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Private InHome and Online Math Tutoring in Worcester, MA
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Recent Tutoring Session Reviews
"The student and I went through some of the practice tests that he's been doing. He said that on his last practice exam he got the highest score, which is good but there are still some minor mistakes that he makes. We are working on ironing those out in advance of the exam, which is next Wednesday. We also went through one his scantron sheets to review the problems he'd missed. The scantron revealed that he had a little more trouble with the rules of integration: he's good with substitution, but he didn't immediately see an opportunity to use linearity [what is ?_{1 ? e} dx (xÂ_ + 1)/x ?], and he did not appear to remember integration by parts [here is a table of g(x) , h(x), g'(x), and h'(x) at 0 and 1; you know ?_{0 ? 1} dx g'(x) h(x) = 5 ... what is ?_{0 ? 1} dx g(x) h'(x) ? Answer: it's g(1) h(1) ? g(0) h(0) ? 5.]. I showed him that it's the image of the differential calculus' product rule in the integral calculus' domain, and we will continue to go over these types of problems to help him understand them. Still, I think we made a lot of good progress. We'll prepare next Tuesday for the actual test day."
"We started our session with graphing parabolas. We talked about the two methods for finding the vertex of a parabola (completing the square or using the formula). We then talked about how to find the x and y intercepts and use them with the vertex to graph the parabola by hand. Initially, the student was confused about how to know if the parabola will be concave up or concave down, so I explained that when the formula is in the form of ax^2+bx+c then if a is negative, the graph will be concave down and if a is positive, it will be concave up. We also talked about the standard form of an equation for a parabola and how to find the vertex from that. We then applied this concept to word problems such as finding the max revenue or profit when given an equation that yields a parabola. The student overall did well with this concept and seemed to follow it easily. Next, we talked about quadratic inequalities and how to find the set of solutions for a quadratic inequality. The way that the book presented these problems was a bit confusing for the student, so I taught him how to approach the problems a different way and then, once he understood that, we went back and used the technique in the book. He seems to have a good start on understanding this material, which is good since they haven't even started it in class yet. Lastly, we reviewed the two practice sets from the grammar packet that he was supposed to do for homework (on verb agreement and comparisons). We reviewed how to solve these kinds of problems, and he quickly remembered and got the problems right. Next, we talked about correct usage (no double negatives, no redundancies, etc.) and reviewed the first practice set. We also talked about the correct rules for capitalization and practiced with the first practice set. The student will do both second practice sets as homework for next time."
"Reviewing supplemental material, 33 pages out of 40, given to her by teacher. Reviewing graphs, factoring, and inputting equations into calculator. Preparing for standardized testing."
"The student and I studied from his home school curriculum on his computer in Unit 4. We covered the meaning of fractions, how to simplify fractions, how to add and subtract fractions with like denominators, how to generate equivalent fractions, the meaning of decimals, factors and multiples. He took 2 short quizzes and earned 100% correct answers on both. I provided a binder where he wrote notes, using some colored highlighters to help with graphic organization, and I trained him to refer to the notes and use them as models for working on his own. He understands concepts and makes rapid progress, needing help most with saying the math words (for example, naming a fraction with the words "fifths"). I said if he were to work on the unit and needed help to send me an email. It was a very successful meeting."
"We focused on both algebra 2 and physics today, since she has a physics quiz tomorrow on friction forces and vectors and then a math quiz on Monday from chapter 4.44.6 (higher order polynomials). We first reviewed math. Since we reviewed 4.4 last week, we worked mostly on the review packet she had, focusing on 4.5 and 4.6. It dealt mostly with factoring of higher order polynomials, but there were a few graphing problems as well. She grasped the material very well, only having slight issues with solving for the 0s of the polynomials. We then moved onto physics. She has been working with friction forces for the past couple weeks, so she has already mastered those concepts. The material she needed to review was relating those friction forces to acceleration, velocity, normal, and weight forces on ramps (so with an angle). We reviewed some vector properties and went over examples of how to use trigonometry to solve the problem. She will finish and review the physics questions she has to prepare for her quiz tomorrow."
"The student had an excellent tutoring session today. We looked over fractions in her textbook and she really understood all of the new concepts I introduced to her. We started off by reviewing the definitions of numerator, denominator, equivalent fractions, unlike fractions, mixed numbers, and improper fractions. She easily memorized all of the definitions. Then I showed her how to add unlike fractions by changing them to equivalent fractions. It took her a couple of tries to understand the process, but when it clicked she breezed through all of the exercises. Then I showed her how to subtract unlike fractions and again she did very well with this concept. Next, we looked at mixed numbers and she was able to place those numbers on a number graph and she also drew examples of mixed numbers using circles. The student then completed the worksheet that I brought which helped her read and interpret a graph. She quickly answered all of the questions on that worksheet so we continued onto the next section of her textbook. We read the definition of an improper fraction and then she had to convert mixed numbers to improper fractions. I also showed her how to reduce fractions by dividing. Overall, she did very well today with fractions and graphs. I am going to create a couple of quizzes in her school's website."
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