AoPS Intro C&P summer plan for DS12 & public-schooled cousin. Help me think this through, please.

[Noreen Claire]

If you were to set up a summer-long, light-ish course using AoPS Intro to C&P book, for a BA/AoPS kid and his smart, public-schooled cousin to work together (via zoom, email, & occasional in-person visits), would you:

• do only the problems in the book? 
• do only the problems in Alcumus? 
• do a mix of both? 
• ignore the challenge problems?
• other? 

Are there sections/chapters that we can/should skip? (DS12 will likely go back and do those without his cousin after they finish working together.) Any other ideas? I'm going to work through/review the book these next two weeks before they start, but I wanted to get an idea from anyone who had used the book already. Thanks!

[daijobu]

It sounds like you want to streamline the class?  Then, yes, you can do any or all those things.  

We studied the entire book, but didn't do alcumus, probably because it didn't exist at the time, or maybe I was unaware of it.  You can certainly skip the challenge problems to save time; I do that with my students who are short on time.  Chapters 9-15 are fairly different from the first 8 chapters, so there's a natural stopping point anywhere on or after chapter 9.  I think the first 8 chapters are the most fundamental.  

[Not_a_Number]

I'd spend way more time on drawing pictures and the multiplication principle than the book does, lol? Probably not an option, but in my opinion the book doesn't do an adequate job with the fundamentals.