Aiden had a tough class today. When I walked in he was in the fetal position on the ground. He said he had a tough time with the work I gave him yesterday to do with Ms. Teresa while I was out. I looked through his work and he did very well with it. He said he still doesn't understand why we flip the inequality symbol when we divide by a negative. I began to explain it to him using the concept that 3<8, but if we multiply by -1 to make it a true inequality we'd have to flip the sign so that -3>-8. Aiden said he understood that, but when it comes to more difficult problems he doesn't understand it. I realized that Aiden is attempting to conceptualize each step. He's getting caught up in the process. I explained to him that what he is doing is equivalent to when when reading a paragraph, sounding out the phonics of each letter when reading. In other words, he's getting frustrated with himself for not being able to "see" each step he takes. I told Aiden that as long as he understands why we flip the inequality with a basic scenario, then from here he just needs remember to do it (when multiplying or dividing by a negative, to flip the sign). He thinks he is not understanding, but he is! I spoke with Ms. Teresa about it and we both see the same thing. Aiden is questioning his understanding, as if there is more to understand and he "doesn't get it". But he really does. At the end of class I gave him a hug and told him that he needs to trust me that he is where he needs to be right now. He knows what he needs to know and he's doing well. He had tears in his eyes (breaks my heart). I wish I could give him the confidence I have in him, so he can feel it for himself.
Andrew was late to school today. We thought he would have enough time to take his quiz on Arc Length and Area. He worked the rest of the period but did not finish the quiz during class. He will resume next class.
Today Carson and I met on Teams. We have been working with linear equations lately. Today I wanted to show Carson how linear equations could be used in real world applications. We worked on problems like "You deposit $100 into an account. Each week you deposit $5 more. How many weeks will it take to have $310 in your account?" Carson is good at solving these problems, but he has difficultly setting up the equation. We discussed dependent and independent variables. In this case the amount of money (in dollars) depends on the amount of time (in weeks). We discussed rates of change. In this case, the rate is $5 per week. We set up the equation y=5x+100 where y represents dollars and x represents weeks. To answer the question, we substituted y=310 and used inverse operations to solve for x. We practiced multiple problems of this nature, emphasizing dependent and independent variables.
Today Matthew and I discussed applications of trigonometry. We discussed angles of elevation and depression. Matthew answered questions like, "If a fire started 8 miles from the base of a mountain has a 14 degree angle of elevation to the top of the mountain, how tall is the mountain?" I encouraged Matthew to set up a drawing to visualize the scenario. He saw this created a triangle and then recognized that we could use the tangent function to set up an equation and solve for a missing side. Matthew set up tan14=x/8 and used inverse operations to solve. Matthew and I practiced a few more problems using this method.
