Certified Tutors From Central Arizona College

The student and I continued our unit on fractions. The last part of the unit was dividing fractions and mixed numbers, so I reviewed that and gave him practice problems. Then we moved on how to solve different kinds of word problems and determining which operations to use to solve them. He still has trouble determining what the question is asking to do, so we will continue to review that next time.

Today we discussed the topic of direct and inverse variation. As I explained the ideas, she was quickly able to understand the concepts and began being able to complete problems on her own. We worked on real world applications, and she was able to grasp the more challenging ideas.

Today we did reviews on conic sections, to prepare for the student's test tomorrow. We went through one type of problem in detail--give a long equation and organize into the form of one conic section, then do analysis. She was a little confused with the parabolas, ellipses, and hyperbolas. I mentioned that in parabola, she needed to find 3 things: focus, vertex, and the directrix. In ellipses, she needs to find center, foci, vertices, and the endpoints of the minor axis. In hyperbola, she needs to find center, foci, vertices, asymptotes. In ellipse and hyperbola, finding a, b, and c will help her--but be careful that in ellipse, a^2 - b^2 = c^2, but in hyperbola, c^2 = a^2 + b^2. She got a little confused, but finally overcame these difficulties. She made some minor mistakes in organizing the equations at first, but I told her about the Great Wall of Equal Sign--whatever she does on one side she must do the same thing on the other side. At the end she finally did three problems in a row (organizing equation part) without making a mistake. Then she gets better every time on the analysis: finding foci, vertices, center for both ellipse and hyperbola. I wish her success on tomorrow's test. Great work. Great student :-)

We covered inequalities with absolute value functions by going through the student's previous homework sheets. First, we did problems where we solved for x in an absolute value inequality function. This involved first isolating the absolute value part, if necessary, and then "breaking" the absolute value by splitting the inequality into two separate equations that solve for x. She learned that problems with "greater than (>)" or "greater than or equal to", had solutions for x with ranges that were exclusive. So, "or" is needed to describe the solutions: x > a OR x < -a. For problems with "less than (<)" or less than or equal to", the solutions for x had ranges that overlapped and create a bounded range. So, "and" is needed to describe the solutions, and these can be rewritten in a form that is easier to comprehend: -a < x < a (for example). The student seemed to catch onto how to solve these very quickly after a few practice problems, and by the end was solving them perfectly. In the beginning, I gave a quick reminder that dividing by a negative number switches the direction of the inequality (< become >, or vice versa). After this, she remembered to do this for all her subsequent math problems. Then, we did problems involving using the vertex form of the absolute value function to perform translations on the absolute value function and find its slope. I explained that this was somewhat of a review from one of our previous tutoring sessions and she seemed to grasp how to do these quickly.

For the first session, I began reviewing with the student the basic parts of speech in order to determine our starting point. After that, I helped him finish and edit his rough draft paper on black bears. We ended our session with beginning research on his state history assignment.

The student has been doing a great job. I have been focusing on math with him. We have been working on groups of 10, regrouping, addition, money, and time. He has been doing well, with me going over the first half of the problems on a sheet with him and then letting him do the rest on his own. We are also working on adding without using fingers and using more than 1 strategy to do the same problem.