The first two articles presents insights (as does the story—7th article) for the first chapter of Pirkei Avot (the Mishnaic tractate of 'Ethical Principles'), of which we study one chapter each Shabbat until Shavuot (and many repeat the cycle until Rosh Hashana).
The ultimate goal of leaving Egypt was not just to escape slavery, but to forge the Torah Covenant at Sinai--
There is a unique mitzvah for the seven weeks between the two holidays (article #3), Counting Omer .
A major theme of this week's reading, Shemini, is Eating Kosher — see articles #4-5. Article #6 is also for Shemini.