Kate has noticed her hands! She spends long periods of time observing them, puts them in her mouth, and uses them to bat at objects that come close enough for her to touch. We have started introducing her to the first of the Montessori tactile mobiles, a bell on a ribbon. It is developmentally appropriate starting at around 2 months or when the baby starts batting at the visual mobiles, which was 3 months for Kathleen. The bell on a ribbon appeals to her senses of sight, touch, and hearing. It also teaches her about cause and effect, and that she can affect the world around her. This is therefore her first intentional introduction to physical science.
In addition to the bell on a ribbon, we also have a set of ankle bells that a friend made for Kate. She says they are a traditional gift in India for the mother-in-law to give to her grandchild, and they help the baby notice her feet. I started putting them on Kate as an early newborn and her unintentional movements would cause them to jingle. At 3 months she is starting to gain control of her arms and legs and she is starting to appreciate that she can deliberately create the ringing herself.