PJ and I worked on solving equations with multiplication and division. PJ has already mastered this concept - computation wise. However, today we worked on incorporating it into word problems. Together we read word problems that required PJ to first set up the equation and then use it to solve. PJ does a great job of knowing how to come up with the answer. He finds it challenging to write the equation first. This is common and will just take some more practice before he becomes more confident with it.
Ben had a great class today. I got his attention at the beginning of class at the white board. I told him I was going to write some notes and asked if he would listen and he said sure. I showed him how to write a fraction power into a radical/root, by using an acronym "BOTI" which stands for Bottom--Out, Top--In. I showed Ben the problem 8^(2/3) and we wrote it in radical form. Then we evaluated it. Once Ben saw the pattern, I related it back to concepts Ben has previously learned (negative exponents, fractions, and decimals). Ben did very well today.
Today was a challenging day for new content, but Joshua did an excellent job. We discussed inverse trig functions, their graphs, domains, and ranges. We took notes going through the logic of why we have to restrict the domain to make the relation a function. Then we practiced evaluating the inverse trig functions - considering their appropriate domain. These problems require much higher order thinking. Joshua did a great job.
Aiden had an excellent class today. We worked on a mixed review of both fractions and decimals in equations. First we saw a problem with mixed decimals in it. Aiden recalled that if he multiplied by 10, it would turn each decimal into an integer. Then he was able to apply inverse operations to solve the equation. Next, he saw an equation with fractions. He recalled to multiply by the LCM to clear the fractions. Last we saw a problem that involved using the distributive property first, then clearing the decimals. We agreed that we are ready to move on. We had a few minutes to spare at the end of class and Aiden asked me if we were going to be covering Geometry this year. We looked at the course content and saw that we still have two concepts left to cover, statistics and geometry. After some discussion, we decided we would choose Geometry to cover together since he already has a good understanding of statistics. For practice, I gave Aiden a few probability questions. I drew a bag of marbles (he laughed at my drawing and called it a pomegranate LOL). I asked him the probability of reaching in and choosing NOT orange. I asked him questions like, "If we add another orange marble, what's the probability of choosing blue now?" Aiden was able to answer these questions correctly. This solidified our choice to move onto Geometry after we complete Chapter 5 (solving equations and inequalities).
