Comparing Things. Italian - Level 1, Lesson 4.7

Ciao a tutti, it has taken me a while to wrap my head around this lesson. I am still having trouble with more than in using "di".   Could anyone help me in advising when di is used instead of del, della or dei? 
Right now I undestand it as follows: 

di? 
del - masculine
della - feminine
dei - plural

Any assistance to help me overcome this hurdle would be great.

Grazie,

Sno

Ciao Sno-J1, 
Thanks for your question, I will be more than happy to help clarify any doubts you might have!
When it comes to comparisons, the word "di" can be translated as "than".

Let's take again the example given in lesson 4.7:

Lei corre | più veloce | di | te.
She runs | faster (more fast) | than | you.



On the other hand, the terms delle/dei/degli etc. are used when you have a definite article before the noun you are comparing the subject to (i.e. than the)

First, let's quickly look at the set of "compound prepositions" below in order to fully understand:
di + il = del 
di + lo = dello
di + la = della
di + l' = dell'
di + i = dei
di + gli = degli
di + le = delle 

di is a simple preposition, il/lo/la/l'/i/gli/le are definite articles. When we combine them, they become compound prepositions. Here is a very useful thread with more details about this topic: https://members.rocketlanguages.com/members/forum/italian-grammar/compound-prepositions#forum-post-41174

When it comes to comparisons, which compound preposition you choose (from the list above) depends on the definite article required by the noun in the sentence.

For instance:
La tartaruga è più lenta della lepre.
The turtle is slower than the hare.

In this example "della" is a compound preposition (di + la). This is needed because "the hare" is translated as "la lepre" in Italian, and needs the definite article "la". 

Let's see another example:
Carlo è più alto degli altri ragazzi.
Carlo is taller than the other boys. 

In this example "degli" is a compound preposition (di + gli). This is needed because "the other boys" is translated as "gli altri ragazzi" in Italian, and needs the definite article "gli". 

This applies to all other compound prepositions mentioned above.

To recap, "di" can be used as "than" when no definite article is needed before the noun (e.g. Io sono più intelligente di te / I am smarter than you). The other compound prepositions can be used as "than the" when a definite article is needed before the noun (e.g. Il telefono è più costoso del computer / The phone is more expensive than the computer).

Let me know if you would like to see more examples! :)

That is a fantastic explanation.  Thank you so much.  I will revisit the lesson to make sure I can comprehend it thoroughly. I thank you for the time you took in responding and for all of the above information.  It has helped me understand. 

Ciao,
I have another question for "Comparing Things. Italian - Level 1, Lesson 4.7". 
In the section titled Più o Meno? the italian translation for  "The younger boy cries and the older is good?"  is  "Il bambino più piccolo piange e quello grande è buono ?"

Why is quello grande  used instead of  più grande when referring to the older child?