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Session Summaries by Tutors

The student is looking at ellipses. The first set of problems involved drawing the ellipse by looking at the equation and determining the foci. The second set of problems involved writing the equation after being given two sets of information (vertices, co-vertices, or foci). The third set of problems involved determining if an equation was a circle, parabola, or ellipse by looking at the equation and then drawing it. The student wanted to review for a quiz. We talked about each section 8.1-8.4 and wrote out the equations on a sheet together for the purpose of studying them.

Today we practiced graphing more polynomial functions. The student is doing very well when she is prompted as to what the next step may be but still struggles a bit in trying to make decisions. I think the problem stems from her ability to easily memorize equations. She often creates lists of rules and learns them, but if a problem does not neatly fit into a rule there is confusion. Due to this fact, the major focus of the session was on understanding why equations took certain shapes. By the end of the lesson, she was doing very well, and additional practice problems such as the ones we were doing in the book may be beneficial.

First, we worked a problem from "Challenging Problems in Algebra." Next, we worked on quadratic equations with real and complex solutions. Then, we worked on solving polynomial equations by factoring. I gave the student problems to work from his book as well as a difficult problem from the above mentioned book.

The student and I continued to cover introductory trigonometry. His class has started to work on radians, degrees, their respective conversion factors, and their significance in trig. Additionally, we covered formulas for arc length and sector areas, which incorporate the use of radians/ degrees in calculating these. I explained that he would need to treat the chart with the values of radians/ degrees in a circle as landmarks and that he would need to remember them by heart like knowing the multiplication tables, because he would be using them constantly throughout the year. I also gave him a preview of how all of this is related to right triangles as well as the trig functions (sine, cosine, tangent) so that he can start to get a sense of not just the proverbial trees but the forest as a whole. He picked all of this up relatively quickly once he was able to establish a basic level of comfort and understanding of radians since that itself is a rather new concept for students at this stage of math.

The student and I reviewed notes from his Grade 5 math classwork, including but not limited to: finding the least common multiple between two numbers, finding the greatest common factor between two numbers, using the distributive property of multiplication over addition, finding the area of a rectangle using the distributive property, and utilizing the factor tree to find the least common multiple and greatest common factor. The student was cooperative and understood most of the material with some guided practice and prompts.

We worked exclusively on essays today. We first went over the student's outline from last time, tweaking it to fit the specifications of the new SAT. In particular, we focused on how the essay should be analyzing the author's writing. He did one more outline and then wrote an introductory paragraph. He analyzes and reads very well, so our focus shifted to grammar (which he understands the rules for, but should take time to apply to his own writing).

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Session Summaries by Tutors