Wałek do rolowania leży na macie do ćwiczeń.

Because na changes case depending on meaning.

• For location (on something, no movement), na takes the locative case.
• mata is the dictionary form (nominative).
• Its locative singular form is macie.

So:

• mata = mat
• na macie = on the mat

In this sentence, the roller is already located on the mat, so na macie is correct.

Macie is the locative singular form of mata.

Here is the basic pattern:

• nominative: mata
• locative: (na) macie

The locative is commonly used after prepositions such as na, w, o, when they express location or topic.

In Polish, noun + do + another noun is a very common way to say for, used for, or intended for.

So:

• wałek do rolowania = roller for rolling
• more naturally in English: foam roller / roller used for rolling

The word rolowania comes from rolowanie (rolling) and appears in the genitive case because the preposition do requires the genitive.

Because do requires the genitive, and ćwiczeń is the genitive plural form of ćwiczenia.

Here is the idea:

• ćwiczenia = exercises
• do ćwiczeń = for exercises / for working out

So mata do ćwiczeń literally means mat for exercises, which is the normal Polish way to say exercise mat.

Because Polish often uses specific position verbs where English might simply use is.

• leżeć = to lie
• stać = to stand
• wisieć = to hang

So if an object is lying flat on a surface, Polish naturally says leży.

• Wałek leży na macie = The roller is lying on the mat

Using jest would only mean is, and it would usually sound less natural here if you want to describe physical position.

It can mean both, depending on context.

In Polish, the present tense often covers both:

• it lies
• it is lying

So Wałek leży na macie can be understood as either:

• The roller lies on the mat
• The roller is lying on the mat

English chooses between simple and continuous more strictly than Polish does.

Wałek literally means a small roller or cylinder-shaped roller. In fitness context, it commonly refers to a foam roller.

The ending -ek is a very common Polish noun ending and can sometimes sound diminutive or just be part of the standard word.

So in this sentence, wałek do rolowania is the natural Polish expression for a foam roller or massage roller used for rolling muscles.

Yes. Polish word order is more flexible than English because case endings show grammatical relationships.

The neutral order here is:

• Wałek do rolowania leży na macie do ćwiczeń.

But you could also say:

• Na macie do ćwiczeń leży wałek do rolowania.

That version puts more focus on where it is.

So the basic meaning stays the same, but the emphasis changes.

A few key pronunciation points:

• ł sounds like English w
  • wałek sounds roughly like VAH-wek
• ż sounds like the s in measure
  • leży sounds roughly like LEH-zhih
• ć is a soft sound, a bit like a softened ch/t
• cz sounds like English ch
• ń is a soft n, like Spanish ñ
• ę at the end of a word is often pronounced less strongly than a full nasal vowel in careful speech

So ćwiczeń is roughly CHVEE-cheny/CHVEE-cheń, though English approximation is imperfect.

Also, Polish stress is usually on the second-to-last syllable:

• WA-łek
• ro-LO-wa-nia
• LE-ży
• MA-cie
• ĆWI-czeń

This is a very important Polish pattern:

• na + locative = location
• na + accusative = movement toward a place

So:

• leży na macie = it is lying on the mat
• kładzie wałek na matę = he/she puts the roller onto the mat

In your sentence, there is no movement, only location, so na macie is correct.

Yes, functionally it often works that way.

English often uses one noun as an adjective:

• exercise mat
• coffee cup
• tennis shoes

Polish usually does this differently. Instead of stacking nouns, it often uses:

• noun + do + genitive
• or an adjective

So:

• mata do ćwiczeń = exercise mat
• literally: mat for exercises

This is one of the most natural ways Polish expresses purpose.

Yes, you could, and it would mean The foam roller is on the exercise mat.

But there is a nuance:

• jest na macie focuses more on simple existence/location: is on the mat
• leży na macie sounds more vivid and natural when the object is physically lying there

So both are possible, but leży is usually the better choice for an object resting flat on a surface.