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We are now homeschooling my DD8. She picks up on everything very quickly but is very careless. Last year in 2nd grade, she breezed through her schoolwork at her school so she could rush through and still get everything right. This year we are homeschooling her and using mostly 4th grade curriculum, but calling it 3rd grade. She is picking up on everything just fine but she is very careless, rushing through her work. Except now, she makes lots of silly mistakes, because the work isn't super easy.

First, I am wondering if I should be concerned and secondly, does anyone have tips for getting her to slow down and pay attention to what she is doing besides saying it over and over and over.

Also, she picks up on the advanced concepts in the Singapore Math series, but she is moving so quickly that she is not solid on her times tables. I think this is contributing to the silly mistakes. (She made them at the toward the end of the test) I am having play ipad games to work on the times tables at the end of the day, but I am wondering if it is a bad idea to keep moving through the more difficult concepts while she is still getting those down. I have discovered that she is very much like me. She can handle the most difficult word problems and learn a new concept in a snap, but memorizing is not her strong suit.

Extrinsic motivation :-) Set up some system in which she gets something she wants (in our house it's game-minutes, i.e. entitlement to spend minutes playing computer games) for doing things correctly, but not for doing them incorrectly even if "only" through carelessness. Then don't rub it in - it's just the impersonal system that determines she has to do stuff right if she wants < whatever >. You'll need to think about scale quite hard - it shouldn't be so easy to accumulate reward that losing a bit through carelessness doesn't matter, but you also don't want one tiny mistake in a lot of correct work to be devastating...

These days we typically get DS9 to propose and then monitor his own system, which works well though wouldn't have done when we started. Examples: he gets 1, 3 or 5 (depending on level) game minutes for an Alcumus question done correctly first time without help, and when he does a 90-minute maths competition practice paper, he gets 10 game minutes for a good concentrated effort regardless of result, and then an extra minute for every question correct above an agreed baseline. Something like the latter system might work well for you? I think it's important, probably, to count positively - get something for correctness, not have something by default and lose it for mistakes.

I do have a lot of time for Kohn's argument that all such schemes are evil, but they work too well to eschew! I've discussed these arguments with DS more and more and, interestingly, he chose not to have his AoPS challenge problems in the system.

I like your ideas. I do something similar with getting the work done without complaining etc but not for correctness per se. I was also thinking of having her do more practice work if something is wrong so that it doesn't make sense for her to rush and get something wrong because she will just have to work longer. I will try a few things and see if it works.

Is it possible that your daughter is a visual-spatial learner? VSL's can make careless mistakes, have inattention to detail, but can grasp bigger concepts more easily, i.e., harder types of math problems, etc.
https://www.gifteddevelopment.com/Visual_Spatial_Learner/vsl.htm

Another approach is to apply math into real applications like physics and examine the results of miscalculations.... Like the astronauts were flung into space because the thruster setting was too low. Some people latch onto that sort of story impact.

Also,Brownie Math on the iPad has a pretty cool reward system built into it.

As her teacher, you can always mark her grades down for careless mistakes. Then you can make her re-work any problems she missed.

This is what my teachers did to me, because I was always prone to the careless mistake. And it's what my DD is experiencing now, because not only is she prone to careless mistakes, but her previous years of schooling have encouraged more of them (thanks, inventive spelling). DD recently brought home a well-deserved F, and now she's paying some overdue attention to how she spells.

Also, I'd say that if your DD seems to be learning like you, it's probably not a coincidence. Draw from your own experience in order to figure out how best to help your DD learn, because whatever worked for you will probably work for her.