4-2 Solving Systems of Equations by Substitution – We learned that substitution is one method for solving systems of equations. The process involves solving one equation for a variable and substituting the solution into the system’s other equation. This results in an equation in one variable. When you have one of the variables you can solve for the other variable by substituting it into one of the original equations in the system.
Assignment: For homework complete assigned problems.

Today Ben and I organized the different transformation types we've learned: reflections, vertical stretching/shrinking, horizontal shifts, and vertical shifts. We practiced graphing multiple transformations. We discussed how this affected the starting position of the vertex and the slopes of the lines. We also discussed domain and range. Ben did excellently today. There was a time I left to use the restroom, when I came back he had music playing and he had already done 4 problems (which I did not ask him to do). I thanked him for continuing to work without me guiding him.

Ben was not interested in working today. He was looking for excuses not to work. He was searching online all of his ailments and diagnosed himself as having Bronchitis. I let him tell me how he felt, and then we got to work. I wrote on the board a review of the transformations we've already seen. We discussed stretching, shrinking, reflecting, moving up, and down. Today we added onto this concept by translating the absolute value left and right. I showed Ben with a table of values why the + moves the graph to the left and the - moves the graph to the right. At the end, I gave Ben a challenge problem combining all three of the transformations. Ben knew how to graph it. He was able to graph a reflection, translation right, and up, all together. Then I had Ben determine the domain and range. He again, got it right. He seems to really be understanding this content. When he's ready to work, he does very well.

Ben was a whole new person today! He was happy and energetic. I love when he's feeling good like this!! Today we discussed how to transform Absolute Value Functions - up and down. We've already seen how to reflect, stretch and shrink the graphs, but today we shifted them up and down. I gave Ben the equations y=abs(x)+3 and asked him how he thinks it would affect the original graph. He said he thinks it would stretch it. So we tested values for x and saw that the graph actually didn't stretch, but instead shift up 3 units. We discussed how this does not affect the domain, but it does affect the range since the y's on the graph were affected. Ben did wonderfully following along with the lesson and participating.

4-1 Solving Systems of Equations by Graphing – We learned to write a system of linear equations in two variables to represent real-world problems.
Assignment: For homework complete assigned problems.

Ben was not coherent today. It was quite opposite of how he was Friday. He had his head down on the table and wouldn't respond to any questions. I felt bad for him and wanted to help him. But he wanted to be left alone. He ended up getting picked up from school early for not feeling good. Poor guy.

4-1 Solving Systems of Equations by Graphing – We learned to use the graph systems of linear equations in two variables to find an approximate solution. Then we learned that the intersection of the graphs of a pair of linear equations is used to estimate the solution to a system. If two lines intersect at a point there’s exactly one solution. If two lines are the same, there are infinitely many solutions. If two lines are parallel, there is no solution.
Assignment: For homework complete assigned problems.

Ben had a quiz today. We started class by reviewing the problems that were going to be on the quiz, to see if he had any questions. I gave Ben a challenge problem with a fraction in it. He had difficulty with it but after going through it, I realized his confusion wasn't with the Absolute Value concept, it was just the fraction part that threw him off. We will have to go back and review fractions at some point, so he can have the confidence to work with them. But I assured him his quiz would not include fractions. During his quiz, he got distracted quite a bit. I redirected him and he got back to work. He completed the quiz just as the bell rang. I reviewed it quickly and he got a 100%! I was really proud of how he was working through the problems.

3-4 Arithmetic Sequences – We learned to write arithmetic and geometric sequences both recursively and with an explicit formula.
We learned to model real-world situations with arithmetic and geometric sequences both recursively and explicitly.
Assignment: Complete the assigned problems for homework.

Ben was quite late for class today. We had about 20 minutes to review for his quiz tomorrow. I wrote practice problems on the board. Ben had to graph the function and determine the domain and range. As Ben worked, I prompted him with questions to get him started. He did a great job recalling the techniques to graph. The only comments I made were regarding his notation, and to ensure he put arrows on his graph. I think he will do well on his quiz tomorrow.