На уроке орфографии мы проверяем правописание трудных слов в словаре.

Because на уроке uses the prepositional case after на to mean at/in the lesson or during the lesson.

• на уроке = at the lesson, in class
• на урок = to the lesson

So here there is no movement; it describes where the action happens.

Орфографии is in the genitive singular because it depends on урок:

• урок орфографии = a spelling lesson / a lesson in orthography

This is a very common Russian pattern:

• урок математики = a math lesson
• урок музыки = a music lesson
• урок русского языка = a Russian lesson

So in на уроке орфографии, only уроке changes because of на; орфографии stays genitive because it means lesson of spelling.

It is the accusative singular, because it is the direct object of проверяем:

• мы проверяем что? → правописание

However, for many inanimate neuter nouns, the accusative looks exactly like the nominative, so правописание has the same form in both cases.

Because правописание is followed by the genitive:

• правописание слов = the spelling of words
• правописание трудных слов = the spelling of difficult words

So both words are in forms that match this structure:

• трудных = genitive plural
• слов = genitive plural

Russian often uses the genitive after nouns to express of:

• правило языка = rule of the language
• начало урока = beginning of the lesson
• правописание слов = spelling of words

They are close in meaning, but they are used a little differently.

• орфография often refers to spelling as a subject, system, or set of rules
• правописание often refers to the spelling of particular words or correct written form

So this sentence is very natural:

• урок орфографии = a spelling lesson
• проверять правописание слов = to check the spelling of words

Using both in one sentence is not redundant; each word has a slightly different role.

Проверяем is the imperfective present of проверять. It is used because the sentence describes a normal, repeated, or ongoing classroom activity:

• мы проверяем = we check / we are checking

This fits contexts like:

• what we usually do in spelling class
• what we are doing right now in class

The perfective partner is проверить, but perfective verbs do not normally have a true present meaning in Russian. Their present-looking forms usually refer to the future.

Yes, it could be omitted, because Russian verb endings often already show the subject:

• проверяем already means we check

So both are possible:

• На уроке орфографии мы проверяем...
• На уроке орфографии проверяем...

Including мы can make the sentence a little clearer, more complete, or slightly more emphatic. In a textbook-style sentence, keeping мы is very normal.

It literally means in the dictionary.

So the idea is:

• we check the spelling of difficult words in the dictionary
• in more natural English, by looking them up in the dictionary

Grammatically, в словаре is prepositional singular after в.

Compare:

• в словаре = in the dictionary
• в книге = in the book
• в тетради = in the notebook

Yes. Russian word order is flexible, so you could also say:

• На уроке орфографии мы в словаре проверяем правописание трудных слов.
• На уроке орфографии мы проверяем в словаре правописание трудных слов.

But the original order is natural and easy to process. Russian often places information in an order that feels smooth or highlights what comes later.

The original sentence flows well because it first states:

1. the setting — На уроке орфографии
2. the action — мы проверяем
3. what is checked — правописание трудных слов
4. where/by means of what — в словаре

The main stresses are:

• На уро́ке орфогра́фии мы проверя́ем правописа́ние тру́дных слов в словаре́.

A few important ones for learners:

• уро́к → на уро́ке
• орфогра́фия
• проверя́ем
• правописа́ние
• тру́дный
• словарь → в словаре́

Stress is important in Russian because it can move when the word changes form, as in слова́рь → словаре́.

Both are possible, but at spelling class or in spelling class often sounds more natural in English.

Literally:

• на уроке = at the lesson / in class
• орфографии = of spelling / spelling

So depending on context, good translations include:

• In spelling class...
• At the spelling lesson...
• During the spelling lesson...

Russian урок often corresponds to English class in school contexts.