Today we jumped into another lesson on 6.2 Exponential Models. Today's lesson was particularly about finances. We discussed problems such as "If you invest $5,000 into an account paying 1.2% interested compounded quarterly, how much will be in the account after 3 years?" We also created functions to model these scenarios given data points. JPaul understood this lesson quite well. The only errors occured when typing it incorrectly into the calculator. Tomorrow, JPaul has a quiz on 6.1-6.2. After the new lesson we did a Quiz Prep Activity. He recalled about half of the material from 6.1, so we might push the quiz back one more day to better prepare him.

Today's lesson was on Exponential Growth and Decay. We began by reviewing the properties that would transform a Parent Function (shift up/down/left/right, reflect, stretch/shrink, etc.). JPaul was able to recall a lot from his previous Algebra class. The we applied that mathematics to application problems, such as "If a $24,000 car depreciates at a rate of 2.6% each year, how many years would it take for the car to be worth $10,000." We used Algebra to answer these question types, as well as the graphing calculator and the Smart Board. Using visual aids helped JPaul to SEE why we do the math that we do. He asked phenomenal questions and by doing so, we were able to clarify his understanding. He is a curious thinker when he is interested in something. Today's lesson was great!

JPaul got a 74% on this Chapter 5 Test. We calculated his grade and overall he has an 85.6% in the class. He was disappointed in his errors. I had him rework the problems that he missed. He understood his mistakes. To ensure what he has learned is not lost, we will continue to review prior material as we move on.
We started the new lesson with an introduction about Exponential Functions. I asked him about his prior knowledge on this subject, and he was able to recall quite a bit. We discussed the general shape of graphs of exponential functions and what transformations would effect this graph and equations. Tomorrow we will go more in depth.

Today JPaul had a test on Chapter 5 - Radical and Rational Functions. For the first 45 minutes we reviewed problems together from his Review Activity. JPaul took the test in his room by himself with me next door. He asked me one question during the test, “Can there be more than one solution?” I said, “Can you think of a way to check your solutions to see if they’re correct?” He said “Yes!” So he was able to work through it. When he was finished, I asked him to gauge his grade. He said “I probably got a 90% on the last half, but like a 65% on the first half, so probably an 80-something.” I told him I would grade it tonight and we can review tomorrow. We had 10 minutes left to spare, so we sat and chit-chatted about artists, he taught me what NFTs are, and we played the “Wordle” of the Day together. He’s a cool kid.

Today JPaul and I worked solely on a Review activity to prepare for his Chapter 5 Test on Radical and Rational Functions. We completed about 60% of it together and the rest is assigned for Home Learning.

Today we finished up Chapter 5 with the last section 5.6 on Inverse Functions. This section has a lot of computations and less application, so it was a bit monotonous for JPaul. Nonetheless, he pushed through and understood the lesson. We had time at the end of the lesson to do his Home Learning activity together. He worked independently, then paused from time to time to ask questions. In one problem, I told him "That is a function because each x has only one y that corresponds to it." He paused me and said, "But wait, what about the x=1, that has TWO y's that go with it!?" He was right, I was wrong! I love when that happens because it shows me that he understands exactly what is a function, AND he was paying attention enough to correct me (instead of just say "uh huh" and move on). So I gave him a 1% bonus to be applied to his test. Speaking of, his first test is this Wednesday on Chapter 5. Tomorrow we will review for it.

We began today by reviewing yesterday's Quiz. JPaul was annoyed with his simple mistakes but understood where he made errors. We then did a warm up on 5.4 Solving Radical Equations as a review. He recalled how to do the problems, with minimal support. So we were ready to move onto 5.5 Function Operations. We did practice examples online with the Savvas text. We covered adding, subtracting, multiplying, dividing and composing functions. We discussed when the domain would be restricted and how to write that. For another perspective, we watched 3 short videos from Khan Academy. JPaul seems to find this section easy. Yay! The goal is to finish one more section and then he will have a Test on Chapter 5 next week.

JPaul definitely studied last night! :)
We first went over his homework in preparation for the quiz. He felt confident. He took his first quiz on 5.1 & 5.2 and he earned a 86%. The mistakes he made were simple errors. We will review the quiz tomorrow together. After his quiz, we moved onto 5.5 Function Operations. I happen to LOVE this section, so JPaul got a kick out of my nerdy-ness. We used the Smart Board for a Modeling Application activity. We discussed Revenue, Profit, and Cost functions and showed how algebra can be applied to real-world scenarios. Working with money is something JPaul is interested in, so we will continue to use these examples to make sense of these Algebraic functions.

Upon arrival the first thing JPaul said to me was, "I just don't understand why I am having such a hard time with this stuff." He attempted the homework, but it seems the effort was minimal. We discussed what to do when he is working alone and gets stuck. I showed him how to go back to his notes, his practice examples, how to look at each step and use those examples as guidance. I think JPaul knows what to do. We did another mock quiz and JPaul earned a 74%. I asked him what he could do to earn a better scored. He said he needed to practice more. I agreed. Instead of moving onto 5.5, we decided to spend the rest of the session reviewing the problem types he finds most difficult (which are rationalizing and quadratics). I gave him more review homework problems. He explained he has an app on his phone that should help him. Tomorrow he will have a quiz on 5.1 and 5.2 and we will be moving onto 5.5.

Paige’s summer assignment is an intensive review of all PreAlgebraic concepts. Today, we worked on Statistics, Probability, and Geometry.
She did very well. When beginning a problem, she seemed to lack confidence. She doubted that what she was thinking was correct, but the majority of time she was right!! With our short time together, I will try to help her break down those walls, have her realize she’s much more capable than she thinks.