Ben told me he was going to leave class early today due to feeling nauseous. We waited for a bit and then I said, "Well lets do some work while we wait." He was ready and willing to work. I wrote the problems on the board and he said, "This is the worst day to be doing this but ok." And he answered the questions Correctly!!! He knows what he's doing. He only made one silly mistake and when I made the correction he knew immediately his error. I was proud of Ben for working despite not feeling well and knowing he was going to be leaving soon. As we were working his mom came in. I had never met his Mom before and it was nice to chat with her. She said Ben will be online for class the next 2 days.
Lesson 11-6 Adding and Subtracting Rational Expressions – We practiced adding and subtracting rational expressions with unlike denominators. We learned how to add rational expressions with unlike denominators by using the least common multiple of the denominators to get equivalent expressions with a common denominator.
Lesson 11-7 Mixed Expressions and Complex Fractions – We learned how to use complex fractions to solve problems. We simplified complex fractions involving monomials and polynomials.
6-1 Rational Exponents and Properties of Exponents – We learned that radicals can be rewritten using rational exponents. Then we discovered that the properties of exponents can be used to solve equations with rational exponents. We learned to extend the properties of integer exponents to rational exponents to rewrite radical expressions using rational exponents.
Assignment: For homework complete assigned problems.
Ben started class asking if he could have a snack and watch a short video before we began. I allowed him. After 5 minutes, I asked him to put away his things so we could begin. He obliged. We started out with a quick review of the exponent properties we have been discussing. Then we moved into a new concept. Fraction Exponents. As we were working, I realized that Ben does not have the understanding of radicals/roots. So we took a step away from this content to review radicals and how to simplify them. When I feel like he has a good grasp, we will go back to fraction powers.
Today we had class for Ben's first period. He asked me if he could have a few moments to "wake up". I told him sure, but that I'd like to get this circuit done today. After about 5 minutes I gave him a warning that I'd like to get started in a minute or 2. When time was up, I asked Ben to put away his legos. He complied. We worked on a circuit of problems. When we found the answer to one problem, it led us to find the next problem to attempt. I allowed Ben to lead the way. I asked him questions like, "are we supposed to add the powers here or multiply them?" He participated and did fairly well. He needed a few reminders on the rules. I showed him WHY you add powers when multiplying (x^4)(x^3) really means (x*x*x*x)(x*x*x), and you can see there are a total of 7 x's there. So instead of writing out the x's each time, we remember that when we multiply like bases we add their powers. We reviewed multiplying, dividing, zero powers, and negative powers. At the end of class I complimented Ben on his focus today. I told him that sometimes we have to do things we don't want to do to get where we want to go. I told him I know he doesn't have a LOVE for math, but that he's GOOD at it when he does it.
Ben was working on his legos when I arrived. I asked what he was working on and he said, “I don’t know.” (In a rude tone). I said, “Ok Ben.” And got my things out ready for class. He said, “What? What do you want me to tell you?” I told him to put his things away and that we needed to do some work. In between problems he grabbed his Lego piece and said, “I just started working on this. But I’m not sure what I’m creating.” I stopped and said, “Ben, how come when I asked you what that was originally you were rude in your response instead of saying what you just said?” I told him when he responds with one word quick answers it comes off very rude and disrespectful. He apologized and said he comes off rude no matter what he responds. I said not necessarily. It’s ok to not feel like explaining something, or not feel like talking, but there’s also a way to say that without setting the tone the way you did today. He seemed to understand.
I was able to get him to do several problems together. We are still on the same content, properties of exponents, because I want Ben to feel comfortable with this before moving on. The section we’re at in the book assumes Ben has some prerequisite skills that he does not, so before we do the actual Algebra 1 content, Ben needs to have all the properties of exponents down pat.
Ben and I had a great class today. At first he was slow to start, but we had a good convo about music and computer programming, and he was ready to work after that. I told him we haven't been very productive lately, he agreed and said that his mom had mentioned it also and that he needs to work in math class. I wrote some review problems on the board and Ben willingly attempted them. He did a great job recalling exponent properties. He remembered anything to the power of 0 equals 1. He recalled how to multiply like bases (by adding their powers). He needed a reminder about the negative exponents and then was able to complete the problem correctly. Ben mentioned that to get to the courses he needs in college he needs to start doing better in math. I told him he can do it, it's not a matter of ability but just putting one foot in front of the other.
