The second one looks like Mimosa pudica (the one that closes its leaves at contact) I treat it like a weed. Its roots grows really deep hence it's hard to pull out.

Omar

Here is a link that might be useful: Mimosa pudica

Thanks Omar, I'm sure that's it. The flower definitely looks like a mimosa flower, a very pretty weed when it flowers. Only hardy in zone 11? Must reseed easily.

Not native to this area and not evergreen, so may not be worth moving over here.

The other is either ice plant or sedum, might have to wait until fall to see if it blooms or not.

I like them both!

To each his own I guess, I've been trying to collect seeds from one small mimosa species like that evey year before my husband runs over it with the mower. :=(

There are definitely varieties that are native to North Texas.

Here is a link that might be useful: Sensitive Briar

I have the sensitive briar growing in 8a-b. I think their are different varieties of it. I had a horrid variety when living in Hawaii. It is considered a pernicious weed their. It sends out rooting runners from a central deep taproot and stays low to the ground sending thorny arms everywhere. It can not be chopped with a lawnmowers since the arms are often below the sod. It is a thorny bane to all barefooters and we are many in Hawaii. We used to shake our heads at the touristas that thought it such an exotic plant and would buy them to take home. Then I moved to Central Texas and met their well behaved cousin for sale in a Native Nursery. I like them now. They grow wild on my land. They do not take over. I let them go. My girl friends in Hawaii think I am crazy now too. I would NEVER take the type that has invaded there home.

Shirley, I think your first picture is portulaca pilosa,(Kiss-me-quick), a Texas native wildflower, or weed, depending on your point of view. It is said to appear in stressed lawns in July and August. The tiny blooms only open for a very short time in the early morning, but reseeds at a tremendous rate. It thrives in drought conditions.It comes up between the pavers in my paths.
Jim

Portulaca pilosa looks right. I have some portulaca growing in my containers and they are very similar. The leaves on the native one are closer together. Wildflower or weed? That's easy, it's a wildflower. No stressed lawn here since there is no lawn, it's been thriving with no water in the toughest spots so definitely a keeper.

The second one is probably Sensitive Briar because it's native to this area and that answers the question I had about the hardiness. I will try to rescue it from the mower. It won't be the first time I've dug up weeds from the neighbor's yard.

I just call it wild moss, Jim, and pull it as fast as I can. It can be such a pain.

I'm with you Carrie! It and purslane too.
Jim