Recent Tutoring Session Reviews
"We did practice from Chapter 4, focusing on the fact that we must use certain rules for certain equations. The student worked to memorize those rules."
"This session was focused on getting the student prepared for her test tomorrow by doing derivative problems."
"We went over the student's homework problems covering critical values, the first and second derivative test, concavity, and graphing polynomials using the first and second derivative."
"The student and I continued to work on probability tonight. The problem sets that he worked with were more complex this session, as we worked on theoretical probability. We practiced with problems that involved spinners, multiple dice, multiple coins, and weather predictions. The student seems to have a knack for solving these kind of problems. We also started working on problems that deal with odds, for example 3:1 in favor of an event happening. These problems consisted of converting from probabilities, percentages, and odds into different forms. Finally, we worked on some review problems for an exam that he must make up. The problems that we covered in the review dealt with rate of change and factoring quadratics. The student was very focused and worked very well."
"The student's class turned to complex numbers this week, incorporating many of the ideas of quadratic equations and their properties into these new problems and their solutions. Complex numbers refer to numbers written as the sum of an imaginary number, denoted as i with a non-zero coefficient, and a real number in the form a + bi, where a and b are both non-zero real numbers. The student had some difficulty at first with the concept of i; i itself is a non-numerical representation for the square root of -1. i^2, therefore, is equal to -1; when you multiply the square root of a number, x, by itself (square root (x) * square root (x)), you will always get x. In his homework he was presented many problems that appeared similar in form to factored quadratics (e.g. (i + 7)(i - 6)) and which he was tasked to simplify. His first instinct was correct: to treat i like a variable and FOIL the parenthetical terms to re-write the equation (e.g. i^2 + i - 42). The trick here then became to simply the i terms as much as possible; in this given case, i^2 is equal to -1 and the equation can be simplified to -1 + i - 42, and then after adding and subtracting like terms, further and finally simplified to i - 43. As soon as he realized this trick, he understood that this problems mainly tested his ability to accurately and precisely FOIL as well as pay due diligence to positive and negative values incorporating -1 for i^2. We were able to get a lot of repetitions in his homework and he felt very confident in his work and his understanding by the end of this session. Next week we will continue with math to make sure that he is still making progress and stays confident in his problem-solving abilities."
"We covered mostly ratios and percentages during our session. She did well after I explained the topics. She had a bit of trouble setting up the ratios from a word problem, but after doing plenty of examples, she improved. Her assignments also covered comparing fractions, decimals, and percentages in order to list them from greatest to least (or vice versa). She didn't show any difficulties for those problems. The last topic covered was recognizing numbers as whole numbers, integers, or rational numbers. I recommended that she try some multiplication drills every day so she can get better and faster at multiplying and dividing."