Today Ben and I focused on negative exponents, their meaning, and how to simplify them. We worked on the white board. I wrote the reminders of how to work with negative exponents. I showed Ben a basic example of 3^-2. We recalled that negative powers do not mean the value is negative, it means 1) move the power and 2) make it positive. So 3^-2 is 1/3^2 which is 1/9. I wrote out similar problems, prompting Ben to respond to questions like "Should we add the powers here or subtract?" Ben was a bit distracted, but eventually responded. Eventually Ben said he sees what I'm doing but he doesn't understand why and it's making him confused. He wanted to know WHY we make the powers positive and move them. I didn't know exactly how to answer him either, so we looked up a video online. While we were watching it, it brought up another concern as why anything to the zero power equals 1. Recess started as we were exploring these ideas. Tomorrow we will resume trying to understand this process and hopefully it will help Ben understand the Why's behind our methods.
Today Carson and I continued working with the Pythagorean Theorem. We worked with Coffee stirrers. Carson cut them in lengths of 3cm, 4cm, 5cm, 6cm, 7cm, 12cm, and 13cm. We practiced putting them together to create a right triangle. What we noticed is that some lengths were too short or too long. But then we found that 3,4,5 worked together. I had Carson check that 3^2+4^2=5^2 when he checked it worked. So we proved that those side lengths would create a right triangle. Next we worked with 5, 12, 13 and found this also created a right triangle when we checked the pythagorean theorem. Next we discussed what happens when the side length isn't a perfect whole number. For example if we got sqrt 72, we discussed how we would used the factor tree to break it down into a product of primes and then reduce.
Today Matthew had a quiz on Logarithms. He worked hard the entire class. He asked me a few questions while he worked to clarify the problem. We will go through the problems and grade it tomorrow.
Today JPaul had a quiz on Logarithms. He worked hard the entire class. He asked me a few questions while he worked to clarify the problem. We will go through the problems and grade it tomorrow.
Christopher wrote sentences for his spelling words. We read The Watsons Go to Birmingham and discussed it. I helped him identify separate sentences in his writing.
Today we started in AP Classroom by going over the problems he had assigned for homework. He did great on one assignment by getting 9/9 on it. The other assignment had a 4/6 on it. The two problems he got wrong were extremely difficult, and I would have gotten them wrong, too. We looked at the teacher's key for an explanation and we were able to determine the error we made and fix the mistake. Next we looked at the Unit 2B Review. Joshua did excellently on it!! I told him he is better at logarithms than he thinks he is. We still have one more section to complete and then Josh will take the Unit 2B Test.
