We were supposed to meet online via Teams today. I was logged in ready to go and Ben never came online. I contacted the school to let them know. They checked on him and encouraged him. He first said he forgot. Then he still never showed up. I had a lesson ready for us.
Today we reviewed the various topics we've discussed this quarter. We tried a word problem where Ben had to set up the equation himself to solve it. We need to work more on these after break. Then we solved a system- Ben chose to do so by graphing. He got stuck because one of the intercepts was a fraction. So I showed him how to complete it. Then showed him how substitution could have been an easier method.
Today Ben and I explored problem types where the approach to solving is unknown. It was up to Ben to determine which approach he would try. I gave Ben a problem and he decided he would solve by graphing. As he worked to graph the lines, I simultaneously worked it out using substitution. Then we compared our solutions were the same! Ben prefers graphing over the other 2 methods, but I think it’s because he has the most practice with it. I am trying to get Ben to see the usefulness in the other approaches.
Today Ben and I practiced a set of solving systems of equations. Ben had to determine which approach he would use to solve the system. He had difficulty with these problems today. He did seem a bit less interested today. He wanted to work on his digital designs, so I encouraged him to finish working with me and then I would give him time to do his work. He agreed. I helped Ben as he worked through the problems. He needed a lot of guidance in the right direction. But he pushed through it.
3-2 Linear Functions – We learned that linear functions can be represented in multiple ways, using words, tables, graphs, and rules. Function notation is a way to write the rules for a function f. The output of the function f (x), means that f is a function of the input variable x.
Assignment: For homework complete assigned problems.
3-2 Linear Functions – We watched a video and then completed problems where we had to write a linear function rule from data in a table. Then we practiced finding f(x) for various input values.
I had Hudson do problems from Lesson 2-8 Literal Equations and Dimensional Analysis, 2-7 Percent of Change, 2-6 Ratios and Proportions, and 2-5 Solving equations Involving Absolute Value to prepare for his midterm exam tomorrow. We decided to do a few extra percent problems and word problems involving dimensional analysis.
Today we covered more in depth, the Elimination approach to solving systems of equations. I first showed Ben an "easy" example. He recalled how to add the equations to get either x or y to eliminate. Then I showed Ben the more difficult problem types. These are where we have to manipulate the equation first, before we add, in order to eliminate a variable. At one point, I had to leave to use the restroom and when I returned, Ben took the initiative to finish the problem on his own. He did it correctly after just 1 example! After that, I gave him a problem to try on his own that ended up giving us fraction answers. He's really picking up on this content well!
3-2 Linear Functions – We learned to write and evaluate linear functions using function notation. Then we learned to graph a linear function and relate the domain of a function to its graph. Next we learned to interpret functions represented by graphs, tables, verbal descriptions, and function notation in terms of a context.
Assignment: For homework complete assigned problems.
