I believe that with NMF, I would look at Texas A&M. The NMF scholarships come with a non-resident tuition waver. You may be able to get the total cost in your range.
If your student is NMF, I believe that Texas Tech has a full ride scholarship program (tuition and housing). They have a good engineering program, but it is in Lubbock.
NMFs typically have better options than Lubbock 
But the goal here may be to find full tuition rather than full ride scholarships- 10k from parents + 5.5k federal loan + a summer job and they covers room and board.
DO run the NPC on many colleges, especially HarveyMudd and Northwestern which are excellent for math and will take into account the fact you’re a family of 8. But also St Olaf, UMN, UArizona, UMaryland College Park.
Reaches for everyone but typically very generous with need based aid: Williams, Princeton, MIT, Uchicago, Caltech.
Wow! Thanks for all the info . . . you folks really deliver. And thanks for your patience, too, as figure out how to ask what we’re asking. You make a newbie feel welcome.
It looks like finances are the biggest issue. Wisconsin has had excellent math, a nice Honors Program math sequence- son did grad level courses as part of his honors degree. Check out the math grad programs rankings from US News and World Reports for ideas, also check on some other potential majors. Being in a stellar STEM department does mean interaction with top professors. Cross reference with affordability. UW likely will not meet your cost needs although it is a fantastic school- academics and campus et al.
Utah is obviously not east of the Mississippi, but has a strong math program and good OOS merit aid. It’s certainly a good safety choice for admissions purposes and a very pleasant location.
Full tuition is not hard to get (you don’t need NMF for that, though 4.0UW appears to be quite important to them) and in addition they have 30 full ride (Eccles) scholarships per year. Here’s a relevant example:
https://unews.utah.edu/university-of-utah-student-awarded-prestigious-churchill-scholarship-2/
If you don’t mind a private college, Franciscan University in Steubenville is friendly to homeschool students. They are VERY conservative Catholic though (which is exactly what we are looking for, but you might be seeking different options.)
What is her goal with math? Engineering? Applied math? Computer science? Do you have financial need? Maybe some of the tech schools would be a good choice, if the aid is enough.
@MYOS1634 You can write off Texas Tech if you want. I do realize that Lubbock is what it is. However, the University is one of the top 25 favored by HR recruiters. Further, if the family has financial concerns and multiple children, then Tech has them covered. Full tuition, full room and board, plus stipend, and study abroad covered for NMF. Further, it has excellent programs in certain fields. It has a well regarded honors program as well.
No, it isn’t Harvey Mudd or Princeton. But, this student is guaranteed admission to Tech, guaranteed a full ride to Tech, and guaranteed to be a bigger fish in a smaller pond. It all depends on the experience the student wants coupled with the cost the family is able and willing to absorb.
But would TTU be as suitable as tOSU if the student wants to study math at a highly advanced level?
https://math.osu.edu/courses
https://catalog.ttu.edu/content.php?filter%5B27%5D=MATH&filter%5B29%5D=&filter%5Bcourse_type%5D=-1&filter%5Bkeyword%5D=&filter%5B32%5D=1&filter%5Bcpage%5D=1&cur_cat_oid=5&expand=&navoid=597&search_database=Filter#acalog_template_course_filter
While not a safety for anyone, her stats seem like she’d be a viable candidate for all women’s colleges like Wellesely or Smith, both of which may offer significant Financial Aid. They both have strong math programs.
Here is an option I would consider. Ohio University has an Honors Tutorial College. It is very selective and while you seem to be very qualified they only take one or two candidates a year in the various disciplines. However, if you are not accepted to the HTC they will accept you to their regular Math Program. If accepted to the HTC you would receive a full tuition scholarship (maybe more you will have to speak with them). If not there are others scholarships you would definitely qualify for. Good luck.
https://www.ohio.edu/majors/undergrad/programs.cfm?programID=14443
https://www.ohio.edu/honors/future-students/programs/math.cfm
@ucbalumnus That’s a fair question, but looking at the financial aspect. A full ride at TTU is still cheaper than in-state at tOSU, which leaves funds for graduate school (if that is the goal). Again, my point is that if financial concerns are important, one should not discount an automatic total cost of attendance scholarship.
While not a safety, Rensselaer might provide a package worth her consideration.
When I went to Wellesley (mumble mumble) years ago, my roommate was home schooled and a math major. About half of her classes in her major were at MIT. We didn’t stay in touch, but from what I read in the alumni magazine she is doing quite well for herself.
OP, I say this with all due respect, but I’m curious about the fact that she’s taken a lot of college math classes, but scored less than an 800 on the Math PSAT. Has she taken subject tests? I say that only because, typically, kids who are taking college math classes are easily scoring both an 800 on the SAT math and 800 on SAT II math. Those will be the kids she’s up against. I presume her SAT score will be higher than PSAT score, so possibly nothing to see here.
Also, Otterbein SAT math averages are fairly low, so I would still have her take subject tests and maybe AP exams in the event that none of the Otterbein classes transfer to the schools she’s looking at. My encouragement to her/you is to have her cover all her bases as a homeschooler.
My homeschooled son did both community college and AP exams for his STEM subjects, simply because we didn’t know what would transfer. In the end, MIT actually took his community college math classes for transfer credit, so he was able to start in upper division math classes (as a math major). MIT only took one AP score, and didn’t take any of his multiple physics college courses for transfer credit, as per their policy of placement rather than credit.
I second the idea of UAH. My middle son loved his visit there; their STEM programs are strong and financial aid is great. Alabama would be another one to consider if she’s NM.
@sbjdorlo PSAT math top possible score is 760. (Depending on the test date, 750 is -1 or -2)
Also look at Bryn Mawr – it’s one of the few full-need schools that also offers merit and they’d give merit for her stats. Cross reg at Haverford, Swarthmore, and UPenn – so good math offerings. Also a studious environment. Free frequent transport to the schools.
Also look at Union College in NY – one of the few LACs that has tech programs. The FA is really good. Also needs women. Potential downside is its partying reputation. If she can ignore that then she might like Union for the many other things it offers.
Also look at Connecticut College and Wheaton College in mass. They both have exchanges with mathy places. Conn Coll you can cross the street to the Coastguard academy and take STEM that may be high enough level. Also they offer a 2+1+1+1 program with Dartmouth, allowing study away in Jr. year, return to graduate in Snr year and then one more year at Dartmouth to graduate from there.
Google also 12 college exchange for schools that participate in this exchange program. That might give you some flexibility
Only you can run npcs to see if schools are even in the ballpark. Many of the schools mentioned are great schools with great aid, but the aid is only great for your family if it gets your cost below$10000. Case, for example, gives merit around $25-30k for the stats you posted which is not low enough for $10k. You really need to spend time with NPCs to see if need based aid will work at all.
Our college sr graduated with a similar scenario and also needed costs to be around $10k and it had to be merit, not need based. (our number of dependent kids at that point was also 6 but we have never seen much of an impact due to family size bc kids aren’t overlapping in college.) Not all u’s allow UGs to take grad level courses, so that became his first filter. Merit, automatic and then competitive, his second. Then he contacted depts about UG research. Then we visited.
I know it is in your backyard, but the HTC would probably be a great fit. She could apply to competitive scholarships like Top Scholars atUSCarolina. Spend time looking at the scholarship link on the FA forum. You should find several u’s to research further.
Fwiw, we are homeschoolers and my kids’ courses completed at home have been accepted without question and they have been awarded competitive merit, so I wouldn’t be concerned about that. Just make sure you prepare course descriptions, a counselor letter, and a school profile detailing your student’s approach to submit in addition to the transcript.
Math offerings:
Bryn Mawr: http://www.brynmawr.edu/catalog/2017-18/areas_of_study/math.html
Connecticut: https://www.conncoll.edu/departments/mathematics/courses/
Ohio: https://www.ohio.edu/cas/math/undergrad/courses-resources/ugcourses.cfm
RPI: http://catalog.rpi.edu/content.php?filter%5B27%5D=MATH&filter%5B29%5D=&filter%5Bcourse_type%5D=-1&filter%5Bkeyword%5D=&filter%5B32%5D=1&filter%5Bcpage%5D=1&cur_cat_oid=10&expand=&navoid=233&search_database=Filter&filter%5Bexact_match%5D=1#acalog_template_course_filter
UAH: http://catalog.uah.edu/undergrad/course-descriptions/ma/
Union: https://catalog.union.edu/content.php?filter%5B27%5D=MTH&filter%5B29%5D=&filter%5Bcourse_type%5D=-1&filter%5Bkeyword%5D=&filter%5B32%5D=1&filter%5Bcpage%5D=1&cur_cat_oid=14&expand=&navoid=499&search_database=Filter&filter%5Bexact_match%5D=1#acalog_template_course_filter
Wellesley: http://wellesley.smartcatalogiq.com/en/2017-2018/Course-Catalog/2017-2018-Course-Catalog/Departments-and-Programs/Department-of-Mathematics/Mathematics-Courses
Wheaton: https://wheatoncollege.edu/academics/programs/mathematics/#program-tabs-courses
Compare to The Ohio State University: