Award-Winning Test Prep & Academic Tutoring in Ventnor City, NJ

Today was our last session, so we wrapped up loose ends. We practiced a few more questions involving combinatorics and reviewed rates. We practiced a number of sample questions involving rates of travel and of work.

Today the student and I reviewed the homework she was assigned from school, which covered solving for surface area of cuboids and complex cuboidal figures along with simplifying fractions. She understood everything and figured out how to simplify the complex cuboidal figures to solve them. In general, she is incredibly pleasant to work with- she is determined to get the correct answers and works hard.

In our second session, the student and I continued to chew on the unit circle and the implications certain angles have on the shape of the corresponding right triangle drawn from the center of circle to the point at which the angle sweeps to. She was able to use the cutouts we made last week to locate the correct points and reference angles on the unit circle and seems to be able to visualize the triangles and recognize the sine and cosine intuitively. However, there are still some moments where she confuses the opposite and adjacent side of the triangle. I believe this is stems from a difficulty visualizing the correct triangle for the given reference angle. Thus, we spent most of the session practicing drawing the correct right triangle for a given angle. This requires many steps including finding the Point (P) on the unit circle, identifying the Reference angle (R) from the x axis and then visualizing/drawing the correct Triangle (T). From there it should be trivial finding the opposite. adjacent and hypotenuse sides. The crucial step between identifying the reference angle and the correct triangle is where she has the most trouble so we used a song to help her remember to repeat the three steps PRT so that she can see with absolute clarity which side is longer and which is shorter especially on the 30, 60, 90 degree triangle which is the most challenging. If she practices these steps to a tee developing her consistency and stubborn adherence to visualizing the correct triangle, I believe she will have no trouble on her upcoming test this Friday in trig.

The student and I spent most of the time working on her math review packet, which included topics from the entire semester. We worked on solving algebra equations and inequalities and interpreting data from histograms and pie charts. She also created more science flashcards using her vocabulary terms from the chemistry unit. I quizzed her over the flashcards until she had learned the definitions of all of the words. We also reviewed the vocabulary from the flashcards she made during the last session. She is retaining the information very well.

We started class with word problems that tested the student's understanding of operations including multiplication, division, and subtraction. She knew how to do the math, but lacked the confidence to set up the problems properly. In her workbook, we did the unit review, and her answers were 99% correct. I assigned a lot of homework for her to complete over the weekend to encourage more independent work.

In yesterday's session, the student and I worked on some of the new subject material he had gone over in class last week. The material was on elemental and polyatomic ions - specifically what they are and how to identify them. We also did a lot of research for his upcoming final project on polystyrene. I left him with the task of asking his teacher what he should do for the question regarding the boiling point of polystyrene since it seems to be unavailable in the literature.