Compare:

• dzieci szukały = the children were looking
• chłopcy szukali = the boys were looking

In the Polish past tense plural:

• -li is used for masculine-personal groups
• -ły is used for non-masculine-personal groups

Even though dzieci means children, grammatically it goes with szukały.

Rano means in the morning or, depending on context, this morning.

So:

• bo rano dzieci jej szukały = because the children were looking for it this morning / in the morning

It is an adverb, so it does not change its form.

Yes. Polish word order is fairly flexible, and rano can move depending on emphasis.

For example:

• Rano dzieci jej szukały przed lekcją.
• Dzieci rano jej szukały przed lekcją.

These all mean roughly the same thing, but the emphasis shifts a little. The version you were given is completely natural.

Bo means because and is very common in everyday Polish.

So:

• Temperówka jest w szufladzie, bo... = The sharpener is in the drawer, because...

You could also say:

• ponieważ = because, since
• gdyż = because, as

But bo is the most natural, conversational choice here.

In a normal full sentence like this, jest is needed.

• Temperówka jest w szufladzie = The sharpener is in the drawer

If you said just:

• Temperówka w szufladzie

it would sound incomplete, like a note, label, or headline rather than a regular sentence.

Polish sometimes omits to be in special contexts, but not normally in a straightforward sentence of location like this.

Because szukać describes the process of looking for something, not a completed result.

Here the idea is:

• the children were looking for it before class

That fits the imperfective well. It does not say they found it; it just describes the action of searching.

So szukały is the natural choice.

Yes. Temperówka is a feminine noun, and that matters for forms that refer back to it.

For example, the pronoun is:

• jej = of her / of it

Here jej refers to temperówka.

So the sentence structure depends partly on:

1. the verb szukać requiring the genitive
2. temperówka being feminine singular

Polish does not have articles like English a and the.

So temperówka can mean:

• a pencil sharpener
• the pencil sharpener

Which one is meant depends on context. In this sentence, English would most naturally use the, because it sounds like a specific sharpener already known to the speaker and listener.