It has been quite the year taking Geometry, but alas, with the new school year ahead, my lessons regarding such must come to an end. This will be the last It All Adds Up Geometry edition, and beginning with a monthly schedule this Fall, I’ll be moving on to Algebra II.
Thus, I must conclude this season with where we began: proofs. Proofs, as a refresher, are step-by-step ways to prove a mathematic hypothesis true. We’ve dealt with proofs at their basics, like in Algebraic Proofs | It All Adds Up, and then applied what we learned in geometry to proofs, like with definitions, triangles, and segment geometry.
At first, proofs were incredibly confusing. There were so many seemingly unnecessary rules and requirements, and infinite possibilities. However, as time went on, they almost became a relief to the memorization-dependent processes we began discussing. Honestly. Unfortunately, later on in the year, proofs didn’t tie in with the curriculum, so we let them be.
The good thing is, the most important thing when dealing with proofs is foundation. Over time, you’ll get the hang of your basic theorems, and over the general makeup of your proof. You’ll begin to identify patterns, and from there, as you learn more and more, you can apply such information in the same way. Remember, there might be infinite ways to prove something correct, and there may not be a clear right or wrong (though at the most basic level, especially in education, there are pretty regimented processes).
In the end, things will begin to make sense. Don’t worry.
Over the past season, there have been two main topics that I wished I could have covered. (To be honest, I probably covered <5% of our curriculum on 12 and Beyond).
The first was one of the most difficult topics for me, though simple in observation. True, in the end, it really comes down to elimination. There are plenty of great tables out there to study from, but here‘s the one I used.
Second, in the last edition, I had mentioned that I wanted to cover Surface Area and Volume of polyhedrons, or 3D polygons, but I decided against it as it is mostly formula-based. And, going into the next season, I’m continuing to focus on more concept-based learning. For reference, though, here’s a Quizlet with such formulas.
I came into Geometry with a negative outlook, and left with quite a positive experience. The class was incredibly enjoyable, and went so much more in-depth than just ‘shapes’. In fact, I loved that much of Geometry incorporated aspects of Algebra, and as a result, Algebra (and Geometry) both became more real-world. In all, I’m really looking forward to continuing to gain knowledge and achievement in mathematics.
Thanks for joining me through my geometric journey!
Stay tuned to the Global Interests for news on the new season!