If she is set on engineering, focus on schools that do not require her to pick a particular type right away. Two that come to mind are Clemson and Valparaiso University. Both have programs that provide wide exposure to types of engineering and related advising before the student picks one. Both also have other “ mathy” majors if engineering ends up not being the right path.
Many kids and parents think that because the student likes to tinker, is into robotics, or cars, etc. that they’ll be good engineers. Then they are shocked when they find out that engineering isn’t tinkering but is applied math and physics with pretty heavy lifting at that.
Sure, some disciplines can involve “tinkering.” My son has a ME concentration in mechatronics. He designs circuit boards and when the PCB arrives, he “stuffs” them with their chips, capacitors, resistors, etc. She’d probably hate that.
He’s also into fluid mechanics and goes to a school that has a very high emphasis on labs. Continuum Mechanics, Viscous Flow and Compressible Flow did not have labs (at a school where everything that can have a lab does, even vibrations and rotational dynamics). They were all essentially applied math classes, and very complex math at that.
As @turbo93 alluded to, IE diverges into other high maths. I’d suggest you summon him back to describe what IEs do.
@boneh3ad is into high speed aerodynamics, also very mathy, but completely different maths than IE. He can well describe what he and the engineers who stay on the physics side of things do.
I’m in no way trying to dissuade her from IE. It’s just that IE is different than what most people think of engineering. They’ll describe it better, but think of it as engineering of processes and systems rather than of things.
Hope that helps!
What year is she? My kid who was thinking about engineering got a lot out of the Rose Hulman Operation Capapult program for rising seniors. One thing they do is spend time learning about the various engineering disciplines. My D mostly enjoyed the camp, but decided that she did not want to be an engineer after all; that was a valuable outcome, too.
Yeah, I never enjoyed building stuff as a kid. I just loved the idea of using math to design buildings!
My son doesn’t like to tinker either but loves applying math /science to figure out stuff. IE is a natural for him.
Also he did these summer programs. Michigan State University for Robotics. Milwaukee School of Engineering for CS think basic programming but a lot of fun. Made things move etc with programming. Berkeley for overall engineering but like putting groups against each other in competition. He really liked this a lot. They had to all work together to figure each event out.
During the school year he did. https://www.acementor.org/
This was more civil /construction but done in again competition style and multiple engineering disciplines with engineering mentors almost one on one. Totally awesome program.
Thank you all and @momofsenior1, An math degree is one of the majors she is thinking of. She wants to be employed. Does not really see herself going to grad school right now. She is a 10th grade currently. I should her stuff about Actuary career but it seems most of those jobs are in the NorthEast and we are in Texas. She does not like snow.
Thank you all for the great suggestions. I will start looking for some engineering summer camps.
I missed that you daughter is only a sophomore. Plenty of time to expose her to different potential career paths. Her interests may also change and develop between now and college. My daughter did a lot of growing in those years and really narrowed in on her interests.
My D did well in Math but was sure she did not like math. She later discovered a purpose for her math skills in Chemistry class.
So she was glad to have good math skills to plug in to the chemical formulas.
You might want to look at the camp at Missouri S&T. I’ll link it below. Plus, if she’s REALLY adventurous she can do Explosives Camp the week after! 
I would give one caution though about any summer camp. They will be based around things students of those ages can conceptualize. That means mainly hands on stuff. Even undergrads don’t get a really firm handle on engineering until they are very deep into it. Don’t let a camp cloud her judgement based on a very incomplete picture. She should definitely spend time with faculty and discuss her concerns.
https://futurestudents.mst.edu/summer-camps/jackling-introduction-to-engineering/
@BingeWatcher I did not tinker as a young girl. I baked! I don’t have an aptitude for building. I didn’t fix cars with my dad. Despite this, I became a mechanical engineer and studied solid mechanics. My course work required a solid foundation in math and physics. I have never built a thing. But, I can tell a designer why their part will fail and how to fix the design or how operating specifications should be modified. Not all engineering disciplines involve building. Therefor, I would not discount engineering.
My daughter liked math and chose Industrial Engineering with a math minor and some CS courses thrown in. She loves it. She has basically cobbled together an Operations Research major. Look that up. I think Carnegie Mellon has a major called ‘decision science’ which is very mathy and similar to Operations Research. Georgia Tech has an Ops Research emphasis within their IE department. All of these majors are very math heavy.
I seem to have been tagged fairly late in this conversation so, in all honesty, I am not 100% sure what question I’ve been summoned here to answer. It seems it has to do with math-heavy versus hands-on type work, so I suppose that is where I will direct my comments.
Nearly every flavor of engineering has topics and career paths that involve no tinkering or building whatsoever and others where there is lots of tinkering and building. In all honesty, most engineering jobs are desk jobs that require little to no time with hands on hardware.
@boneh3ad, I summoned you here to talk about that, but more directly, the math of fluids, and what a math loving student might find attractive. Maybe contrasting that to the math path an IE would take.
It really depends on what flavor of fluids you are talking, but it invariably involves a lot of partial differential equations, and often can involve a lot of statistics and numerical methods. Perturbation theory is another fun one.
To be honest, thinking about the type of math associated with a specific discipline is secondary at this point. I loved math but didn’t enjoy fluid mechanics. Similar math applied to solid mechanics was much more interesting. What will matter is finding the subject matter that you care about and is interesting to you. The math is a tool to understand technical matters more deeply and solve problems.
Thanks @VMT. No slight to solid mechanics intended. I knew from my son’s experience that fluids was one example. Heck, I didn’t even know what a tensor was until he got fairly deep in the subject. I think the take home message that you and @boneh3ad helped affirm is that there are many engineering disciplines beyond IE that a math lover who isn’t particularly hands on could enjoy.
@eyemgh. No worries. I didn’t even think there was a slight?.
That you guys. I think D and I need to see if we can talk to some of the engineering faculty at the local U.
Just to add on most engineering jobs don’t need you to build. I hate working with my hands. Almost all my classes and my internship has been theoretical.