Here’s what I used to think about vertical alignment (in a nutshell):
You look at the overarching ideas and understandings plus the discrete facts and skills of each course and make sure there are no significant gaps or overlap, although you do want some things to “spiral” throughout the grade levels. We never really broke that word “spiral” down, we all just used it as if we had a common understanding of what it meant. You also, of course, make sure that things are increasing in difficulty and not the other way around.
Here’s what I now think about vertical alignment:
You can take at least four of the most fundamental and powerful concepts of a discipline (e.g. power for Social Studies and energy for Science) and you write out statements of conceptual relationship that apply to the grade level content and increase in sophistication throughout the grade levels.
Note: this is not the only way to articulate vertical curriculum alignment of conceptual understanding and it is certainly not complete, we still have to look at knowledge and skills alignment. And, most importantly, these are not the only concepts that will be taught at each grade level! It’s simply one way to ensure increasing sophistication of some of the fundamental and powerful concepts of the disciplines. It also works best for content-centered disciplines (math, science, social studies) than for process-centered disciplines (language arts, music, etc.)
Here are a couple examples:
Science 6th Grade – 12th Grade

6th grade Earth Science Earth’s energy comes from the sun and from geothermal sources.

7th grade Life Science Organisms require energy to survive.

8th grade Physical Science Energy transforms from one form to another.

9th grade Earth/Environmental Science Humans use both renewable and non-renewable resources as energy sources.

10th grade Biology Life depends on mitochondria and chloroplasts because they are important energy-related organelles.

11th grade Chemistry Molecular structures help determine potential energy levels.

12th grade Physics Motion and energy demonstrate a quantifiable relationship.

Social Studies 6th Grade – 12th Grade

Concept: Power (sub concept = economics)
6th People in power tend to control resources to keep themselves in power and increase their power.
7th People in power tend to create structures and institutions to keep themselves in power and increase their power.
8th A nation can create a system that limits power and therefore reduces the chances for those in power to keep and increase their power.
9th People in power often use religion and trade to maintain and increase their power.
10th Economic structures often shape the distribution of power in the world.
11th Economic power contributes to a person’s ability to express or utilize their individual rights.
12th Economic power mixes with political power to create systems that advance the interests of certain groups.

Can you see how this kind of vertical alignment is much more sophisticated than a traditional way of doing it?!