In Italian, partitive articles indicate an indeterminate part of a larger whole, and are comprised of:

• The preposition DI + the Definite Article (il/lo/l’/la/i/gli/le)      

 
This is similar to…

• Un po’ di

And to the indefinite adjectives…

• Alcuni/Alcune
• Qualche

All four of the above take the meaning of “SOME”, “A LITTLE”, “A FEW”, “A BIT OF”… and can sometimes be interchangeable.
 
 
Much like in English…
The singular form indicates part of a whole.        eg. some milk, some sugar
 Forms: del/ della/ dello/ un po’ di

• del pane / un po’ di pane
  

            some/a little bread   

• dello zucchero / un po’ di zucchero
  

           some/a little sugar

• della carne / un po’ di carne 
  

           some/a little meat
           
The plural form indicates a certain number of with respect to many     eg. some horses, a few books
Forms: dei/ degli/ delle/ alcuni/ alcune / qualche

• dei libri / alcuni libri / qualche libro*
  

           some books

• delle mele / alcune mele/ qualche mela*
  

            some apples
 


DI  + the definite article
       The preposition DI (of/by) + the definite article can be used for both singular and plural nouns; it is formed by combining ‘di’ with the definite article as shown in the table below:

These forms precede nouns that take the article used to create the form.
For example:

• il latte    the milk 
• ​del latte   some milk

            **latte is masculine singular and begins with a “plain” consonant, so it takes il

• la pasta    the pasta
• della pasta    some pasta

            **pasta is feminine singular and begins with a consonant, so it takes la

• i libri    the books
• dei libri     some books

            **libri  is masculine plural and begins with a "plain" consonant, so it takes i

Do you see the pattern?
 
 
Un po’ di
Un po’ di means “a bit of”/ “a little”; it is used with singular collective nouns only.
*po’ is the truncated version of poco; in writing, the apostrophe must be used.
 
For example:​​​​​​

• Un po’ di pasta

           a little pasta/a bit of pasta

• Un po’ di latte

           a little milk/a bit of milk

• Un po’ di zucchero

           a little sugar/a bit of sugar

• Un po’ d’acqua

            a little water/a bit of water

note: “di acqua” is typically not used in spoken Italian to retain fluidity.

Alcuni/Alcune
Alcuni and alcune are used with plural nouns only.
Alcuni is used with masculine plural nouns.
Alcune is used with feminine plural nouns.
 
For example:

• alcuni libri

           some books

• alcune studentesse

            some students [f.]

• alcuni stivali

            some boots

• alcune api

             some bees

Qualche*
Qualche is a bit unusual, compared to the previous partitives. It is invariable (it never changes), and it is used with singular nouns only. Despite being used with singular nouns, the meaning remains ‘some’ or 'a few', so we make adjustments in translating to English.
Qualche is not interchangeable with “un po’ di”.
​For example:

• qualche libro

             some/a few books

• qualche studente

            some/a few students

• qualche minuto

           some/a few minutes         

• qualche volta

            sometimes  ​

***The di + the article  and alcuni/alcune forms are also how we form a plural for the indefinite articles (a/an)
For example:

un albero    >>   degli alberi / alcuni alberi 
                       
una penna      >>    delle penne / alcune penne 
                   
un libro      >>    dei libri / alcuni libri         
​                          
uno spazzolino     >>    degli spazzolini / alcuni spazzolini      ​

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Pratica!