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Tonight's session revolved around algebra, including both current material and review material. We went over the difference between domain and range, the definition of a function, and the vertical line test with interpretations. We also reviewed the definition of complementary versus supplementary, as relating to angles and triangles. We closed the session out by reviewing the sum of angles for a triangle and different types of parallelograms.

During this session, the student and I finished working on some of his homework assignments, including practicing for two presentations for tomorrow.

We covered a review worksheet going over factoring polynomials without solving them. Some of them were the typical ax^2+bx+c, but others were more complicated and even had up to x^4 and the key was to factor out x's first. I think it was a good session because he had more energy than yesterday and this topic was more recent in his memory. He has an exam tomorrow on this and I feel pretty confident about his ability on this topic. As long as he doesn't make any minor arithmetic mistakes, he should be fine.

We covered volumes of revolution and completed many problems from the text book. These covered both the disc and washer method and the student determined the definite integral and input the integral into her TI calculator to compute the volume. We computed a couple of volumes revolved around the y axis as well as the x axis which requires a different setup for the integral. The student has the second part of her test tomorrow and I think she will do well.

I had the student write all known capital and lowercase letters with no model. I assessed his recognition of letters and letter sounds. We also worked a little on numbers and rote counting. We then read some kindergarten-level books that focused on the sight words "the" and "can." He is improving in all concepts we work on. There is room for improvement in his letter sounds and writing letters. These are areas we will work on the most in the next tutoring session. I left his grandmother with sets of flashcards as well as feedback on what letters, sounds, and numbers he knows so she can work with him on the ones he struggles with.

We went over how to determine whether a relation between sets is a function, how to determine the domain of functions, piecewise functions, and interval notation. The student did not struggle too much and understood most of what we went over, but she made a few mistakes that we quickly corrected. The material we covered is introductory material, and she was fairly enthusiastic given what we covered. One of strategies I gave to determine the domain of a function was drawing out a number line and shading in the portion of the line in which the function was well defined. This number line is used to put the domain in interval notation. Because of the little mistakes that were made, I would encourage her to do some more practice since practice makes perfect, especially since she understood everything we covered.