Today we discussed the Perpendicular Bisector Theorem and Angle Bisector Theorem and applied it to solving triangles. We pulled problems from the text book. Andrew drew the triangles and labeled the sides. Then depending on whether the side lengths or angle measures were given, Andrew was able to solve for the missing sides/angles by applying the theorems. Next, we defined the words altitude and median. We drew various shaped triangles and using different colored pens, we highlighted the altitudes/medians in each.
This afternoon, Quinn worked on a reading task after we got settled in class. Quinn remembered the chapter we were on (chapter 26) and was happy to read along with me using a clear ruler to hold his place. He grew very excited to pass page 100.
Today we spent the class reviewing the homework assigned last night. Joshua had difficulty with it. Conceptually he understood most of what was asked, but he made several calculation mistakes. I asked if he felt pressure for time, or had outside distractors? He couldn't determine anything. I think I have been doing most of the direct instruction instead of having him lead the problems. Next class I will have him work through most of the problems rather than have him watch me. He needs to practice more himself.
Today we continued working with absolute value functions. Ben has shown mastery in the ability to graph the function. We reviewed what makes the function stretch, shrink, and reflect. Then we considered the domain and range. Ben now knows the domain of abs. value functions is all real numbers. Next we determined the range is either all positive numbers or all negative numbers. I asked Ben how we can tell if the range would be positive or negative, and with some help, he was able to determine that if the leading term is positive, the range would be positive and if the leading term is negative the range would be negative.
Andrew and I had our best session yet. We discussed the old and evolved meaning of "all men are created equal." We discussed how MLK evolved that understanding and expanded rights to more people and we also learned how the 1st Amendment has tension with the previous understanding of "All men are created equal."
PJ and I had two sessions today. In the first class, we began with a warm-up on 6x6=36. We discussed it, I sang it to him, and then I had him write it 10 times. Throughout class, I quizzed him, "What's 6x6?" I am going to repeat this process until I know he has it memorized. Next we moved into evaluating algebraic expressions. PJ understands this concept well. He struggles when it comes to working with decimals still. In order to keep his interest, I will only give him harder problems towards the end of class.
In the second class, I started by asking him what 6x6 is. He knew it! Next we pulled problems from the textbook. PJ practiced substituting the given values into the expression and using the order of operations to simplify.
Today Aiden and I continued with simplifying algebraic expressions. While working through the problem 5x+2y-3x, it prompted us to review properties. We discussed the distributive, associative, and commutative properties. I showed Aiden using variables what it means for expressions to possess these characteristics (ex: a(bc)=(ab)c). Then we used constants for more concrete examples (ex: 2(3x4)=(2x3)x4). Aiden noticed independently that these properties would only apply to addition and multiplication. For example a+b=b+a (3+4=4+3) but this would not be the case for subtraction since a-b is not equivalent to b-a (3-4 not= 3-4). In the expression 5x+2y-3x, Aiden got 2x+2y. Then he practiced substituting random/made up values for x and y and confirming that whether we substituted those values into 5x+2y-3x or 2x+2y, we would get the same result. I explained to Aiden that is what equivalent expressions are. They may look different, however, after simplifying completely, they are in fact, the same.
