Your brain and how it works within your body is a complex adaptive system.
Ecosystems seem like an obvious choice, and there are a number of examples that could be found in that area. Also, the interactions of objects in our solar system.
I have taught physical and life science, however this next year I will teach earth science. As far as a phenomenon in physical science that follows the characteristics of a Complex Adaptive System, I would like to propose that the way that molecules move in a liquid is such a phenomenon. Molecules in a liquid slide past each other, they can’t freely move in all dimension as molecules in their gas form do so. Together molecules in a liquid usually flow downward because of gravity, but it can look beautiful. Ok, so after looking at the definition, liquid molecules are complex and difficult to predict; dynamic as it moves constantly; and they are adaptive as they move depending to the environment around them.
The solar system is an Complex Adaptive System. The planets rotate at different rates which explains why different planets may have a specified amount of days per year, also why the planets have certain temperature based onits location and the pattern it follows on its orbit.
A complex adaptive system, in my opinion, would be food chains/webs. Fewer predators can result in more prey which can result in an increase in predators which can lower prey numbers.
I agree on ecosystems and food chains/webs.
Interactions between species, responses between the immune system and pathogens, behavior of atoms and molecules, weather patterns, cycles in nature such as the water cycle. Each part or “individual” is just following a simple set of rules, but as humans we notice and describe the larger patterns as phenomena that we name and teach 
I agree with the immune system and pathogens being an example.
The biosphere and the interactions between living things that make up the biosphere is an example of an complex adaptive system.
In life science the ecosystem is a perfect example. In Earth the rock cycle and water cycle are great examples, when you think about it science is full of examples.
For an excellent book about Complex Adaptive Systems found in nature, you guys should read “The Quark and the Jaguar” by Murray Gell-Mann.
My lesson cycle is a complex adaptive system. This example is admittedly more adaptive than it is complex.
In my subject I think the topic “solubility” forms a pattern an could be used as an example of a complex adaptive system because “like dissolves like”.
In my grade level students are to learn about adaptability of a species and how/why they have adapted over time. I believe that this is a complex adaptive system because the animals/plants have figured out that they need to change in order to survive in the environment. We discuss how some animals have changed colors because of where they live and if they were a different color they would stand out to predators.
The human body is a complex adaptive system.
The ecosystem, cell generation, electrical currents
The two topics that come to mind are ecosystems and the hydrologic cycle. Both have complex patterns and some identifiable trends while both also adapt to change in the environment.
We will be study Earth and Space science this year. The motion of the galaxies fit the criteria of a complex system.
That’s true especially if you think of the body on the cellular level.
In ecosystems the behavioral adaptations of organisms depend on complex adaptive systems, such as migrations of the monarch butterflies.
Food webs would be an example of a complex adaptive system. The pattern of predator prey with energy flow (10% rule).