Today Carson and I met on Teams. We did a lesson review on properties of exponents. I showed Carson a problem from yesterday where the problem required using multiple exponent properties to simplify. Carson attempted the problem first, but had some gaps in his understanding. So we decided to scaffold the concepts. I had him grab a pen and paper and set up a box with the titles: properties, Definition, and Examples. We went through the properties together. For example Multiplication, x^a*x^b=x^(a+b), then we did an example 3^4*3^6=3^7. We discussed the properties division, power rule, and negative exponent. We did examples of each pausing to ask Carson to make sure he was following along and understanding. Once we wrote down all of the properties, we went back to the problems to put the properties to use. We will review this more tomorrow.
Today I pulled problems from an online resource for Aiden to get practice with the new concepts we learned yesterday. We started with drawing a picture of two lines intersecting and two of the opposite angles were measured (8n) and (9n-5) each. Aiden recognized that these were vertical angles and they were equal. With help, he set up the equation 8n=9n-5. Aiden was able to solve for n and then find the angle measure. This problem led us to bring up solving equations with variables on both sides. This concept we haven't seen a lot of, so I recommended to Ms. Teresa to cover that concept in more detail in his Enrichment class. Next, I drew a picture of two intersecting lines and I labeled the two adjacent angles as (6x+19) and (x). Aiden recognized that these two angles are supplementary. With help he set up the equations 6x+19+x=180. Again, he was able to solve for x and then find the angle measures. Aiden is doing well with this concept. He was bummed today that he wasn't able to come up with writing the equations (on his own with no guidance from me). I explained to him that this was the 2nd day of doing these problem types and he is just getting used to thinking through all of these steps. He's where he is supposed to be!
Today PJ and I worked on real world applications with ratios. PJ was asked to compare two quantities and then reduce them to simplest form. PJ has been doing a great job with this new content conceptually, he is finding it challenging being able to write it down and show the work behind the process. We will practice this. As a challenge I gave PJ a ratio of numbers and had him find 3 equivalent ratios. He got them easily!!
Today Josh and I first went through the Free Response Questions he had for homework. The first one he got all 9/9 points. I was so proud of him! The second he got 6/9 points which is still really good! Next, Josh asked me if we could go through some ACT Math practice since he is taking it on Saturday. We discussed a trig problem requiring us to set up triangles within a triangle. Next we discussed a polynomial problem where we had to find the coefficients. They were quite tricky but we got through them.
Ben started the class expressing his frustrations regarding a new teacher of his. I tried to help him by saying things like, "the teacher means well", "he's got to get to know you", "it's almost the end of the year", "You are able to get through this with some positivity". He did not want to hear me, he just wanted someone to validate his feelings. I understood where he was coming from but also tried to encourage some resilence - which he is capable of.
Today we had MAPS math testing. Ben was ready for it. He told me he would try his best. It took him a while to get started. The room lighting, the font, the screen brightness were all factors in delaying his start. Eventually, we got there. He asked if he could work the problems outloud and I encouraged him to do so. It was really wonderful to hear his thought process as he worked the problems through. He's extremely bright. He got through only 4 problems during the class period, but he did them with intention and I am pretty sure he got them all right so far. I thanked Ben for working hard and told him I was proud of him.
Today Aiden and I discussed the idea of complementary and supplementary angles. We defined the words as complementary being two angles that have a sum of 90 degrees, and supplementary being two angles that have a sum of 180 degrees. We drew pictures to model both scenarios. Then, we were given a situation where Aiden needed to set up an equation, solve for x, then find the angle measure. Aiden did an excellent job working with the idea of solving equations with variables on both sides (a concept we've not thoroughly discussed). He kept saying, "Who knew angles were so interesting?" :) Great day!
