Today Ben took a Quiz on Solving systems of equations by graphing. He got a 102% on it. He answered a question on finding the solution by graphing, and another question where he had to explain what lines would look like if there is no solution. For the bonus, he explained how there would be infinitely many solutions. I'm so proud of him! Next I showed Ben how we could use substituting to solve these systems (instead of graphing). I explained that systems can be solved 3 different ways, however, depending how they're set up, one method may be easier over another.
Review for test on Topic 2 Linear Equations. We practiced how to write an equation in point-slope form from a graph. Then we practiced writing the equation from two points on the line. Next we practiced how to use the standard form to plot a graph, find the slope, and x, y-intercepts. We reviewed the steps to write and graph linear equations in standard form. We practiced changing from standard form to slope-intercept form.
Assignment: For homework complete assigned problems.
Relations and Functions – We learned to identify functions and their components in a variety of forms such as graphs, tables, and ordered pairs. Next, we learned that a relation is a function only if each element of the domain is assigned to exactly one element in the range. Finally, we identified constraints on the domain based on real-world problems.
2-4 Parallel and Perpendicular lines – We learned to write equations to represent lines that are parallel and perpendicular to a given line. We graphed lines to show an understanding of the relationship between the slopes of parallel and perpendicular lines. Then we solved real-world problems that involve parallel are perpendicular lines.
Assignment: For homework complete assigned problems.
Today Ben was 15 minutes late for class. I found him eating Chik-fil-a in the Art Room. I confronted him on the importance of being in class on time. He apologized.
We worked on his white board, starting with a review on what it means to solve an equation. Ben listened while I provided direct instruction. I showed Ben two lines, and had him direct me on how to graph them. He told me where to plot the y-intercept and how to rise/run from there. I showed Ben how the two lines intersected, and at that location is the solution to both equations. I showed him how we can substitute the x and y values back into both equations and it would work/make sense. Next I showed him two parallel lines. I reminded him that parallel lines have the same slope. I asked him, since parallel lines never intersect, what could the solution be? He said, No solution?? I said YES! He really does a great job of using his intuition to come up with solutions. Tomorrow we will discuss what happens when there are infinitely many solutions.
Quiz on Lessons 2-1 to 2-3.
2-4 Parallel and Perpendicular lines – We learned to write equations to represent lines that are parallel and perpendicular to a given line. We graphed lines to show an understanding of the relationship between the slopes of parallel and perpendicular lines. Then we solved real-world problems that involve parallel are perpendicular lines.
Assignment: For homework complete assigned problems.
Ben was late for class today. We only had 10 minutes to go, so Ben shared with me what has been making him happy lately. It was the philosophy that there is no point to life, but that there is beauty in trying to find its meaning. And while we are destined to die, the need to rebel against the negativities that we face along the way. He said the world is inevitably going to end, so if we rebel against it and make the most of it, we can make our journeys here positive. I loved that he shared that with me. I said, "So what I'm hearing from you is that negative things may happen to us, but if we alter our perception, we basically have control of our own happiness." He agreed. He said this new philosophy is helping his overall happiness. That made me really happy too!
2-3 Standard Form – We learned to write and graph linear equations in standard form. We discovered that the standard form of a linear equation is helpful for identifying the x- and y-intercepts. These are used to graph the line and aid in understanding the constraints within a real-world context.
Assignment: For homework complete assigned problems.
Standard Form is useful because sometimes it's helpful to find the x and y intercepts. And it also gets to be useful once you start studying quadratics which is when you have x squared. However most of the time people like to use equations that are either in point-slope form or slope-intercept form.
