I was curios about "карандаша"'s origins... Some further digging didn't let me disappointed.
Genitive Case - 1 In Russian “I have” is expressed by «У меня (есть)» structure. The owner is in the Genitive case.
"The of-case". It is one of the most universal cases. How do you make the forms? Here is the regular pattern:
|ENDING||Genitive sg.||soft stem|
|zero-ending masculine and -о/-е neutral||сок / молоко||сока / молока||конь ----> коня|
A zero ending means that the word ends in a consonant or a soft sign (which is just a way to show the final consonant is "soft"). In the Nominative singular, a Russian word can only have the following endings: а, я, о, е, ё or nothing ("zero ending").
Genitive of Negation
If you use «нет» to say that there is "no" something or you do not have it, the object is always in Genitive:
У меня́ есть я́блоко → У меня́ нет я́блока
Здесь есть рюкза́к → Здесь нет рюкзака́.
"of" (possession): яблоко мамы = mom's apple
"of" (amount): чашка чая, много чая = a cup of tea, a lot of tea
A huge number of prepositions require this case. Yes, «у меня есть», «У неё есть» only use «меня» and «неё» because «у» wants Genitive.
For он, она and оно Genitive doubles as a non-changing possessive "his", "her", "their": его, её, их. initial «н» is used for him/her/them with the majority of prepositions (doesn't affect possessives)
A little side note: some nouns of foreign origin are indeclinable. It means that all their forms are the same. Foreign nouns that end in о/е become like that (кофе, метро, радио, резюме), as well as all nouns that do not fit into Russian declension patterns (see above).
This includes female names that end in anything other than А or Я. A few -ь-ending names are an exception (Любовь and Biblical names like Юдифь).
So, all of the following names are automatically indeclinable: Маргарет, Мэри, Элли, Дженни, Рэйчел, Натали, Энн, Ким, Тесс, Жасмин.
I am away
Russian also uses the Genitive to state that someone is "away", "not there": Мамы сейчас нет. In English such use would correspond to "There is no mom at the moment", or even "There is no me now". We are not hard on that particular construction in the course, but it is important to know it all the same.
Added bonus: when a verb directly acts on a noun, the noun is called a direct object and is in Accusative. In Russian, only -а/-я nouns have a unique form for it. Others just reuse the Genitive or don't change anything (Nominative)
Карандашей is pencils in the genitive case.
Source: http://www.alphadictionary.com/rusgrammar/genplur.html (#3, stem ends on hush (Ш))
In the Russian language incline (change in cases) nouns, adjectives, numerals and pronouns. In the modern Russian language only inflectional type in which the accusative is not identical to any other and has a special shape — declension nouns in -a, -я in the singular (рука —руку). subsidiary questions for accusative case are - Кого? Что?(Whom? what?)
This is absolutely inconsistent and should be fixed. It does not accept "A boy has no pencil" and "A boy does not have a pencil". It insists it must be "The boy does not have a pencil". There is no context enforcing "The" and it must accept negation of a noun (not only negation of a verb) - because it's grammatically correct and it accepts it in other exercises.
каранда́ш (karandáš) [kərɐnˈdaʂ] m inan (genitive карандаша́, nominative plural карандаши́, genitive plural карандаше́й) "pencil" In Russian from the 16–17th centuries. Borrowing from a Turkic language. Compare Turkish karataş (“black slate”), composed of kara (“black”) + taş (“stone”), Tatar кара таш (qara taş, “graphite, black lead”). The origin of epenthetic -н- (-n-) is unclear. Perhaps it was added in colloquial Russian speech to ease the pronunciation. Compare каланча́ (kalančá) for the same epenthesis. Wiktionary