These are sprouting up all over my yard and, in addition to wanting to get rid of them, I'd like to know what they are.
Shotweed - Cardamine spp. Good luck getting rid of them - the only thing I've found that works is 2,4-D (roundup) and even then it's not 100% successful.
Grass around them looks like annual bluegrass indicating a moist and compacted surface. Shotweed also grows where it is moist. Manage the soil differently and the habitat for these will disappear. Small spots of exposed bare soil can be seen between the plants, possibly mulching with wood chips alone would be enough to cut out most of the opportunity for weed growth.
Bittercress may be a more common name for the plant in your area as it is here. And a correction to what lorax said... Roundup is not 2,4-D, but glyphosate. 2,4-D is a common active ingredient found in selective herbicides used for broadleaf weed control, whereas glyphosate (Roundup's active ingredient) is a broad spectrum weed killer. 2,4-D can be applied at suggested rates over turf; glyphosate would kill the grass. A selective herbicide containing 2,4-D should do the job if done correctly, however you're likely to have a million little seeds in the soil waiting to germanate, therefore consider the use of pre emergent.