The Grand Canyon is an excellent example of superposition and crosscutting, because it is extremely deep, wide, and long, and has thus exposed many layers of rock. Superposition states that layers of rock above other layers will be younger, if undisturbed. Since the Grand Canyon is so deep and has so many layers, it has been possible to date the layers, and prove this theory. The theory of superposition is based on the knowledge that rock layers form on top of one another, i.e. a volcano erupts, laying down an ash layer, the a mudslide dumps some other materials on the top, then maybe the wind blows stuff above that etc. 

The Grand Canyon also demonstrates crosscutting, but it proves it through superposition.The Law of  Crosscutting Relationships states that if a layer cuts down through an otherwise undisturbed body of rock, the layer cutting downwards will be younger. This is proven by the fact that for a layer to cut down, it has to be 
In England, the peppered moth population suffered some drastic changes. As the trees were turning black, due to pollution coloring their bark. There were a few theories explaining why this was happening. One was that the pollution was also dyeing the moths' wings, as it was the trees' bark. The most prominent one, however, was that the moths were adapting to suit their environment better. The moths were originally colored to suit the peppered shade of the tree bark, as to provide a form of natural camouflage. As the trees became darker, the darker moths were harder for predators to see and thus survived longer. There had been very few dark moths seen earlier, as they were spotted and eaten quickly.

One of the main scientists promoting the theory was Kettelwell. Kettelwell went through a long series of experiments to test that the black color was actually a genetic mutation, and that it was rapidly spreading through the population due to natural selection. All of these test confirmed Kettelwell's theory, and as England's pollution is decreasing, and most scientists belief that as that happens the population of light moths will go up as well.
When organisms face a situation with limited resources and overpopulation, they begin to compete over the decreasing amounts of food, water, and space. The organisms will fight each other, and many will not live very long. The organisms with beneficial traits, such as longer claws, being taller, running faster, etc. will live longer than those without, and pass those traits on to their offspring, who will live longer, and so on. The changes will build up over time until the other organisms die out completely, or become a different species.

Take for example, a herd of horse-like animals, that eat leaves on trees in Africa. If the resources become limited, such as all of the leaves being eaten off the lower parts of the trees, it is likely that some organisms will begin to starve. The organisms with longer necks would be able to reach leaves still, and survive to produce offspring. Those organisms could eventually eat all the leaves on their part of the tree, and so only the longest of the longest necked animals would survive. Their necks could keep genetically stretching over a period of time, until all of the organisms had an extremely long neck, creating the giraffes. 
When making paper pet families in Science I learned a multitude of things about genetics. First of all, I learnt that when there is a parent with homozygous dominant alleles, the children from that cross will all have the phenotype of the parent with homozygous dominant alleles. Also, I learned that a lot of things don't turn out exactly how probability says they will. My paper pet family only had one male child, and five female children, even though the odds were 50/50. However, the skin color ended up turning out 2/3 blue and 1/3 yellow, even though the odds on that were also 50/50. (There was a heterozygous and a homozygous recessive as parents.)

The paper pet families taught me much about genetics and probability, and I was able to put much of the knowledge that I learnt from it into use in many other situations later in the year. The paper pet families made it easy to understand Punnett Squares, and helped me with other "genetics problems." Although I would have most likely been able to do well without the practical experience of the paper pets, it would have probably taken me longer, and the concept would have been harder to grasp.