Tu is the 2nd Person, so the conjugation of ter is tens while the conjugation of tem is for the 3rd Person Singular of Ele/ela and você (also o senhor/a senhora, a gente). It is similar to English in that you/we/they have, s/he & it has (but far more complicated).
Because the tu conjugation is unique the pronoun can be dropped as it can be inferred by the conjugation of the verb.
"Tens" can only be used with the 2nd Person Singular (tu) while in Brazilian PT, "você" is a 3rd Person treatment pronoun so shares a conjugation with "ele" and "ela" and "a gente" (which in Brazil means, "we" replacing the 1st Person Plural pronoun) so the pronouns are more necessary in Brazil than in Portuguese outside of Brazil but, everywhere context still needs to be established to be able to drop pronouns and there is no context on Duo, except that which comes with conjugations unique to one pronoun.
Other conjugations that are unique so do not need a pronoun on Duo are the 1st Person Singular and Plural ("I" and "we" – though sometimes "vamos" seeks it for clarity as it can mean "let's go" without or, "we go" with) and, 2nd Person Plural (vós) which is really only used near the Portugal borders these days (though, "vosso/a" still gets a lot of use).
English is not a "pro-drop" language, and at any rate this conjugation would be too ambiguous covering too many pronouns (you, we, they, I) to be of use. The bonus to pronoun repetition is easier to learn verbs...
Portuguese (as with most Romance/Latin-based languages) is a pro-drop language and in this case tens – which is 2nd Person Singular conjugation of the verb ter – can only be used with "tu" and no other (hence why there is no need to include tu in the sentence):
However, for the 3rd Person conjugations, especially in Brazil (less so in Portugal and the other Portuguese speaking places) it is more ambiguous so the dropping is often avoided when it could mean s/he, it, and/or you (você form) and even us (when using a gente) among others. It also covers, "have a farm" in the Imperative (command sense) for tu and, tem in particular works in the more colloquial, "there is a farm" (replacing há in that case... which is really pretty much Brazil only as EU PT that also covers Portuguese in Asia and Africa does not use "tem" in this way).
I was confused a bit too.
Actually, in English "TO have a farm" would be absolutely correct. However, that would be an infinitive form (infinitivo pessoal), which wouldn't use "tens" at all. It'd be something like "para ter", which is a conjugation I don't think Duolingo ever gets to teaching, especially at this level.
The purpose of this unit is to train you on knowing the difference between tu & voce. That's why they are leaving the pronoun out in the lesson. But as Scutigera $ Paulenrique say, it's OK to drop it normally too.
Duolingo does have Tips and notes on the web version which is now accessed through the lightbulb button next to the Start button on the skills that have it. https://www.duolingo.com/skill/pt/Basics-2/tips-and-notes https://www.duolingo.com/skill/pt/Tu-or-Voc%C3%AA/tips-and-notes
Here is a convenient verb conjugator: http://conjugator.reverso.net/conjugation-portuguese-verb-ter.html
There is a skill set for Infinitives further down the tree.
I would like some clarification if someone knows. When I first was learning Portuguese I was told that, although it was possible, in Portuguese the subject pronoun is not omitted nearly as often as Spanish and Italian. Even the Eu and nós forms were generally included. Recently I have seen a lot more omitted subject pronouns. In regions where tu is not used, I understand that it is more likely to need the subject pronoun to understand. But is this something that also has a regional component, or Is Duo just trying to be more representative of the variation out there.
OK. That makes some sense. Portugal is still mostly a pro-drop language and Brazil is becoming less so. That makes sense. I guess I would take an additional leap and assume that those regions of Brazil where they still use tu they would tend to use other more European features of Portuguese.