Together, we prepped for Rachel’s quiz. She stated that she wanted to focus our time on inverse of functions.
We discussed what the inverse of a function is in principle.
We graphed a very basic example function and its inverse.
We worked on problems from her study guide trying to cover a variety of sections in our limited time. We covered about half the sections.
Rachel seemed to understand the concept well enough. However, she may have benefited from a more fluid mastery of the basics that needed to be performed in order to algebraically manipulate the inverse equation to solve for y.
Today was Ben's birthday so we took it easy. We still did some work. First I put some review problems on the board and had him walk me through the steps. We used the exponent rules to multiply like bases by adding their powers, and divide like bases by subtracting their powers. Then I introduced to Ben the concept of negative exponents. I showed him an example and then had him practice. He did great!
Today PJ and I worked on adding and subtracting similar looking terms but are actually unlike terms. PJ did great with this concept. He had to add and subtract terms like z with z^2. He did a great job using the order of operations to combine like terms correctly.
Today we worked on the problems that Joshua had difficulty with in AP Classroom. These were difficult problems. They took a lot of higher order thinking (for me too!). We were able to get to the solutions and solidify our understanding. We practiced using our calculator to solve difficult equations. We also got practice using properties to simplify.
Today Matthew and I discussed what the common log is. I showed him that if it doesn't show the log base number, then it is automatically assumed that it is 10. We practiced simplifying logs with base 10. Then we talked about the number e. I showed him how to use it in his calculator. Then I explained the Natural Log and how it has a base of e. We practiced using the calculator to evaluate these logs.
Today we began by continuing with taking notes on older material. I presented to Aiden a "Chapter Highlights" that has key tidbits from each chapter/section with examples. He found that to be helpful, but also requested we take notes. I asked him if it was ok if we use the first 5-10 minutes of class for review, but then the rest of class we focus on new material. He agreed.
We are now in Chapter 5 which starts with writing two-step equations. We looked over the problems we've previously done to make sure Aiden knew what the plan was. Next we pulled some problems from the textbook. Aiden was asked to read the word problem, then choose the correct expression that matches the scenario. He did a great job explaining his choices as well as why the other expressions were set up incorrectly. Next, Aiden was given an expression, and he had to come up with a scenario that the expression could represent. He had me giggling with his ideas. He's hilarious.
He did well today!
Today Carson and I started by proving the sum of the interior angles of a triangle is always 180 degrees. We practiced using this theorem to find the missing angle measures in triangles. Next, we proved the theorem that the exterior angle of a triangle is equal to the sum of the two opposing interior angles. We then practiced using this theorem to set up and solve equations. Lastly, we did a few challeng problems that combined the theorems we discussed today, with the previously learned information about parallel lines and transversals. Carson is doing really well with this content.
