Relationship : Look to the future! At least that is how I imagine this particular common topic. We learn in writing class that relationship is asking questions like "what comes before" and "what comes after", which at first glance does not seem to be about relationship at all. A relationship etymologically speaking is a connection. Connections seem to be made in the present, but that isn't true. We don't instantly form connections with people. It takes time. Building a relationship involves multiple events which we all tell and retell and connect to our lives. Some relationships are so deep that they make up our identity. Our identity in Christ is based in the past and what He has done for us. Our identity in marriage is constantly developing over time. When we think of relationship as something that connects our future to our past through the present, then we see why it is often pictured as a time line. How does this work in mathematics?
The instant that I wrote about Geometric proofs in circumstance, I realized that I lost my chance to show how relationship works in a proof. It's almost too obvious. In order to go from the given to the conclusion, you must form connections. Check. Done. We've explored relationship. That example is too simple, however, and relationship occurs repeatedly in mathematics. For example, in word problems we have a story with a beginning, middle, and an end. We start a word problem by reading it, but we often get bogged down with the details. If John knew what his day was going to be like in the morning, he might have stayed home. Instead in a single morning, our math text has him driving to work, getting stuck in traffic, stopping for coffee, seeing an accident, and then driving home on back roads. Is his entire day really just driving? No. Of course not. Our rate problem relies on the details surrounding his commute to and from work and so it shares the minute details from the drive. How do we proceed with a word problem like this? We ask ourselves relationship questions: "what time did John leave for work?", "what came first on his commute?", "what came next?", "how did John avoid these problems on his way home?". We proceed much like we did in the geometric proof by working from "what do I see and know?" to "what can I figure out from what I know?"
These connections are essential for building brains that can solve problems, and not just John's commute problem. The skills we use here will serve us well when we encounter all sorts of situations, even relationship problems.