First we started by reviewing Ben's test he took last week. He got an 85%. I was really proud of how well he did!! We went through the problems he got wrong. He still didn't understand what to do so I explained them to him. Then we discussed what happens when two different lines intersect, and how we determine what their solution is. First I showed Ben an example on the white board. I graphed two lines and showed they intersected at (2,3). Then I showed him how when x=2,y=3, they both solve the equation. Next, I gave Ben 4 problems to try. He was slow to start, but then he remembered what to do. He was able to complete all problems correctly!

2-2 Point-Slope Form – We learned to write and graph linear equations in point-slope form. We analyzed different forms of a line to interpret the slope and y-intercept of a linear model in the context of data. We learned how to use the point-slope form of a linear equation to write the equation of a line using the slope and any point on the line.
Assignment: Complete the assigned problems for homework.

Lesson 7-1 Multiplication Properties of Exponents, 7-2 Division Properties of Exponents, 7-4 Scientific Notation
We practiced using the properties of exponents to simplify exponential expressions. We reviewed how to simplify expressions containing negative and zero exponents. Hudson is going to send me his math review for the test on Thursday so that I can send him the answers to check.

graph/ equation

Today I had Ben graph a given line. We discussed what solutions the graph has. I showed him how the ordered pairs of each point on the line actually solve the equation. I asked Ben to give me a few that he thought would work. We tested the coordinates to see if they made sense mathematically. I asked Ben how many solultions a line would have. He thought about it but then determined there would be infinitely many solutions on a line (it continues forever). Then I gave Ben a random equation of a line and asked him to come up with a solution (reminding him there are infinite possibilities). He was able to choose values for x, substitute them in, and determine the appropriate y value that corresponds to it. At the end of class, I gave him an assignment to do for homework. I told him he could take a break for the remainder of class or work on his homework. He chose to continue working! He finished the assignment right before the bell rang and he did it all correctly! Way to go Ben!

Ben was 18 minutes late to class today. I assumed he was in the bathroom (each time I checked the bathroom was occupied), so I continued to wait. Then I checked the art room and he was there playing a game on his computer.
Today we discussed what it means to be a solution to a linear equation. We touched on the subject before break, but today seemed to be a good review. We discussed how when seeing the line graphed, we can identify what points go along the line. Then we discussed how to determine if a pair of coordinates is a solution to the equation. We did this by substituting in the values for X and Y and determining if the equation was true or false. I showed Ben what it would look like when the solution works and when it doesn’t. Either the equation will be a true statement, or it will be false resulting in something like 2=6. This is going to lead us in to solving systems of equations.

2-1 Slope-Intercept Form – We learned how to identify a positive or negative slope from the slant of a line. Then we reviewed the formula to find the slope when you have 2 points on the line. Next, we practiced finding the y-intercept and the equation of a line that passes through 2 points. We practiced sketching the graph of a linear equation in point-slope form. We analyzed different forms of a line to interpret the slope and y-intercept of a linear model in the context of data. We learned how to use the point-slope form of a linear equation to write the equation of a line using the slope and any point on the line.
Assignment: For homework complete assigned problems.

Ben was in a great mood today. He was listening to music when I entered and he told me he had Art work today. I asked him if that was his way of asking if he could have some time to work on it and he said Yes. I told him that I wanted to accomplish one task today, and if we have time left over, he can work on his art project. He agreed. First I did a tutorial with paper and pencil on his desk. I explained to him the concept of asymptotes. That it is essentially an imaginary line that the graph approaches but doesn’t touch. I showed him both vertical and horizontal asymptotes and how that would affect the domain and range. Since the graph doesn’t exist at those locations, we have to skip over those values when stating the domain and range. The first problem I showed him had a horizontal asymptote at 3 and a vertical asymptote at -2. We recognized the graph extends toward negative and positive infinity but does not exist at those locations where the asymptote is. So instead of stating the domain is (-inf,inf), we had to say (-inf,-2) & (-2,inf). Similarly for the range instead of (-inf,inf), it’s (-inf,3) & (3,inf). Then I wrote a challenge problem on the board. Ben said he disliked these problems. I reminded him how GREAT he did on yesterday’s lesson, this just had some values we skip over. He worked through the problem and reached a solution. With the time left in class, I allowed him to listen to music and work on his art. It was nice to hear his music choices, I enjoy his style.

2-1 Slope-Intercept Form – We learned how to write linear equations in two variables using slope-intercept form to represent the relationship between two quantities. Then we interpreted the slope and the intercept of a linear model. We practiced solving linear equations in the slope-intercept form, y = mx + b, where m is the slope, and the line intersects the y-axis at (0, b), so the y-intercept is b.
Assignment: For homework complete assigned problems.

Today we worked on the white board using expo markers to show Ben different graphs of relations. We worked with linear, quadratic, cubic, radical, rational, sine, cosine, and ellipses. We discussed how the x and y values on these functions/relations correspond to each other. Ben was able to use the vertical line test to determine if the given graph was a function. Ben is grasping these concepts quickly. I see it is giving him confidence to get started with the work right away. I'm so proud of his progress!