Today I substituted for David. He was to use his A to Z word chart from yesterday to create a self essay. David worked diligently the entire period. I noticed he was not using proper capitalization and punctuation. I asked him, "Does Ms. Christy allow you to write your i's like that?" He said No. He likes to write the essays first and then he goes back and edits them. I actually thought that was a good idea, so his editing doesn't get in the way of his thought process/flow.
Andrew entered class 10 minutes late. He said he had a headache and was going to go visit his Grandpa in the hospital. So he was going to leave early and miss class. I spent the class preparing materials.
Today Aiden and I worked on the Midtopic Review from the textbook. We already completed the first few, but since he has spent a few days with MAP testing, we reviewed them together. We reviewed the vocab words: coefficient, variable, and constant. Then we discussed the WHYS and HOWS of combining like terms. We saw a word problem that sparked the discussion of the differences between 2(3x) and 2(3+x). Aiden understands the distributive property in that 2(3+x) is equivalent to 6+2x. However, we were grappling with the idea that 2(3x)=6x. Aiden is curious why the 2 isn't applied to the 3 AND the x. We replaced x with 2 and showed how the two would not be equal in that case. I explained that 2(3x) actually means twice 3x so 3x+3x, which would result in 6x also. We wrote it out how 2(3x)=2(x+x+x)=(x+x+x)+(x+x+x). In all cases we could see that there is 6 total x's. I showed him that if we applied that 2 to both the 3 AND the x, there would be too many 2's. It would result in double what we want. Aiden followed along understanding the explanations. However, he is trying to understand that when you multiply 2(3x), the 3 is already being multiplied to the x, so once you multiply the 2 to the 3, it's ALSO affecting the x. We are going to resume with this concept tomorrow. Once Aiden understands WHY 2(3x)=6x, he'll be able to do the computations without question. He's on his way!
Today we spent reviewing logarithmic equations. Joshua had some difficulty with the portion of his homework involving inverses. We spent time to review those concepts, redo those problems, and try new problems. Joshua and I had a good discussion about proper notation. We used Khan Academy to verify how to prove that two functions are inverses. I noticed that some of Joshua's explanations were getting lengthy. I encouraged him to use the concept of "less is more" when providing explanations. I explained to him that if at any point Joshua says something ambiguous or something that could be proven wrong he may risk losing credit. Instead, Joshua should write the minimum required to make his claim.
Today Ben finished his MAP Testing. He had difficulty with it. There were many questions that we haven't seen yet, so I told Ben to give his best guestimate. At the end of class, we had 10 minutes left to spare. So I allowed him some free time on the computer.
We had two sessions today. PJ worked on his MAP Testing today. He was really trying hard. The problems were more 6th grade friendly than yesterday's. One point, PJ asked if he could use a calculator. I said sure and offered him mine. He said no, he wanted to use his phone's calculator. I said, "You're not supposed to use your phone during the test, but if you only use the calculator, than OK." He began to use it. I was working on my computer and after a minute or two I realized he wasn't working. I leaned over to see what he was doing and he flipped his phone's screen back to the calculator. I told him to give me his phone. He wouldn't. He agreed to put it away. At the end of the test, I told PJ I was disappointed that I trusted him to use his calculator on the phone and nothing else, and he betrayed my trust by playing around instead. He apologized. I told him next time he wants to use his phone in class I might be hesitant.
Our next class we finished the MAP Testing. We had 10 minutes left to spare so I allowed PJ to have some free time on the computer.
Today Joshua and I worked on Logarithmic functions. We started with drawing the graph of an exponential function. We recognized the asymptote, domain and range. Then we discussed since exponentials and logarithms are inverses, we could swap their x's and y's and we would get the new function. We then discussed the logarithm function's asymptote, domain, range. Then we practiced if given two functions how to tell if they are inverses without actually solving. We used the composition of their functions and if it results in x, then they are functions. Anything other than x would determine they are not functions. Joshua disliked logs at first, but I think since he's starting to get a better understanding of them, he's starting to not mind them so much.
Today Ben worked on his MAP Testing again. This time he was much more focused and willing to work. He complained about each problem, but he got through it. He did not finish the test and will have to resume next class.
Carson and I met on Teams today. We continued discussing reflections of figures in the coordinate plane. We reviewed the challenge problem we did last class where we reflected a triangle over the line y=-1. We discussed how the x-coordinates stayed the same, but the y-coordinates changed. Next, I gave Carson another challenge problem. This time it was a trapezoid being reflected over the line x=2. This time our y-values stayed the same but our x-values changed. Carson did a great job of coming up with the rule to map the pre-image to the image.
