Basic content:
If you expect them to get into Algebra 1 in 7th grade, you need to cover pre-algebra,now. This is essentially one equation with one unknown. I would make sure you cover this very solidly as there become a lot of problems later on when kids lack the ability to manipulate sides of an equality. It is important that they get some solid practice with mechanically "doing the same thing to both sides of the equation" E.g. adding to both sides, not "throwing it over from one side to another and then reversing the sign". You need to take the time and give them lots of drill.
Assuming too much brains/knowledge:
In general, you need to be cautious about assuming your level of knowledge or even brains in kids with much less experience and whose brains are not physically mature. I see this problem all the time (expert blindness). I'm not saying not to progress the kids. Just to be sensitive to your likely blind spot and to watch for it.
Learning what you will teach:
It is also good that you recognize your level of ignorance of the content. Math prof is fine, but you need to get yourself up to speed on the content for this course. A question on SE is not adequate to educate yourself. IOW, you need more detail than my first para here. But at least you recognize your gap.
Go get some competing textbooks and read them (maybe outline them in topics covered, not saying read word for word) so that you have some basic feel for typical pre-algebra content and how much it may vary.
In addition to learning what topics are covered, you should practice a homework problem or few; work through some of the examples, etc. Don't just assume you are smartypants math prof. Make sure you can do all the manipulations. And also, it puts you in some "walking in their moccasins" so that you get the feel of what the students must learn. After all, your own experience will be in dim past.
In addition, glance over the content in the year before pre-algebra (I can't even recall what that was) and of algebra itself. This is so that you have sufficient battlespace situational awareness that you don't give the kids a gap. For the year before and after, I think just looking at their past year book and likely next year book is sufficient (don't need to look at competing texts). You don't need to work any problems here either.
Once you have done all that (maybe 2-3 long evenings), you will be able to at least converse about the content with some baseline. At that point, I recommend interviewing a couple teachers (you will have generated some questions from the task I gave you). Go over content coverage, likely hard/easy parts, and ask for a few tricks. Do this with real teachers face to face.
This site is mostly junior college pre/calculus teachers. It has weak coverage of K-12. There are also blogs, forums etc. in the greater web (not SE) where you have middle school teachers. But I would try for some face to face. But at least an electronic exchange with them will be better than at MESE. In addition, do your "task" first, rather than reaching out before you have educated yourself.
Level
Note, that I have a little confusion as to their level. In the dark ages, Algebra 1 was stereotypically 9th grade. Pre-algebra was 8th. Kids who were one year advanced covered Algebra 1 in 8th. Of course these kids may be a couple years ahead. And there has been some movement to push 8th grade algebra for all (a failure). But certainly the most advanced kids may be able to handle Algebra in 7th. The point I am making is just to make sure that you know their real level (this is a key thing to assess) and don't miss out on some grade 5-8 content that they need to be getting.
Offspring
Treat your boy similarly to the other students (no familiarity or references to family/home life) and ask him to call you Mr. Umptifratz. Don't be harsh with him. But just have a normal teacher/student mode of engagement. No favoritism or the converse. Talk to him ahead of time, so he understands the need for this and is actively supporting this policy.
Class time
Use a book/workbook. Do not just invent what you want to talk about (same applies for college courses...just pick a book as a scaffold...it may not be perfect but nothing is, including your mishmash).
Try to keep it active, with some games, drill, solve and pass papers, etc. But do not make it math contest focused because then when do they learn basic content. Teach a standard pre-algebra course.
Mesh with other 2 days
This is actually kind of a puzzle to me. How do they learn all the stuff they need for her class, with less time. how does your stuff work, when they don't have full year of her stuff. Etc. But at least we know it's a puzzle. Baseline, I assume that she will be covering stuff from standard 6th or 7th (whatever that is, advanced arithmetic?) and you will cover pre-algebra, which is stereotypically 8th? But I am not sure if this is correct.
You should at a minimum review what content will be covered in their regular course, so you know it. I guess if the class is structured so that they just spend a lot of time drilling arithmetic, perhaps your smart kids can just do with less drill (there) and simultaneously learn pre-algebra on 3 days per week. Possible maybe. But keep your finger on the pulse and see how things are going. Ideally the other teach covers major principles on the 2 days she has the kids and uses the other 3 for more practice. (I imagine she has a bigger class and you are selecting out the top kids for a few days/week?)
She also may know a lot about basic middle school math, so you should consult her as one of your face to face interviews. (Not just how you mesh together, but she may have advice for you on your own 3 days/week. She is an SME.) After doing the "task" so you are educated enough to ask better questions and learn more.
This whole thing sounds tricky in and of itself, so it is important not to have any rivalry with the other teach (one more straw on the donkey). Be down to earth and talk to her as a colleague and win her over.
