Learn Hardcore Russian: Учитель дал двум студентам одинаковое задание. - The teacher gave the same assignment to two students.

In this sentence the number is in the dative, because it goes with студентам (dative plural). So you must use the dative form двум, not два.

Why does студентам end in -ам?

Студентам is dative plural of студент.

For most masculine and feminine nouns ending in a consonant (like студент, учитель, мама), the dative plural ending is:

-ам after most consonants:
- студент → студентам
- брат → братьям (with a spelling change, but same ending)
- подруга → подругам
-ям after certain consonants and soft stems:
- учитель → учителям
- герой → героям

So студентам = to students (dative plural).

What case is задание, and why does it look like the nominative?

Задание here is in the accusative singular as the direct object of дал:

gave what? → одинаковое задание

For neuter inanimate nouns ending in -о / -е, the nominative and accusative forms are identical:

Nominative: задание (the assignment is hard)
Accusative: задание (I did the assignment)

So it looks like nominative, but grammatically it is accusative.

Why is it одинаковое задание, not одинаковые задания?

Both are possible, but the meaning changes slightly:

одинаковое задание – the same assignment (one specific assignment that is the same for both students)
одинаковые задания – identical assignments (plural; could suggest separate copies/versions that are equivalent)

In this sentence, the idea is that there was one job/task, and it was given equally to both. That’s why the singular задание is used, and the adjective одинаковое agrees with it in:

gender: neuter
number: singular
case: accusative (same form as nominative for neuter)

So: одинаковое задание.

Why is the adjective одинаковое in that form?

Adjectives in Russian must agree with the noun in gender, number, and case.

The noun here is задание:

gender: neuter
number: singular
case: accusative (but same form as nominative for neuter inanimate)

The standard ending for a hard-stem neuter adjective in nominative/accusative singular is:

-ое (spelled -ое but often pronounced close to -aye)

Examples:

новое задание – a new assignment
интересное задание – an interesting assignment
одинаковое задание – the same assignment

So the form одинаковое is required by agreement with задание.

Why is it дал, not давал?

Дать and давать are an aspectual pair:

дать – perfective (focus on the result, a single completed act)
давать – imperfective (focus on process, repetition, or habitual action)

Дал is the past tense masculine singular of perfective дать:

Учитель дал… – The teacher gave (once, completed).

Давал is the past tense masculine singular of imperfective давать:

Учитель давал двум студентам одинаковое задание – The teacher used to give / was giving (repeated or ongoing in the past).

In the original sentence, we’re talking about one specific completed action, so the perfective дал is natural.

How is дал formed from дать? It looks irregular.

Yes, дать is irregular in the past tense. The stem changes:

infinitive: дать
past tense:
- masculine: дал
- feminine: дала́
- neuter: дало́
- plural: дали

This doesn’t follow the regular pattern of adding -л to the infinitive stem. You just have to memorize the past forms of дать as special.

Can the word order be changed, like Учитель одинаковое задание дал двум студентам?

Yes. Russian word order is more flexible than English. The neutral, most common order here is:

Учитель дал двум студентам одинаковое задание.

Other orders are grammatically possible, for example:

Учитель дал одинаковое задание двум студентам.
Учитель одинаковое задание дал двум студентам.
Двум студентам учитель дал одинаковое задание.

Changes in word order usually affect emphasis or what is presented as “new” information. The original order is neutral and clear: who (учитель) – what did he do (дал) – to whom (двум студентам) – what (одинаковое задание).

Why is the verb дал masculine? What if the teacher is a woman?

In Russian, past tense verbs agree with the grammatical gender and number of the subject.

The noun учитель is grammatically masculine, so the verb must be masculine past:

Учитель дал… – The (male or unspecified) teacher gave…

If you specifically mean a female teacher and want to mark that in the grammar, you typically use:

учительница (feminine noun)
→ Учительница дала двум студентам одинаковое задание.

Now the verb is дала (feminine past), agreeing with учительница.

What is the difference between задание, задача, and упражнение?

All can be translated as task/exercise, but usage differs:

задание – a task or assignment to be completed; very common in schoolwork, homework, and instructions.
- домашнее задание – homework
задача – a problem or task, often something to solve (especially in math, physics, logic).
- математическая задача – a math problem
упражнение – an exercise (practice activity), like drills in a textbook or physical exercises.
- грамматическое упражнение – a grammar exercise

In this sentence, задание is best, because a teacher is giving an assignment.

Could we say Учитель дал одно и то же задание двум студентам instead of одинаковое задание?

Yes, and it is natural Russian. The nuance:

одинаковое задание – the same/identical assignment (emphasizes sameness in quality/type)
одно и то же задание – literally “one and the same assignment” (emphasizes that it is exactly the very same specific assignment)

Both usually mean practically the same thing here, but одно и то же задание can sound a bit more explicit about “exactly the same assignment.”