Im Gefrierschrank liegt dasselbe Eis wie letzte Woche.

Im is a contraction of in dem.

• in = in
• dem = the in the dative case

So im Gefrierschrank literally means in the freezer.

German very often contracts:

• in dem → im
• an dem → am
• zu dem → zum

Because in is a two-way preposition in German.

With two-way prepositions such as in, auf, unter, über, German uses:

• accusative for movement toward a destination
• dative for location, when something is already there

Here, the sentence describes where the ice cream is located, not where it is being put.

• Im Gefrierschrank liegt ... = it is in the freezer

So the dative is required.

Because German main clauses follow the verb-second rule.

That means the finite verb must come in the second position, no matter what comes first.

Here, Im Gefrierschrank has been placed first for emphasis or style, so the verb must come next:

• Im Gefrierschrank | liegt | dasselbe Eis wie letzte Woche

If you started with the subject instead, you would get:

• Dasselbe Eis liegt im Gefrierschrank wie letzte Woche.

That is grammatically possible, but the original sentence emphasizes the location first.

German often uses specific position/location verbs where English would simply say is.

Common ones are:

• liegen = to lie, to be lying
• stehen = to stand, to be standing
• sitzen = to sit, to be sitting

For many objects, German prefers one of these instead of plain sein.

Here, Eis is treated as something that is lying in the freezer, so liegt sounds natural.

• Im Gefrierschrank liegt das Eis. = The ice cream is in the freezer.

Using ist is not impossible, but liegt is more idiomatic and more physical/spatial.

German often chooses the location verb based on how something is imagined physically.

• stehen is used for things conceived as upright: bottles, glasses, chairs, a cupboard
• liegen is used for things conceived as lying flat, resting, or just being placed somewhere without an upright orientation

Eis here is not thought of as an upright object, so liegen is the natural choice.

This is one of those things that can feel a bit different from English, because English usually does not care as much about the object's position.

It is nominative, because it is the subject of the sentence.

The verb liegt does not take a direct object here. The thing doing the lying is dasselbe Eis, so that is the subject.

You can test it by asking:

• What lies in the freezer?
• Dasselbe Eis.

That makes it nominative.

Dasselbe means the very same or the same exact one.

It is written as one word in German.

It changes form to match the gender, number, and case of the noun:

• derselbe for masculine
• dieselbe for feminine
• dasselbe for neuter

Since Eis is neuter singular, the correct form here is dasselbe.

So:

• dasselbe Eis = the same ice cream / the very same ice cream

Not quite.

Traditionally, German makes a distinction:

• dasselbe Eis = the very same ice cream, the identical one
• das gleiche Eis = the same kind/type of ice cream, but not necessarily the identical item

For example:

• If it is literally the same tub of ice cream still sitting there, dasselbe Eis fits best.
• If two people each have a chocolate ice cream of the same type, that is more like das gleiche Eis.

In everyday speech, many native speakers do not always keep this distinction strict, but learners should know the traditional difference.

It means as last week or more naturally as last week’s / as there was last week.

This is a comparison with dasselbe:

• dasselbe Eis wie letzte Woche = the same ice cream as last week

German often leaves out repeated words in comparisons when they are easy to understand. So the full idea is something like:

• ... dasselbe Eis, wie [im Gefrierschrank lag] letzte Woche.

But German does not need to repeat all of that.

Because wie is used for equality/sameness, while als is used for difference/comparison of inequality.

• so groß wie = as big as
• größer als = bigger than
• dasselbe ... wie = the same ... as

So in this sentence, wie is correct because the idea is sameness.

Because German often uses time expressions like this without an article.

Common examples:

• letzte Woche = last week
• nächsten Monat = next month
• letztes Jahr = last year

This is similar to English, where you also say last week, not the last week in this kind of expression.

So wie letzte Woche is completely normal.

It is best understood as a time expression used adverbially, and such expressions are often in the accusative in German.

So:

• letzte Woche = accusative time phrase meaning last week

Even though it comes after wie, it is still basically a time expression, not the object of a verb.

For many learners, the important thing is simply to memorize expressions like:

• letzte Woche
• letzten Sonntag
• nächsten Monat

as standard time phrases.

Yes, that is understandable and grammatical.

But liegt sounds more natural if you want to describe where the ice cream is physically located.

Compare:

• ist = just states existence/location in a general way
• liegt = gives a more concrete, spatial sense

German often prefers the more specific location verb, so liegt is a very natural choice here.