Lovemydd, a lot of what you've written sounds similar to my dysgraphic ds' experiences at the same age/grade. Please know that there may be other reasons (quite a few other reasons) why you're seeing these issues in your dd, but I wanted to point out the overlaps with dysgraphia just for your knowledge. If you haven't googled dysgraphia yet, you might want to take a quick look.
Polarbear,
suggested Xtramath.com to improve math fluency. DD hated it and complained about training to be a calculator.
Your dd clearly has something going on impacting her ability to show her work in math... but I did want to point out one other thing... math fact fluency isn't something that's necessarily age-appropriate in 3rd grade, no matter how high a child's IQ or math conceptual ability. Some kids are ready to become "math calculators" in 3rd grade, others aren't going to develop quick fluency with math facts until they're almost into middle school. And really, if you think about it, you don't really need math fact fluency until you get to math such s algebra/etc where you want your facts to be readily-accessible so you can focus on the deeper more challenging work. I realize a lot of elementary school teachers are bought into the math-facts-drills so you have to deal with it on some level, but for *most* kids, who don't have anything else obvious going on, I wouldn't worry about math facts not being automatic in 3rd grade.
She started saying things like “I hate math. All I do is learn tricks to solve things I already know how to solve.”
My kids had this same issue to with the way math is taught in our elementary schools - here a lot of the elementary school math is programmed to "explain" math in ways that people who don't naturally understand math will "get it" - which can be absolute torture for the 50% or more of kids who *do* understand math and can just learn it straight-up

The mad minute tests at school are the bane of her existence. She can never finish more than a third of the problems.
Have you ever had her do a "mad minute" for you at home, answering orally instead of writing down the answers? The "mad minutes" were the first place we *really* noticed our ds' dysgraphia kicking in - (before we knew he was dysgraphic). His teacher required students to be able to complete a certain number of math problems correctly before progressing up to the next set of math facts - and ds was stuck on "fact set 1" - forever. This didn't make sense to us, because we knew that ds was good at math. The problem wasn't the calculation - it was the writing - his answers were all correct, but he couldn't write fast enough to complete the work.
It's also possible she could have an challenge associated with calculating the math facts too - having her answer a set of facts orally at home will help you tease out if it's the math that's the issue or her handwriting speed.
She has no difficulty with forming her letters-in fact she has beautiful penmanship. Even her teacher commented on how she doesn’t write but draws each letter – that is part of the problem. [quote]
Actually, that might be part of the diagnosis. That is essentially what dysgraphics do - they draw their letters, because they don't develop automaticity of handwriting. Dysgraphics can have amazing drawing abilities - my ds was so good at drawing that adults jaws would drop when he showed them his work (not saying that to brag, but to illustrate a point). This was one of the reasons we never suspected he had any challenges at all related to fine motor skills or handwriting. My ds is in high school now but if you ask him, he'll tell you he draws his letters, and he has to think about and remember how to draw them each time he uses handwriting.
[quote]Her pencil grip does seem weird to me but she says she is comfortable. And as I said before, she can draw for hours and not complain.
Does her pencil grip when she's writing the same as when she's drawing? When our ds was learning to write, he defaulted to the same pencil grip he used when he drew - it worked well for drawing but wasn't the grip that was taught in school for handwriting. If you google dysgraphia you'll find info on pencil grips - some types of dysgraphia have odd pencil grips, others don't.
I have asked her about what is causing her trouble writing and she does not have any real reasons that I could pull out from her.
She's still young enough she might not really know why she has trouble. My ds didn't really start to be able to verbally express what was challenging about writing until he was around 9 years old.... but otoh, he also has an expressive language disorder in addition to dysgraphia. One thing you could do to see if it's the handwriting or a combination of handwriting + difficulty with written expression is to ask her to "write" the answers to her homework or write a story by telling it to you orally, and compare the output of # of words and ease of output to a similar exercise using her handwriting.
Regarding talking to the doctor, can I just make an appointment for this even though it is not really an urgent issue or should I wait 6 months for our annual visit?
You could start by just faxing or emailing the dr a description of the things you've noted here, express your concern and ask for his/her advice (be sure to mention that your dd's teachers last year and this year have noted the trouble with writing). The dr might recommend an appointment now or instead might make a referral to a private evaluator (that's what happened with us when we realized we needed to figure out what was up with our ds in 3rd grade - we asked via fax, our ped gave us a referral). Our current ped would most likely want to make an appointment first, but they will make an appointment for concerns such as this.
I have personally observed her palms sweat when asked to write more than a few sentences at a time
This is interesting... same thing happens with my ds, happened a lot when he was younger. I never made the correlation to having to write, just thought he was a kid with sweaty palms - but it did happen only when he had to write!
Which brings up another thought... there are a few of us on the list who's children are diagnosed with Developmental Coordination Disorder, which impacts more than just writing (but dysgraphia seems to be associated with it). DS also has some issues with fluctuations in body temperature which I suspect are associated with his DCD... this is probably absolutely *nothing* that is going on with your dd, but if you've noticed she's been slow about other developmental milestones such as walking, learning to ride a bike or tie her shoes, is slow with buttons/zippers etc... it's possible she has either some type of motor challenge or DCD. Please take that with a huge grain of salt though - you haven't mentioned anything so far that is outside of dysgraphia itself, other than organizational challenges (which are common with DCD).
I'd do two things now, possibly 3: 1) email or fax your pediatrician and ask for advice, and 2) consider requesting an evaluation through the school. Make the request in writing, and mention that both this year's teacher and last year's teacher mentioned the speed of her math fact fluency and handwriting as issues. If you'd like specific advice on how to initiate the request etc, let us know. The third thing can wait until you need the advice specifically, or you could make the call now - see if you can find a local parent advocate's group - there may be a group local to you, these groups are federally funded and should be able to provide brief free advice re the advocacy process with school, and they were a *huge* help for me when I was first advocating for my ds because they have *local* knowledge of your school district and quite possibly your specific school and teachers/SPED process etc.
And... I'll add a 4th thing... this I'd start doing now. Scribe for your dd for her homework for the time being (she tells you what she wants to say, you write it down). Let her start keyboarding at home - either by using a program like "BBC Mat Typing" or by just letting her hunt and peck around doing whatever she wants to on the computer. It's not necessary to learn traditional touch typing - students who are slow at handwriting can dramatically increase their output via adapted keyboarding (where they come up with their own key mapping by trial and error).
And... talk to your ds' teacher and ask if she can start trying out a few informal accommodations in the classroom *now*. Oral response for math facts "mad minutes", keyboarding for Language Arts/etc. Your teacher may or may not be willing, but it's worth asking. Once you make the request for an evaluation through the school, the school may automatically start a process called "RTI" (Response to Intervention), in which they could try out accommodations such as keyboarding.
The one thing to be aware of while working through a school eval vs private eval - the school is going to be looking at how to enable your dd to be successful in her academics; the private eval will (if there's an issue) begin the process of creating a map for how to be successful in *life*. Although school and life overlap quite a bit in 3rd grade, these are essentially two different objectives. Having a professional who was not concerned with providing what had to legally be provided through school for one year, but who was able to objectively look ahead at how our ds' challenges would impact him in the long term at different life phases was extremely helpful to me in making a plan for advocacy at school. Hope that makes sense!