Looking at your citation of the Cambridge dictionary, I think I see your problem. The first meaning, a type of rock, is clearly a noncount noun. The second meaning, a stick of that rock, is listed in the dictionary as either a count or noncount noun. But the dictionary's example refers to a piece of chalk, which is how we normally speak of classroom chalk. As Erik points out, we normally count chalk by "pieces" or "sticks." I believe that artists who use chalk in their work may sometimes--though not always--speak of "chalks" but in this case they would be referring to chalks of different colors. Example: "I use many chalks in my work: green, blue, etc." I don't think there's any easy route to learning count and noncount nouns in English. Perhaps this web page may be helpful: http://ajaja.paradoxinc.org/Basic/Grammar/CountAndNoncount.html

I'm not sure what your exact question is, but here are some examples of English sentence using the word "chalk": "Our classroom is supplied with plenty of chalk." "I have a big box full of chalk." "There are more than 100 pieces of chalk in the box." "We went through a lot of chalk in math class." So, we can say "one piece of chalk" or "two pieces of chalk" or "one stick of chalk" or "two sticks of chalk" or "many sticks of chalk" or "a lot of chalk". But, at least here in the US, we would NOT say "two chalks" or "three chalks". Hope this helps!

I don't quite understand your question...what are you trying to ask?