Award-Winning Test Prep & Academic Tutoring in Lockport, NY

"Today we covered the geometric series. The student started the lesson by bringing up some problems regarding to evaluating finite geometric series. I showed him the most direct approach: write down the general formula S = a + ar + ar^2 + ar^3 + ... + ar^(n-1) = a[(1 - r^n)/(1-r)], where a is the leading term and r is the common ratio. Then substitute the values into the formula S = a[(1 - r^n)/(1-r)]. He was on the right approach, but made some minor mistakes such as subtracting fractions and dividing fractions, but he managed to correct them quickly once I pointed them out. After watching him doing two or three problems and correcting his occasional minor mistakes, he was confused on how to find n. I told him that n stands for the number of terms, and that made a lot of sense to him. Therefore, he finished with the finite geometric series. We then moved onto the infinite geometric series, which he liked more because he did not have to worry about determining what n was--it was infinity. I showed him that there were only two cases, either |r|<1 (converges to S = a/(1-r)) or |r|>1 (diverges). I showed him why these statements were true. The comments I gave him were to organize his work more effectively. This would allow him to do problems far quickly: write down the general formula, and plug the variables with the known numbers, then compute directly. I always let him do problems himself. In cases when he made a minor mistake, I would cue him and let him discover and correct them. After he finished each problem, I showed him my solution (even though his answers were correct), just to give him a faster approach, without confusing him. He understood this topic conceptually, which greatly pleased me. Next time I will emphasize more on organizing his work more effectively. In this way he will minimize the likelihood of making minor errors."

"Today was the first session for the student and I. I gave the student a review exam to help me understand her strong points and where she needs work. The student let me know that she had difficulty with the factoring and exponents. I learned from her how she learns math as well. I will review her exam this evening and take notes on what we should begin with."

"Tonight, we worked on basic Geometry terminology such as supplementary and complementary angles, and problems in the Chapter 9 review about rotations and other types of transformations. The student was very quick to pick up on the rules for rotating a figure about the origin by both 90 and 180 degrees. He was also good at recalling algebra to solve problems involving midpoint and bisected angles. I gave him some general study pointers, including how to decide which material to study first and how to keep a running list of topics he understands and doesn't understand, to prepare for his exam this Thursday and other exams throughout the year. "

"This was a good first session with the student. We worked on a few pre-calc problems involving properties of quadratic equations. With our remaining time, we worked on a few PSAT-related math questions. "

"Today we started by doing some addition and subtraction problems with missing numbers. We talked about how we could find a missing number by knowing the answer and one other number. For example if we had 5+_=9, then we can subtract 5 from 9 to find the answer. We then did some 3 digit by 3 digit subtraction. She did well with borrowing one place value over, but had a little bit of a hard time with borrowing two place values over. We spent a majority of the time today working on time. I brought a clock with movable hands with me today. She did much better subtracting/adding hours because she could visually see herself doing it with the clock. We will continue to work on this tomorrow. "

"The student had a test yesterday so we talked about some of her strengths and weaknesses and how she felt about it. I started the session off with a mini quiz that she got 7/10 on. We then worked on converting measurements and she seemed to understand that well. She was having a hard time figuring out when to divide and multiply, but after I explained it she understood. She felt very confident about converting and she was great at it! We were able to complete two worksheets on converting as well as a few additional problems involving mixed numbers. "

"Last night the student completed the homework problems from her textbook and marked the ones she had questions on. Today we went over those questions, which were mainly on graphing and interpreting residual plots. She has a strong understanding of which variables we are solving for and how residuals take the place of the y-variable. She also understands the important concept that the residual plot should not have any clear patterns. The least squares regression line (LSRL) was another concept we went over, and how squaring and adding the residuals determines which line is the best fit for the data. I shared a video from an AP Statistics teacher that she can review, as well as step-by-step instructions for how to calculate the residuals on her graphing calculator. She said she feels more confident for her quiz tomorrow and I definitely believe she understands the material very well! "

"The student and I engaged in a lot of conversation to prep for future assignments as well as to strengthen his conversational skills in English. He has another paper to complete this month in his English 122 course, in which will address an ethical and controversial issue. We brainstormed topics, and he picked one. We brainstormed some major arguments that fit in with this topic, and must structure the essay from opposing views on the topic. In our future sessions we will be working on his ethics essay in English 122. Our next session will review the work he has completed toward this writing goal. "

"Today in geometry we talked about the some properties of similar triangles, including how angle bisectors produce proportions, as well as how parallel lines and transversals produce similar triangles. In biology we talked about the human genome, SNPs, haplotypes, pharmacogenomics, and gene therapy. We discussed why we care about these things, and how they could affect us in our everyday lives. We also finished up the unit review, and talked about some things that he needed to change on his essay. "

"Today the student worked through some assignments that covered more linear regression. It focused mostly on the meaning and application of the r^2 value that can be computed for a square's linear regression. He seemed like he understood most of the concepts; he just needed help with using his calculator to perform the necessary calculations. "