1. We are all familiar with the custom of answering 'baruch Hu, u-varuch shmo' whenever we hear a 'bracha' of 'baruch ata Hashem'.
Are you aware of the source for this custom?
In case you aren't, first - attempt to understand the meaning of the statement baruch hu u-varuch shmo'.
Then, read the opening three lines of 'shirat Ha'azinu" (32:1-3), paying special attention to 32:3!
As you can translate 32:3, be sure that you understand its context. Relate this pasuk to the above question.
Then, see Rashi on 32:3. According to Rashi, how would he have answered the above questions? See also the commentaries of Rashbam & Seforno on 32:3.
Finally, see Mishna Brura - Hilchot Tefilla 124#5 note 22.
2. Note the 'style' of shirat Ha'azinu as it appears in a Sefer Torah, i.e. the 'ladder'-like manner in which its psukim are written. Then, compare that style to the style of shirat ha-yam, i.e. Shmot chapter 15. Similarly compare these styles to the styles of:
shirat ha-melachim in Yehoshua chapter 12,
shirat Devora in Shoftim chapter 5, and
shirat David in Shmuel II chapter 22.
Notice how we find two types of 'style' in this regard. Can you relate the 'style' of each shira to its content?
Can you explain how these 'songs' relate to key events in Jewish history?
3. Compare the opening two psukim of Sefer Yeshayahu with the opening pasuk of shirat Ha'azinu.
In your opinion, is Yeshayahu using this parallel to the opening lines of shirat Haazinu for simply 'poetic' reasons, or does this carry thematic significance as well?
In your answer, relate to both the primary theme of shirat Ha'azinu and the primary message of Yeshayahu's prophecy.
[See Chizkuni on 32:1!]
4. Compare 32:36 [and its context] with II Melachim 14:23-28, especially 14:26!
Would you say that the navi's use of the phrase 'efes atzur ve-efes azuv' is intentional? Relate this to the prosperity which Israel enjoys during the time period of Yerov'am ben Yoash.
Note the mention of the prophet Yona ben Amitai in Melachim II 14:25! In your opinion, is this the same prophet Yona of Trei Asar (that we read for Maftir on Yom Kippur)?
If so, can you relate this prophecy to that Sefer?
1. Review 31:14-30, noting how these psukim form the introduction to shirat Ha'azinu. Note especially 31:17-21! And 31:28.
According to this introduction, what is the primary purpose of shirat Ha'azinu? In what manner will knowing this song help Am Yisrael cope with situations of distress? How will it help resolve those situations as well?
2. Next, review the opening psukim of the shira (i.e. 32:1-9). In your opinion, which psukim serve as an 'introduction', and what pasuk actually begins the shira itself?
[In other words, after the introduction, what is its opening 'statement'?]
Relate this opening point to your answer to the above question. Could you consider 32:7 as another type of 'opening statement'? Can you explain its thematic importance as well?
3. Now, study the remainder of shirat Ha'azinu.
In addition to translating each pasuk, attempt to follow its theme and flow. Be sure to relate this theme to your answer to the above questions (and to the topic of its introduction in 31:17-21).
Be sure to see Ramban & Seforno on 31:17.
[Do these commentaries support your conclusions?]
4. Finally, review the concluding psukim: 32:44-47. How does 32:44-45 relate to 31:14-30?
In your opinion, does 31:46-47 relate only to the shira or to the entire sefer (or possibly to the entire Torah)? Relate to the word 'ha-devarim' in 32:46 and to the simple pshat of 32:47 (compare w/5:28-6:3).
Based on these psukim, explain the thematic connection between shirat Ha'azinu and the main speech of Sefer Devarim.
5. Note Chizkuni on 42:44.
Then see Ibn Ezra on 42:44. Relate this to Ibn Ezra on 31:1.
1. Note the phrase 'be-etzem ha-yom ha-zeh' in 32:48.
Compare with Breishit 7:13 and Shmot 12:51.
Can you find a thematic connection between these three psukim and their context?
See Rashi on 42:48.
2. In relation to the Torah's use of the phrase 'shamayim va-aretz' in 32:1, relate 32:1 to 30:19, 31:28, and 11:10-17.
Then, see Rashi & Rashbam on 32:1, noting how these psukim can help you appreciate their commentary.
Can you explain why they both quote 11:17.
See also Rashi on 30:19!
[See also Ibn Ezra & Chizkuni on 32:1. In what manner are their commentaries different than Rashi's?]
Now see Ramban on 32:1. Relate to Ramban on 30:19!
Note how his peirush differs with Rashi's.
Can you explain what Ramban considers 'derech ha-pshat' and 'derech ha-emet' in this regard?
What is the difference between them in approach? In your opinion, do these two approaches contradict or complement one another?