Award-Winning Tutors in Port Chester, NY

We covered: 1) explaining and calculating the average rate of change; 2) finding the equations of the tangent line and the normal line at a given point; and 3) calculating velocity and acceleration as rates of change.

The student and I worked on collecting like terms. She understood the basics, but needed to gain confidence collecting when there were integers and powers involved. She also began keeping a math notebook to help her process the learning. I taught her how to make vocabulary foldables so she can quiz herself. Her vocabulary includes examples as well as non-examples. We also talked about the best way for her to take notes from a math text - she included step-by-step problems with the rationale written out for each step. I graded her preassessment that she had finished for the day. She has already mastered decimals, adding and subtracting integers, writing equations from statements, basic percent problems, prime factorization, graphing coordinate pairs, and finding the area of triangles/quadrilaterals/complex shapes. She has minimal misconceptions with graphing inequalities, base 10 form, rates, and simplifying expressions. She will receive support around fractions, unit rates, unit conversions, and statistics.

We worked on SAT math. The student had a good attitude. We went over geometry strategies about drawing pictures and determining geometric quantities in diagrams. We also worked on translating word problems to equations. The student is improving and has now seen most question types. Extra practice is a math and verbal section.

I continued to work on concepts from algebra with Student A. I started by having her do a few more problems dealing with fractions and the distributive property, and after that she worked through her nightly homework. By now the rust is gone, and she shows impressive early mastery of the material. She could solve the homework problems on her own, with many of her questions having the form "Am I doing this right?" I am very happy to see that she has gotten good grades on homework so far. She struggles a bit with the tougher problems that I give her; at this point she only sees about two 'moves' ahead, easily handling a problem that asks e.g. given two fractions to find a common denominator and then add, but getting stuck if she is given two mixed numbers and asked to convert them into fractions, and then find a common denominator and add (even though she understands each step taken individually). This does not worry me one bit, and I expect that she will be able to solve more complex problems in good time. I want to encourage this development by giving her a few tougher (multi-step) problems during each session, especially since I get the impression that she has not been hugely challenged by the problems assigned so far, although she seems not always to realize this (hence "Am I doing this right?"--the answer almost always being "Yes!"). Building her confidence will be a point of focus moving forward. With Student C I started by having him do a few more problems that require him, in effect, to convert a geometry problem into an algebra problem he can solve, and I am happy to see he is picking up what I am putting down. Like his sister, he has been able to handle assigned problems with relative ease, and I plan to take a similar approach to his development, having him do a few tougher problems during our sessions to supplement less challenging assigned material. He is very capable and rarely makes the same mistake twice. I would not be surprised if he wound up being one of the strongest students in his class. However, most of this session was devoted rather to a paper he had been given by his geometry teacher. The paper was a fairly difficult, even unorthodox assignment, which asked students to read the first three sections of Euclid's Elements (definitions, postulates and common notions) and assess whether they form a suitable foundation for modern mathematics. I was delighted to see this sort of thing in a high school math class, since the latter are generally not known for encouraging students to ask such deep questions about mathematics. I hope he got something out of writing this paper together and I look forward to working further on these important skills. It is not so simple to have him do a 'problem' in this area (compared to geometry), in particular one which is not too time consuming, so I will have to see if I can come up with bite size exercises that emphasize skills like organizing paragraphs, making arguments and using evidence.

Today we started a world history project on the economic history of Mexico. We started by going over US-Mexican history, from the Mexican American War and land acquisition to NAFTA. We listed exports and imports and talked about the maquiladora system and how it contributed to US wealth in manufacturing sectors.

The student and I began by reviewing his notes and filling in the missing summary from today's notes. Then we went over the difference between lateral and total surface area; what the area equations are for rectangles, triangles, and circles; and how to find the lateral and total surface area of a rectangular prism. I also taught him the material he will be using later this week on how to do the lateral and total surface area of triangular prisms and cylinders. I was very adamant about him showing all of his work so that as he progresses from 7th grade into his private school, he will be used to the large amount of writing required.