Today some homeschoolers had their weekly algebra class. They are coming along well, and getting a good grasp of the subject. After class and after I got home, I sent them their assignments for the week. In today’s email, however, I decided to add some detail as to what we covered in class — sometimes I’ll write up a summary like this, sometimes I won’t. So sometimes parents get a good, detailed, written report of what a class or a student in private tutoring covered.
But this email sketches out what typically happens in my classes and private tutoring sessions, so I decided to post it. (But in this post I added a few things to the email to illustrate more of what we had actually done in class, instead of reporting only some of the highlights.)
Students:
Today we started class by looking at one reason why we need to learn to graph linear inequalities (which topic we covered last week): so we can graph, evaluate, and criticize the graphs we use and find in statistics. Graphs of inequalities play an important role in statistics. Then we worked an inequality together: p. 434 #22.
Then instead of doing more inequalities, we started working on graphing linear systems, to make sure we’d have time to cover that topic first. We started out with some motivation: knowing how to find points of intersection is a critical part of understanding how some people navigate, or locate a position on the earth’s surface, using LORAN. LORAN works by finding the intersection of two hyperbolas, as we saw in class. We are not yet ready for working with hyperbolas or systems of hyperbolas, of course; we need to work with lines first. We will build up to hyperbolas one step at a time. (In looking at the LORAN example, we were able to introduce some classic properties of hyperbolas, ellipses, and circles, so we had an idea how a hyperbola was generated and how it was different from other conic sections. And we were able to see how LORAN depends on the basic idea D = RT.)
