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.
Rachel, Samantha, and I had a brief conversation in Spanish involving 3 or 4 common questions in familiar tenses.
We reviewed por, para. They shared two acronyms that they are using as pneumonic devices. They took a practice quiz online and earned a 19 out of 20 with minimal assistance.
We reviewed material from their last section.
We discussed their recent presentations on which they both got A’s!
We discussed strategies to improve presentations and good class habits to improve their grades.
Rachel and I briefly discussed her new material including combining functions like fx and gx. She stated that she was very confident and comfortable with this material so we reviewed the topic from the week before.
When she first looked at the material, she had a momentary lapse in her ability to interact with the material. We used this opportunity to pretend that this was a test and practice recouping from a tough situation. We wrote out a systematic approach for her to attempt these situations including a series of questions and approaches.
We then worked out the solution to several equations with roots.
We discussed solving equations with square, cube, and higher power roots.
We took the time to graph the equations to help give Rachel a visual of what is happening and went so far as to graph the negative of each root as well to show how to make educated approximations of possible sensible answers.
Rachel, Samantha, and I started by discussing their goals for last semester and how effective they were in achieving them. We discussed their Spanish midterm exam.
They identified oral assignments and presentations as the categories in which they could most efficiently earn more points this semester.
We then worked on the presentations that they will give tomorrow.
They took turns giving presentations. I gave feedback regarding pronunciation, vocabulary, choreography, timing, and strategy
Rachel and I discussed her midterm math exam and how successful she was in accomplishing her academic goals.
We then worked on graphing square and third roots. We discussed translations of the most basic graph. We looked ahead to future concepts like graphing the negative portion of the graph. We also covered details like how to specifically enter the equations into a graphing calculator.
Rachel and I reviewed together the midterm review that was put together by her teacher.
I asked her to determine the order in which we proceeded so as to give priority to the items she deemed most appropriate.
One theme of this session was to review the algebra required to perform the given mathematical task, but to also provide simple effective ways to check her work. This time I showed her how to check graphically using her calculator. Another theme was pausing to understand what the question was actually asking us. A third theme was going back to basics specifically, multiplying two sets of parentheses (aka foiling or the box method). We also reviewed factoring. I highly recommend that she visit these core skills with frequency in the new year.
We were able to cover every topic that she wanted to review except for imaginary numbers. We ran out of time for this topic. She is to go and speak with her teacher about this prior to the exam for this review.
Rachel, Samantha, and I discussed their Midterm review sheet.
I reviewed the answers on Rachel's sheet for each problem. They asked me about the questions with which they had struggled in class. I pointed out typical problematic areas for students. One point of note here is that Rachel had a few incorrect answers on her study sheet even though they had gone over the problems in class. When asked about it she mentioned that it can at times be difficult to understand the teacher saying B or D when giving out answers to multiple choice problems. We discussed one strategy for this but we may benefit from further trouble shooting in the new year.
We also discussed the test prep that they will do between now and the test.
They are to prep the information that they will pour on to the page when they get their exam.
