着 (zhe) part 2: Expressing actions in progress (full form)

We learned using durative particle 着 (zhe) is one way of indicating a continuous action in Mandarin Chinese in the previous blog. In this blog, we will introduce 着 (zhe)'s good friend,  在 (zài) and 正在 (zhèngzài), which can be used before verbs to express that an action is ongoing or in progress. The complete patter is: Subject + 正在 + Verb + 着 + Object + 呢. (Note that: You may see all sorts of variations of it in Chinese people's daily communication because the full form is rarely used completely.) Let's take the verb phrase 看书 for example. There can be myriad ways to say "He is reading a book.":

• 他在看书。He is reading a book.

• 他正在看书。He is reading a book right now.

• 他正在看着书呢。He is reading a book right now.

• 他正看着书呢。He is reading a book right now.

• 他在看着书呢。He is reading a book.

• 他在看书呢。He is reading a book.

• 他看着书呢。He is reading a book.

• 他看书呢。He is reading a book.

Please fix the problems in the following sentences:

1) 我们上在汉语课。

2) 我们在着上汉语课呢。

3) 我们在正上汉语课。

4) 我们正在着上汉语课呢。

5) 我们 上汉语课着呢。

Can you use at least five ways to say "She is singing." by using verb phrase 唱歌?

Reference:
http://resources.allsetlearning.com/chinese/grammar/Expressing_actions_in_progress_(full_form)