Today I had Ben work at his Dry erase board. First I showed him an example of finding an equation of a line with a given slope through a given point. I showed him two ways to do this. One way using the point slope form, and one way using the slope intercept form. I asked him questions as I worked at the board. Then I had him decide which way he prefered (He said slope intercept form). Then we created a new problem and Ben worked it out. He got distracted a few times, playing with the Expo markers, but he was easily redirected back to work. He was able to solve the problem using both ways. He again decided that he prefers working with the slope intercept form.
Today we continued with Point Slope Form. Ben was in much better shape today. He apologized to me about yesterday. I asked him why, he said he was out of sorts yesterday but felt better today. He was focused today and in a great mood. He was receptive to learning and made jokes as he worked. It was nice to see. Ben was given a slope and the point the line passed through and was asked to write the equation of the line. He was confused with it at first, but we ended the class with him completing a problem correctly all on his own. I think with a little more practice he will do great.
Today we intended to finish up Chapter 2. However, as we were working on Parallel and Perpendicular Lines I realized we needed to go back and review Point Slope Form. I gave Ben direct instruction on what the point slope form is and how it is applied. Ben struggled with this concept today. He seemed to forget some of the basic information he's learned (what slope is, that points have coordinates x & y). He would say things to get off the topic, try to distract from what we were working on (for example: make comments how my 2 looked like a z, or that my when I wrote (1,2) he thought the 1, looked like an 11.) I called him out on avoiding the topic, which he didn't like but I knew what he was doing. I know what Ben is capable of, so I'm not going to allow him to use those tactics to avoid working.
Lesson 4-2 Writing Equations in Slope-Intercept Form – We practiced writing an equation of a line in slope-intercept form given the slope and one point. Then we wrote equations of a line in slope-intercept form given two points.
Lesson 4-3 Writing Equations and Point-Slope Form – We practiced writing linear equations in different forms. Then we wrote an equation of a line using the point-slope form given the coordinates of one known point on the line and the slope of that line.
Lesson 4-4 Parallel and Perpendicular Lines – We practiced writing an equation of a line that passes through a given point, parallel to a given line. Then we practiced writing an equation of a line that passes through a given point, perpendicular to a given line. We were given an equation in standard form, which we converted to slope-intercept form to identify the slope of the line. Then we used point- slope form to obtain the new equation of the line parallel or perpendicular to the given line.
Ben had a wonderful class today!! He was sharp and willing to work. He did the assigned homework. We reviewed it and it was done perfectly. Today I presented to him a 2.3 Lesson Quiz. I wanted to ensure he has this material down pat before we move onto the next lesson. He does! Ben began working without me asking him to. He knew exactly what to do. The only comments I made to him were the notations he was using, how to organize his work, and clarifying the directions. Mathematically, Ben has shown mastery in understanding standard form, intercepts, and graphing lines. Additionally, many students find word problems difficult, but Ben was able to set up and solve a problem involving 2 different priced items with a total budget. Great job Ben!
Today we continued working with Standard form. For a warm up, I gave Ben a linear equation in standard form. He knew exactly what to do. He found the intercepts, plotted them, and graphed the line. Then we applied this concept to the real world. We used the example: If you want to purchase nuts for a trail mix, you have $40, almonds cost $8/lb and cashews cost $10/lb. How could we write an equation to model this situation. Ben knew to write 8x+10y=40. We had 10 minutes left to spare in class. I gave Ben a homework assignment and allowed him to work on it in class. He asked if he could listen to music while he worked. I allowed him. He worked diligently the remainder of the period.
Today we reviewed graphing lines. We used the expo markers to write on his desk. First I did an example and had Ben follow. I showed him two methods of graphing lines in standard form. One, doing algebra to get the equation from standard form to slope intercept form. Two, using x and y intercepts to graph. We compared both methods of graphing. Ben decided that using intercepts was much easier. Then I gave him 2 problems to try on his own. He did them perfectly with no help. Way to go Ben
Today we began by Ben sharing with me his work from English. He is required to write a Poem and he wanted some help using a Simpson's episode as a theme. I was impressed with what he already had completed. I tried to help him, but I think he decided he'd rather work on it himself, as I was not much help (LOL sorry Ben, I'm a math girl!). We continued with our lesson on intercepts. We reviewed that on the x-axis the y values are always zero. And on the y-axis the x values are always zero. We discussed that when finding an intercept, we can cross out the opposite variable (or Ben likes to think of it as exploding into smitherines and eventually disappearing). Once we found the intercepts, Ben used them to plot the coordinates and then connect the dots to form a line. Ben is really picking up on this content!
Hudson and I used the standard form of a linear equation to find and plot a graph of the line. We determined whether equations were linear by plotting the line through finding the X and Y intercepts. Then we used the slope – intercept form to find the X and Y intercepts and graph the line. We determined the rate of change from a graph of a line. We found the slope and y-intercept of a line that passed through two points.
