One of the Russian words for half is половина. It is perfectly regular in declension. Sample sentences:

The verb замечать/заметить means “to notice observe.” It conjugates like this:

The thing you notice goes in the accusative case:

You can also follow the verb with an entire clause. The clause usually begins with что, but it can also begin with a question word used as a relative pronoun:

English is interesting in terms of comparatives. Sometimes you can use a comparative with -er, but you can't use a comparative with “more.” Thus “cuter” is okay, but “more cute” is not. We call the -er form the simple comparative. Sometimes the “more” form is okay, but the “-er” form is not. Thus “My life is more interesting than yours” is okay, but “My life is interestinger than yours” is not. When you use “more” with an adjective, we call that the compound comparative. Russian also has both simple and compound comparatives. The word used for compound comparatives is более. The более form is almost always acceptable in Russian:

Note: Задача really means assignment or taks, but in certain contexts like арифметическаая задача it can mean the equivalent of equation. The normal word for equation is уравнение.

Another word that means bigger is больше. In this meaning it is what we call a comparative adjective:

Just as with other comparative sentences, if чем is followed by a simple noun phrase in the nominative case, you can make an equivalent phrase without чем by putting the noun in the genitive. Thus the second and third sentences from above can be rephrased as:

One thing you can't do with больше is to make a sentence like “John lives in a bigger house than Victor.” When “bigger” directly modifies a noun, Russians have to use either «больший» or «более большой», thus:

Больше has other meanings as well. We will explore them over the next couple weekds.

Now here's a subtle detail of the Russian language. It's one that will trip you up at first when you start reading Russian if you aren't paying attention. Although большой means big, there is another word больший that means bigger, greater, or larger. Since Russians don't usually write stress marks, the presence of о or е after the ш is often the only written indication of which meaning is implied. Больший declines like this:

Sample sentences:

As part of your Russian reading strategy in your early years, you might want to pause when you come across большой and больший. If you spot a е after the ш, then remind yourself that it means “bigger.” That helps in the singular of most forms. Alas, only context can tell you which one the author had in mind in the plural.