Today we did a Mock Quiz to prepare for Ben's Quiz tomorrow. Ben did very well. I had Ben lead the problems, with me only interjecting to give assistance when needed. Ben showed that he knows how to find the slope given a graph, equation of a line, or two points. Ben showed that he can graph a line when given the equation. Ben showed that he understands horizontal lines are y=# with 0 slope and vertical lines are x=# with undefined slope. I think he is ready for his quiz tomorrow.
Today we discussed how equations in standard form can be graphed using two approaches. First we reviewed how to manipulate an equation in standard form to slope intercept form. Ben was slow to get started. He closed his eyes a lot and the pencil fell out of his hand as he was writing. I asked if he got enough sleep and he said yes but was still tired. We continued. Ben eventually was able to get the equation in slope intercept form and graph it. Next, we reviewed intercepts. I showed Ben that to find the y-intercept you make x=0. And to find the x-intercept you make y=0.
Ben took a Quiz yesterday. I graded it with him today and he got a 90% on it. His only error was from plotting a line with a slope of 4/3 instead of -4/3. Ben is doing really well with this content. After we reviewed the quiz, we discussed linear equations in standard form: ax+by=c. We talked about how a, b, and c are just constants. I showed Ben how you can apply algebraic manipulations to turn equations from standard form into slope intercept form. At first, Ben was rusty with his algebra, but then Ben was able to easily manipulate the equations. At the end of class, we discussed x and y intercepts. Tomorrow, we will go deeper into this topic.
Our morning started out by discussing neurodivergence in brains. Ben told me he forgot to take his medicine this morning and might be a little off because of it. I asked him what meds he took and he explained it was for his ADD and depression. We pulled up some research on ADHD and Autism and discussed how he is affected by it. Then we did a Mock Quiz on Linear Equations. Ben did VERY well. He usually starts out slow, as if he is confused on where to begin. But today I did not give him any hints on where to begin. He pondered for a while and reached the solution on his own. I was so proud of him. He showed me he can identify a slope and y-intercept given a graph or equation. He showed me that he can write the equation of a line given it’s graph, or two points the line passes through. He is picking up this information very well.
We discussed Ben's current grade is a 72%. Because of his low test grade, it's bringing his average down. I am confident he will do much better on this next test. We began to review for it today and he will take a test on Monday. Today's review included: finding the slope of a line given the graph, the equation, or points the line passes through, Graphing lines given the equation, determining the equation of the line given a graph and/or points the line passes through. For the very first problem, Ben said, "I don't know how to do this." I said, "Yes you do Ben." He said, "NO I DONT." I said, "Ben, you might have trouble getting started, but I KNOW YOU KNOW THIS STUFF. Take a second to think about the given information." He wasn't happy. I reminded him, "What two things do you need when working with a line?" He responded unsure, "Slope?" I said YES! And reminded him the y-intercept. He knew exactly what to do! He just needed a little confidence boost-reminder. Ben did excellent working today. He went to the bathroom, I told him to leave his phone, and he was only gone for a few minutes.
Hudson and I worked on solving the second page of the review for the test tomorrow. First we investigated how to set up absolute value algebraic equations when given two points on a number line. After a few examples, Hudson solved several of these with no problem. Next we solved three literal equations. Then we set up and solved problems requiring conversion of units. Finally, we used dimensional analysis to solve several word problems.
Ben was absent for the first 10 minutes of class. When he returned we got started on word problems. Ben is picking up on this material quickly (compared to students I've taught in the class). I told Ben that when he puts his mind to it, he is capable of doing hard things. He's very bright, sometimes just getting him to do the work is the challenge, not the actual work itself. I'm very proud of him lately. Today we wrote linear equations to model population increases, temperature decreases, and other similar real world scenarios. We used the equations we wrote to predict future amounts. Ben did an excellent job today.
Ben was gone for the first 12 minutes of class in the bathroom. When he returned, I asked him to graph a line, with no help or hints from me. He knew exactly where to begin. He plotted a point on the y-axis. His only error was plotting it with a negative slope instead of a positive slope. It was a great attempt though. Then we moved on to showing how linear functions are used in the real world. We used the example of earning money over time. We discussed how if no money is spent, the line would show a positive slope. Then we moved onto a word problem activity. Ben did very well with it. We used scenarios like, "Write an equation to model the cost it would take for a consultation if it costs a $50 flat fee and $25 an hour there after." Ben was able to write C=25h+50 very easily. We covered multiple examples and Ben wrote the correct equation each time. Way to go Ben!
Hudson and I worked on solving algebraic equations involving absolute value, number lines, and proportions. Next, we determined the percent change for increases and decreases in value. Then we evaluated expressions for variables with a given value. There is a test on Thursday so I will find similar problems to the ones that are more of a challenge for Hudson.
Today we discussed how to find the equation of the line given: 1) The slope and y-intercept, 2) The graph, and 3) Two Points the line passes through. At first, Ben is slow to get started. He needs reminders on how to approach the problem. I am hoping through more repetition he will gain the confidence to know how to approach the problem, instead of answering, "I don't know," each time we begin a new problem.
